Citation
Pulmonary vascular resistance in fetal and neonatal goats

Material Information

Title:
Pulmonary vascular resistance in fetal and neonatal goats
Creator:
Gilbert Raymond Dwight, 1944-
Publication Date:
Language:
English
Physical Description:
x, 186 leaves : ill. ; 29 cm.

Subjects

Subjects / Keywords:
Hypoxia ( jstor )
Lungs ( jstor )
Mathematical models ( jstor )
Pressure ( jstor )
Pressure reduction ( jstor )
Pulmonary artery ( jstor )
Resistors ( jstor )
Starlings ( jstor )
Vascular resistance ( jstor )
Ventilation systems ( jstor )
Dissertations, Academic -- Physiology -- UF ( mesh )
Goats ( mesh )
Physiolgoy thesis Ph.D ( mesh )
Pulmonary Circulation ( mesh )
Vascular Resistance ( mesh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph.D.)--University of Florida, 1971.
Bibliography:
Bibliography: leaves 180-185.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Raymond Dwight Gilbert.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
000897567 ( ALEPH )
25665313 ( OCLC )
AEK6246 ( NOTIS )
AA00004937_00001 ( sobekcm )

Downloads

This item has the following downloads:


Full Text












Pulmonary Vascular Resistance in Fetal and Neonatal Goats












by

Raymond Dwight Gilbert), l4 -


A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA IN PARTIAL
FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY







UNIVERSITY OF FLORIDA
1971




/
Pulmonary Vascular Resistance in Fetal and Neonatal Goats
by
Raymond Dwight Gilbert ~
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA IN PARTIAL
FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1971


ACKNOWLEDGEMENTS
The author wishes to acknowledge all those persons who have helped
him in his work as a graduate student.
In particular he would like to express his gratitude to his
supervisory chairman, Dr. Sidney Cassin, for the time and effort he
devoted to this investigation and for the facilities and laboratory
space he made available to the author. To the other members of his
committee, Dr. A. B. Otis, Dr. Wendell Stainsby and Dr. David Williams
go special thanks for their time and helpful suggestions.
The author would also like to thank his fellow graduate students
for their help and encouragement. To Dr. Jack Hessler the author
extends his special appreciation for his assistance throughout this
investigation. Also to Dr. Ian Hood for his help in examining sections
of lungs the author is grateful. He also wishes to thank his wife,
Mrs. Sandra B. Gilbert, -for; Jierv-help in the preparation of this
dissertation-.; __ z-t- -- RE CL


TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS i i
LIST OF TABLES v
LIST OF FIGURES vi
ABSTRACT lx
INTRODUCTION I
MATERIALS AND METHODS 6
Mathematical Model 12
P¡ Versus Pa. 12
P¡ Versus Q 22
Physical Model 24
P¡ Versus PQ 24
P¡ Versus Q. 26
Animals 27
Fetuses 27
Neonates 35
RESULTS 36
Mathematical Model ... 36
P¡ Versus PQ 36
Pj Versus Q~ 47-
Physical Model 57
P¡ Versus PQ 57
P¡ Versus Q 77
Animals 90
Fetuses 90
Neonates 121
DISCUSSION 126
Mathematical and Physical Model 126
Pj Versus PQ 126
P¡ Versus Q 128
Animals 132
SUMMARY AND CONCLUSIONS 140
iii


APPENDIX 1
141
APPENDIX 2 175
BIBLIOGRAPHY 180
VITA 186
iv


LIST OF TABLES
Table Page
1. P()2> ^C02 anc' PH 'n pulmonary arterial blood in
fetal animals In which both lungs were unventilated,
ventilated with fetal gas and ventilated with air. . 96
2. P02> PC02 anc* pH 'n pulmonary arterial and venous
blood in fetal animals in which both lungs were
unventilated, right lung only ventilated with fetal
gas and right lung only ventilated with air '09
3- Po2 ^C02 anc* PH 'n Pulmonary arterial and venous
blood of fetal animals before, during and after
infusion of bradykinin 117
4. P02 PCO2 an(l PH 'n l^*- pulmonary arterial and venous
blood of newly ventilated animals before, during
and after infusion of bradykinin 120
5. P2> PC02 anc* PH 'n left pulmonary arterial blood of
newborn animals in which both lungs were ventilated
with air, 10% and 5% O2 12^
6. Data from fetuses in the unventilated fetal state (F),
during ventilation of both lungs with fetal gas
(VFG) and with air (VA) 176
7. Data from animal 15 from table 6 177
8. Data from ventilated animals before (B), during (D)
and after (A) infusion of bradykinin 178
9. Data from animal 5 from table 8 179
V


LIST OF FIGURES
Figure Page
1. Diagram of a one tube model containing a Starling resis
tor arranged to provide a constant inflow pressure . 8
2. Diagram of a one tube model containing a Starling resis
tor arranged to provide a constant flow lo
3. Recording from program 1 of the relation between Pp^'
and PQ in a one tube model ]!|
4. Diagram of a four tube model containing a Starling res
istor in each tube 17
5. Diagram of surgical preparation of animals 30
6. Recording of the relation between pulmonary artery
pressure (PAP) and pulmonary venous pressure (PVP)
in an unventilated feta 1 animal 33
7. Recording from program 1 of the relation between P¡
and PQ in a one tube model: effect of increasing P$. 38
8. Recording from program 1 of the relation between P¡
and P0 in a one tube model: effect of increasing Rp. 40
9. Recording from program 2 of the relation between P¡
and PQ in a four tube model: flow occurring in all
tubes 43
10. Recording from program 3 of the relation between P¡
and PQ in a four tube model: flow occurring in a
partial number of tubes 46
11. Recording from program 4 of the relation between Q.
and P¡ in a one tube model: effect of decreasing
Rp and Pg 49
12. Recording from program 5 of the relation between Q
and P¡ in a four tube model 52
13. Recording from program 5 of the relation between Q
and P¡ in a four tube model: effect of decreasing
Rp 54
Vi


14. Recording from program 5 of the relation between Q
and P¡ in a four tube model: effect of decreasing
?S 56
15. Recording from program 5 of the relation between Q
and P¡ in a four tube model: crossing of the
intercept 59
16. Recording from the one tube physical model of the
relation between P¡ and PQ 62
17. Recording from the one tube physical model of the
relation between P¡ and PD: effect of increasing
PS 64
18. Recording from the one tube physical model of the
relation between P¡ and PQ: effect of increasing
Rp 66
19. Comparison of calibrated resistances of glass tubes
used in the physical model to the resistances
calculated while the tubes were in the proximal
or distal position 69
20. Recording from the three tube physical model of the
relation between P¡ and PQ 71
21. Recording from the two tube physical model of the
relation between P¡ and PQ: flow occurring in
all tubes 74
22. Recording from the three tube physical model of the
relation between P¡ and PQ: flow occurring in a
partial number of tubes 76
23. Recording from the one tube physical model of the.
relation between Q. and P¡ 79
24. Recording from the one tube physical model of the
relation between Q. and P¡: effect of increasing Rp . 81
25. Recording from the one tube physical model of the
relation between Q. and P¡: effect of increasing P$ . 84
26. Recording from the three tube physical model of the
relation between Q. and P¡: effect of increasing Rp . 86
27. Recording from the three tube physical model of the
relation between Q. and P¡: effect of increasing P$ . 89
28. Recording of the relation between PAP and PVP In a
ventilated animal 92
vi i


29.
/
Comparison of proximal and distal resistance and
surrounding pressure in the left lung during
the unventilated fetal state (F), during vent
ilation of both lungs with fetal gas (VFG) and
during ventilation of both lungs with air (VA) .... 95
30. Relation between proximal resistance and pulmonary
arterial P02 ¡n ventilated animals 98
31. Relation between log proximal resistance and log
pulmonary arterial Pq2 in ventilated animals 100
32. Relation between distal resistance and pulmonary
venous P02 in ventilated animals 102
33. Comparison of total resistance (T), calculated in
condition 3, to the sum of proximal and distal^
resistance (P + D), calculated in condition 2,
in unventilated fetal animals, animals venti
lated with fetal gas and ventilated with air 105
3**. Comparison of proximal and distal resistance and
surrounding pressure in the left lung during
the unventilated fetal state (F), during venti
lation of the right lung with fetal gas (VFG)
and during ventilation of the right lung with
air (VA) 107
35. Relation between proximal resistance and pulmonary
arterial P02 in unventilated animals Ill
36. Relation between distal resistance and pulmonary
venous P02 in unventilated animals 113
37* Comparison of proximal and distal resistance and
surrounding pressure in the left lung of unventi
lated animals before (B), during (D) and after
(A) infusion of bradykinin into the pulmonary
artery 116
38. Comparison of proximal and distal resistance and
surrounding pressure in the left lung of newly
ventilated animals before (B), during (D) and
after (A) infusion of bradykinin into the
pulmonary artery 119
39. Comparison of proximal and distal resistance and
surrounding pressure in the left lung of newborn
animals during ventilation with air (A), 10% O2
in N2 (10) and 5% O2 in N2 (5) 123
yiii


Abstract of Dissertation Presented to the
Graduate Council of the University of Florida in Partial Fulfillment
of the Requirements for the Degree of Doctor of Philosophy
PULMONARY VASCULAR RESISTANCE
IN FETAL AND NEONATAL GOATS
By
Raymond Dwight Gilbert
June, 1971
S. Cassin, Chairman
Department of Physiology
Flow through a system of parallel tubes, each containing a Starling
resistor, was considered both theoretically and experimentally. A method
was proposed to calculate resistance proximal and distal to the Starling
resistors by observing the relation between inflow pressure and outflow
pressure. Proximal resistance (Rp) was calculated as inflow pressure
minus the pressure surrounding the Starling resistor (Ps) divided by flow.-
Distal resistance (Rd) was calculated as surrounding pressure minus out
flow pressure divided by flow. This method was used to analyze changes
in pulmonary vascular resistance after ventilation or infusion of brady-
kinin in mature fetal goats and after hypoxia in newborn goats. Deter
minations of proximal and distal resistances were made from measurements
of pulmonary artery pressure and pulmonary venous pressure while pulmonary
artery pressure was kept constant and pulmonary venous pressure varied,
in mature goats ventilation of both lungs with a gas that did not change
blood gases (fetal gas) resulted in a decrease in Rp and Ps. Further
ventilation of both lungs with air caused Rp, Rp and P$ to decrease.
Ventilation of only the right lung with fetal gas did not result in any
changes in Rp, Rq or Ps in the left lung; however, ventilation of the
right lung with air was followed by decreases in Rp, Rq and Ps in the
¡X


left lung. In newborn goats Rp, Rg and Ps increased in response to
ventilation hypoxia (5% 02 ¡n N2) Rp and Ps decreased in unventilated
fetuses after Infusion of bradyklnin into the pulmonary artery. After
the fetuses were ventilated with air, bradykinin infusion still caused
a decrease in Rp, but not in Ps.
x


INTRODUCTION
The pulmonary circulation was shown to respond to changes in blood
gases first in 1946 when von Euler and Liljestrand (l) demonstrated that
hypoxia caused a rise in pulmonary artery pressure in the adult cat.
Subsequently it has been well confirmed that the pulmonary vasculature
of adult lungs constricts in response to decreased P02 (2-5) The
action of the decreased Po£ has been shown to be a local one, in
isolated lung preparations (2-5), as well as being mediated through
peripheral chemoreceptors (6-7). The response of fetal pulmonary
vasculature to hypoxia and ventilation is very similar to that of adult
lungs and has been reviewed extensively by several authors (8-10).
Ventilation of fetal lungs with any gas causes a decrease in pul
monary artery pressure and an increase in pulmonary artery flow (11-16).
Inflation of fetal lungs with saline or dextran containing a low P02
does not cause the same decrease in pressure and increase in flow but
rather results in no change or a decrease in flow (12, 17). The-
reduction of fetal pulmonary vascular resistance (PVR) upon ventilation
with a gas has been shown to be the result of two separate causes:
(1) the mechanical events which accompany expansion of the lungs with
a gas and (2) the local effect on the pulmonary vasculature of an
increase in P02 or decrease in PC02 03, 15-16, 18). Campbell et al.
(19) have shown also that changes in the gas composition of blood per
fusing unventilated fetal lungs will elicit changes in PVR. To date,
no one has reported in the literature any attempt to isolate the site
of these changes in PVR in fetal lungs in response to ventilation and
1


2
to changes in P02 and PC02* Determinations of the distribution of
vascular resistance and of the sites sensitive to hypoxia and hyper
capnia have been made for adult lungs (20, 21). However, similar
determinations have not been made for fetal or newborn lungs.
The effect of drugs on the pulmonary circulation and their relation
ship to the pulmonary vascular response to hypoxia have been studied in
both fetal and adult animals (22-59)* The catecholamines have been
reported to constrict the pulmonary vasculature of fetal lambs even
when given in small doses (0.1-0.5 mg/kg) (15, 55). Epinephrine also
causes vascular constriction in adult lungs that has been localized,
using pulmonary artery and vein wedge pressures, to the venous segment
of the vasculature (22, 23).
Norepinephrine increases pulmonary vascular resistance in both
neonatal and adult animals (2^-27). Barer (28) demonstrated that
norepinephrine increased PVR even in collapsed adult lungs. Hyman (27)
concluded that the effect of norepinephrine in dog lungs was exerted
on all vessels and not localized to one segment.
The effect of the catecholamines on PVR has been blocked with
phenoxybenzarnine, phentolamine and propranolol (25, 26, 29). The
response of the pulmonary vasculature to hypoxia has been shown by
some (26, 28) to be abolished by phenoxybenzarnine or phentolamine;
however, others (25, 30, 31) have indicated these agents have no
effect on the response to hypoxia. Depletion of catecholamine reserves
with reserpine or by adrenalectomy does not decrease the hypoxic res
ponse of either adult or neonatal lungs (25, 29). Cassin (15) showed
that adrenalectomy did not alter the pulmonary circulatory response
to asphyxia in immature fetal lambs.


3
Acetylcholine initiates a large increase in blood flow in the
unexpanded lungs of the fetal lamb, but has little effect on pulmonary
circulation after ventilation has begun (lA). Shepard et al. (32)
showed that acetylcholine decreased pulmonary vascular resistance in
the hypoxic neonatal lamb, but had no effect on nonhypoxic neonates.
In contrast, in the intact adult dog lung acetylcholine has been demon
strated to constrict the vasculature (33). However, Chu et al. (3^) has
observed that acetylcholine dilates the pulmonary vasculature of newborn
human infants. Others (35, 36) have shown that acetylcholine decreases'
pulmonary vascular resistance of normal men and women and in individuals
with primary pulmonary hypertension.
Histamine has been shown to increase PVR in normal adult lungs
(22, 23) and in collapsed lungs (28). Some evidence suggests this
response is larger in the venous segment of the vasculature than in
the arterial segment (22, 23). Bjure et al. (35) has indicated that
histamine injection results in a large increase in pulmonary blood flow
(14). Histamine releasers and antihistamine drugs have been demon
strated to abolish the pulmonary vascular pressor response to venti
lation hypoxia in both isolated and intact adult lungs (27, 37, 38, 39)*
Bradykinin produces a decrease in PVR in isolated and intact dog
lungs (AO, 56, 57), in normal adult human lungs (58, 59), in lungs of
humans with arterial hypertension, pulmonary arterial hypertension, and
emphysema (58, 59), as well as in unventilated fetal lungs of the lamb
(43). However, Hyman (A2) suggested that bradykinin actually caused an
active constriction of pulmonary vins, which was masked by a passiye
dilatation of the arterial segment in response to the increased cardiac
output caused by the bradykinin. Bradykinin is also thought by some


(43) to be the mediator of the decrease in PVR upon ventilation of fetal
animals. No one has attempted to demonstrate the sites of action of
these drugs in the fetal or newborn pulmonary vasculature.
Therefore, the purpose of the experiments to be presented here was
to determine the sites of change in pulmonary vasculature resistance in
response to: (l) changes in the P02 and Pc02 t^ie blood perfusing
unventilated fetal lungs, (2) the mechanical events that accompany
ventilation of fetal lungs, (3) ventilation of fetal lungs with air,
(4) hypoxia in newborn lungs and (5) an infusion of bradykinin in
fetal and newly ventilated lungs. It was impossible to investigate
the sites of action of all the drugs mentioned above at the present
time. Therefore, bradykinin was chosen to be studied because it has
been suggested as a possible mediator in the events accompanying
ventilation of fetal lung.
In order to analyze segmentally the resistance in the pulmonary
vasculature it was necessary to employ a model of the pulmonary circu
lation as described by various workers (44-54). This model is based
on the tenet that the pulmonary circulation behaves in a manner similar
to a system of parallel tubes containing Starling resistors. A Starling
resistor was first described as a thin walled collapsible tube traversing
a chamber in which the pressure surrounding the tube can be controlled.
Evidence to support this model was first presented by Banister and
Torrance in 1960 (44). They showed in isolated adult cat lungs that
at a constant inflow, pulmonary artery pressure was independent of pul
monary venous pressure if pulmonary venous pressure was below tracheal
pressure. This work has been confirmed by others (45, 46). Permutt
et al. (47) demonstrated that at a constant pulmonary arterial pressure,


5
flow is not influenced by changes in left atrial pressure if left
atrial pressure is below tracheal pressure. Pulmonary arterial pressure,
at a constant flow, is linearly related to tracheal pressure with a slope
of one if tracheal pressure is above left atrial pressure (***0 When
left atrial pressure is zero, the pressure to which pulmonary arterial
pressure falls when flow is stopped is equal to tracheal pressure, if
tracheal pressure is above 5 mmHg. If tracheal pressure is less than
5 mmHg, the pulmonary arterial pressure at zero flow remains 5 mmHg,
rather than falling to zero (46). Recently Permutt et al. (48) has
given evidence that pulmonary capillaries are indistensible. Also,
Abraham and Caldini have found that the pulmonary blood volume is
linearly related to the slope of the pressure:flow curve, suggesting
to him that resistance is constant along the straight line portion of
the pressure:flow curve (49).
A new method will be presented in this present study utilizing
this concept of the pulmonary varculature containing Starling resistors,
that allowed resistance to be calculated in two segments of the pul
monary vasculature. Resistance was calculated in that segment proximal
to the Starling resistors and also in the segment distal to the Starling
resistors. The resistance in these two segments was used then to deter
mine the sites of change in pulmonary vascular resistance in each of the
conditions mentioned previously.


MATERIALS AND METHODS
Figure 1 is a diagrammatic representation of the basic model used in
these experiments. This model has been described by others previously
(45, ^6). A constant inflow pressure is maintained in this model by means
of a reservoir which can be raised or lowered. Inflow pressure (Pi), flow
(Q) and outflow pressure (PQ) can be measured at the points indicated in
the figure. The Starling resistor is diagrammed as a collapsible tube
traversing a plexigls chamber filled with water. The pressure tending
to close the Starling resistor (P5) is the hydrostatic pressure of the
water surrounding the Starling resistor. The resistance from the point
at which P¡ is measured to the end of the Starling resistor is designated
Rp or proximal resistance. The resistance from the end of the Starling
resistor to the point at which PQ is measured is denoted by Rg or distal
resistance. PQ' is the pressure just distal to the Star 1 ing resistor.
Outflow pressure can be raised or lowered by means of a pulley attached- -
to the outflow tube. Outflow from the system is collected in a reservoir-
and returned to the Inflow reservoir by means of a Sigmamotor finger
pump.
In order to maintain a constant inflow rate it was necessary to
modify this model as indicated in figure 2. The inflow reservoir was
deleted so that the tube from the finger pump could be attached directly
to the inflow tube. All other aspects of this model are identical to
those in figure 1.
Flow through a system as indicated in figure 1 is characterized by
6


FIGURE 1. Diagram of a one tube model containi
resistor arranged to provide a constant inflow
Q. flow, Rp proximal resistance, Rq distal
P¡ inflow pressure, PQ outflow pressure, PQ
immediately proximal to distal resistance
ng a Starling
pressure,
res!stance,
1 pressure


oo


FIGURE 2. Diagram of a one tube model containing a Starling
resistor arranged to provide a constant flow. Q, flow,
Rp proximal resistance, Rq distal resistance, PAP inflow
pressure, PVP outflow pressure, PVP1 pressure immediately
proximal to distal resistance
f
t


WATER LEVEL
Q PAP
PVP'
S

FINGER PUMP
JA
STARLING RESISTOR


11
the following sets
Condition 1:
Condition 2:
Condition 3:
of conditions:
¡f Pi < PS Q =
if p¡ > ps > p0'
if P¡ > PS < p0'
0
, Q =
Pi -Ps
RP
P? ~ Po
Rp + Rg
Throughout the section on methodology the above conditions or equivalent
conditions will always be referred to by the numbers indicated.
In condition 3 the total resistance (Rj = Rp + Rg) of the system can
be calculated by the equation Ry = -1;. |n condition 2, Rp can be
Q. r
P pc
calculated from the equation Rp = . rq may be obtained in sev
eral ways. Rp can be subtracted from Rj to obtain a value for Rg; or it
may be calculated from the equation Rg =
In order to calculate Rp and Rq in vivo it is necessary to obtain
values for P¡, Ps, Po> Po' and Q. Measures of P¡, PQ and Q are easily
obtainable; however, methods had to be devised to obtain values for P5
and P0'. These methods were derived through further mathematical consid
erations of the characteristics of a system such as that presented in
figures 1 and 2. For purposes of clarity the section on methodology will
be divided into three parts. The first part will deal with the theoreti
cal and mathematical aspects of this system. Secondly, the application
of these mathematical aspects to a physical model will be considered.
Lastly, the use of these concepts in vivo to analyze segmentally pulmonary
vascular resistance will be covered.


12
Mathematical Model
P¡ Versus PQ
Initially it was necessary to observe the relationship between P¡
and Po in a system such as that indicated in figure 2. Equations des
cribing this system were programmed into a Hewlett Packard model 9100A
calculator and desired relationships were recorded on a Hewlett Packard
model HR-98 X-Y plotter. A program was written to evaluate this relation
ship based on the following reasoning. The actual program is given in
Appendix 1 as program 1.
Given: Q is constant
Qin = Qout
Po1 = Q-RD + P0
Condition 1: if Q = 0
then P¡ = Ps in condition 2, or P¡ = P0' in condition 3
Condition 2: if Ps > P01
then P¡ = Q-Rp + Ps
Condition 3 if Ps < Po'
then P¡ = Q-Rp + Po'
The program was given an initial PQ. The calculator was programmed
to calculate P0' according to the equation given. It next compared Po1
to the given Ps, calculated the appropriate P¡ and plotted P¡ against Po
on the X-Y recorder. The calculator was programmed to increase PQ by a
given interval and execute the same procedure just described. This cycle
was repeated automatically until the desired curve was obtained and the
program manually stopped. Typical curves obtained from this program for
several different flows are shown in figure 3- These curves are traced
from the original curves obtained from the X-Y plotter.


FIGURE 3, Recording (.traced from original) from program 1 of the
relation between P¡ and PQ in a one tube mode], Rp = 1,0 mmHgvnin/ml,
Rq => 0.5 mmHg*min/ml, Ps = 5*0 mmHg


60n
40-
P¡
(mm.Hg.)
20-
Q30 ml/min
Q20 ml/min
B
Q*0 ml/min
k
-20
0
(mm.Hg.)


15
According to this model when Q is zero, P¡ = P$ in condition 2, but
P¡ = P0' in condition 3- At any constant flow (or zero flow) P¡ is inde
pendent of P0 as long as P0 is less than P$. Whenever P0 becomes
greater than P$, PQ will influence P¡ in a one to one relationship. In
other words P0 = P$ is the boundary between condition 2 and condition 3
At zero flow the PQ which begins to influence P¡ (point A on figure 3) is
equal to P$, since P0' = PQ at zero flow. Therefore, the PQ at point A
may be taken as a measure of P$. At any constant flow P0' is greater
than PQ due to the resistance along the distal segment. When PQ just
begins to influence P¡ (point B on figure 3) Po' is equal to P$. There
fore, at point B the pressure drop along the distal segment is P$ minus
the outflow pressure at point B (PQg). Distal resistance may be calcu
lated as this pressure drop divided by flow (Rp = ^ ). The Ps
used for this calculation is the value of P0 at point A (P0^) on the zero
flow curve described above. The correct equation for calculating Rp is
then: Rp = This same value for P Rp. If a constant flow is maintained such that the system is in condition
p pq
2 (Ps > P0) then Rp = ¡: Again, the correct equation is actually
Q.
rp Pi: pft.
Q
It was necessary to observe the relationship between P¡ and Po in a
model consisting of more than one tube. Figure 4 is a diagrammatic repre
sentation of a system containing four tubes in parallel. The tubes were
not stacked vertically but were all in the same horizontal plane. Each
tube has a Starling resistor traversing a separate plexigls box. Each


FIGURE 4. Diagram of a four tube model containing a Starling
resistor in each tube. Q. flow, Rp proximal resistance,
Rq distal resistance, P$ pressure surrounding the Starling
resistor, P¡ inflow pressure, PQ outflow pressure,
P0' pressure immediately proximal to distal resistance
i
I


Q pi
P2
R
P3
RP,
r?
-UwmwvaJ-
~
-jWWWWWWp
P|2
XwAW/AvJ-
-jWvVWWWVp
P?3
-IvAV.V.V-V-
-MVAVWWtep
P?4
4fl.WJWVWt4-
/
f*D
U

STARLING
RESISTOR


18
box may be filled with different amounts of water and in this manner
for each Starling resistor can be varied independently. Rpj designates
the resistance from the point at which P¡ is measured to the end of the
Starling resistor in tube 1. The same description applies to Rp£> Rpj
. : a. O
and Rpp The remainder of the symbols used for this model are equivalent
to those described for figure 2.
A program was written for this model according to the following equa
tions. The actual program is given in Appendix 1 as program 2.
Given: Q. is constant
Qin = Ql + Q2 + ^3 + Q4 = Qout
p0' = Q-Rd + Po
PS, < P$2 < PS3 < PS4 and all are constant
Rpj = Rp2 = Rp-j = Rp/, and are represented by R
Condition 2:
State 1: if PQ' < Ps] < Ps2 < PS3 < PSI*
then: Q] = ^
Q* = Pi--" P$3-
q. = pi ~-pi.4.
^ R
and: Q = + ^-1-^ + P¡
solving for Pj:
P. = Q-R + PS 1 + PS2 + pS^ + pS4
' 4


19
This equation is valid only if the P¡ obtained from it is
greater than P$^; that is, if flow is occurring through
all four tubes. For simplicity in this program it was
assumed that the only time P¡ < Ps4 was when 4=0.
Therefore ,in this state and the following states if the
calculated P¡ was less than Ps^ flow was assumed to be
zero. In this state P¡ = PS] when 4=0.
State 2: if Ps] < P0' < PS2 < PS3 < pS4
then: LJLIoI + !i_- PS2, t !Li_--fS.l + Pi, PS.-L
R R R R
Solving for Pj:
p. = 4-R + Pp1 + Ps2 + pS3 + pS4
4
Again, if the calculated P¡ is less than Ps4 this equa
tion is not valid. In this state P¡ = P0' when 4=0.
State 3: if PS] < PS2 < po' < pS3 < PS4
then: Q tL.--Pg.'. + ?.l. -.JV pi ~ -P.S3 + pi ~ PS1,
R R R R
Solving for P¡:
_ 4-R + 2Po1 + PS3 + PS4
p' i
In this state if 4 = 0, then P¡ = P0'
State k: if P$] < Ps2 < PS3 < Po' < pS4
then: 4 = + tKr. fp.'. + Pol +
R R R R
Solving for Pj:


20
Q-R + 3Po' + Psb
5 = n
In this state if Q = 0, then P.; = P0'.
Condition 3:
if PS i < PS2 < pS3 < PS4 < Pq'
Solving for P¡:
o. Q-R + ^Po1
p. 2;
This equation is always valid.
As in program 1 the calculator was given an initial PQ with which
it calculated PQ' according to the given equation. It then made the
appropriate comparisons and calculated the correct P¡ which it plotted
against the original PQ. The program was set up so that the calculator
increased PQ by a given interval and calculated a new P¡ which was
plotted against the second PQ. This cycle was repeated until the program
wari manually stopped.
Leading from program 2 it was necessary to investigate the relation-
shTp>between P¡ and Po in condition 2, states 1 and 2, when Q > 0 yet
th^ resultant P¡ < Ps; that is, when flow was occurring through only a
pffftrial number of the tubes. The following program was written to inves
tigate this relationship. Refer to figure b for nomenclature. In this
program the calculator was also given an initial PQ with which it calcu
lated the correct P¡ and plotted it against PQ. It then raised PQ by a_
giVeh increment and calculated a new P¡. This cycle was repeated until
the5 program was manually stopped. This program is given in Appendix 1 as


21
program 3-
Given: Q is constant
Qin = Ql + Q2 + Q3 + Qi* = Qout
Po' = Q'Rd + Po
PSl < PS2 < PS3 < PS4
Condition 2:
State 1: if P0' < PS] < Ps2 < Ps3 < pS4 then:
= Q-R + PS 1 + PS2 + PS3 + Pst
if P¡ ] < PS/f then:
D Q-R + Psi + PS2 + PS3
k¡2 ^
if P¡2 < Ps^j then:
d. + PS1 + pS2
'3 2
if < PS2> then:
p¡4 = Q,R + pS]
P¡j is valid only if flow is occurring through all four
tubes. If the given flow does not generate a P¡ hgTer~
than Psij then the Starling resistor in tube four will be
closed. If no flow is occurring through tube 4, then
Pi2 be valid if flow is occurring through the re
maining three tubes. If the given flow does not generate
a P; higher than PS3> then the Starling resistor in tube
3 will be closed. In this case P¡^ will be valid if flow
is occurring through the remaining two tubes. Again, if
the given flow does not generate a P¡ higher than PS2


22
then no flow will occur through tube 2, 3 or 4. P¡^
will then be valid for any flow which generates a P¡
less than P$2* The same reasoning applies to state 2.
State 2: if Ps] < Po1 < ?S2 < PS3 < PsZj, then:
n. Q-R + PS2 + Ps^i + Psi* + po
P" ¡T
P11 < PSV then:
D Q-R + Ps2 + PS3 + Po'
v\2 3
if P¡2 < PS3 then:
_ Q-R + PS2 + Po'
P,3 J
if P¡3 < P$2* then:
Pi4 = Q-R + P0
P; Versus Q
It was also interesting to me to study the relationship between Q
and P¡ in a model similar to the one presented in figure 1. Therefore,
a program was written to describe this relationship. In this program Py
was the controlled variable and Q was the dependent variable. The pro
gram was designed to utilize an initial given P¡ to calculate the appro-

priate Q and plot P¡ as a function Q. The computer was programmed to
increase P¡ by a given interval and repeat the initial process. This
could be repeated until the desired curve was obtained. The program to
calculate Q was based on the following relationships. The actual program
is given in Appendix 1 as program 4.
Given: PQ is constant
P0' = Q-R + P0


23
Condition 1: if P¡ < P$
then: Q = 0
Condition 2: if P¡ > P$ > P0
then:
P? P$
Rp
Condition 3- ¡f P¡ > P$ < P0*
then:
P? Po'
Rp + Rq
The relationship between flow and inflow pressure was also studied
in a model containing four tubes such as that presented in figure 4. As
in the one tube model the program was designed to calculate Q from a
given P¡ and plot P¡ against Q. The P¡ was then increased a given incre
ment and Q again calculated and plotted against P¡. This cycle was re
peated until the desired curve was obtained. The calculation of Q was
carried out according to the following relationships. This program is
given in Appendix 1 as program 5.
Given: PQ is constant
Po' < PS 1 < PS2 < PS3 < PS4
Condition 1: if P¡ < P$] < PS£ < PS3 < PS4
then: Q. = 0
Condition,2:
State 1: if Ps]
then:
State 2: if Pgj
then:
< P¡ < PS2 < pS3 < PS4
Pj PS 1
Rp 1
< PS2 < P¡ < PS3 < PS4
= Pj PS1 Pj PS2
RP 1 RP2


24
State 3: if Ps] < P$2 < PS3 < P¡ < PS4
then. A = pi .pSl. P.i fS2. + pj..- psi
then. Q Rp] + Rpz + Rp3
State 4: if Psj < P$2 < PS3 < Ps4
< Pi
then: = Pi PS' + ¡- + Pi ~ P + El -
RPl RP2 RP3 Rpi*
Condition 3 was not included in this program for the sake of sim
plicity. Therefore, care was taken so that PQ' never became greater than
PS] during the construction of the curves from this program. This pro
gram was used to study the effects of changing P$ values while holding--.
Rp values constant and vice versa. The result of changing both P$ and
Rp values simultaneously was also studied.
Physical Model
P; Versus PQ
In order to test the mathematical model presented above and also to
determine if values for the desired parameters could be obtained accurately
a physical model was built. To obtain pressure:flow curves from the phys
ical model an inflow reservoir, as diagrammed in figure 1, was utilized
to maintain a constant inflow pressure. However, in order to obtain the
relationship between inflow pressure and outflow pressure the model was
constructed as in figure 2 in order to maintain a constant inflow rate.
As in the mathematical model, the initial measurements were made in
a one tube system in the physical model. In order to determine the rela
tionship between P¡ and PD, the physical model was arranged as indicated
in figure 2. Rp and Rg were simulated by small bore glass tubes of var
ious lengths. The diameter of the Starling resistor was of such magni
tude that its contribution to total resistance was negligible. The


25
Starling resistor was made by placing two polyethylene sheets together
and heat sealing two strips 1.2 cm apart. The tube thus obtained was
trimmed and cut to the desired length (6.5 cm).. During this procedure
inflow pressure and outflow pressure were measured with Statham model
23 PC pressure transducers. Flow was measured utilizing a Statham model
FT-QC cannulating flow probe and a Statham model M^OOl electromagnetic
flowmeter. Pressures and flows were recorded on a Grass model 5C poly
graph. In addition P¡ was plotted against PQ during the procedure by
means of a Houston model HR-98 X-Y plotter. Saline was used as the pei
fusing fluid. The relationship between P¡ and Pq at any constant flow
was obtained in the following manner: (1) the outflow tube was lowered
so that P0' was less than P$, (2) a constant flow was maintained by the
finger pump, (3) the outflow tube was then raised slowly while P¡ was
being plotted against PQ on the X-Y recorder. This same procedure was
carried out to obtain the relationship between P¡ and PQ at zero flow.-'
During this condition flow in the reverse direction was prevented by the
finger pump which occluded the inflow tube.
According to the mathematical model presented previously, the PQ at
the breakpoint of the curve drawn during zero flow may be taken as a
measure of P$ (point A on figure 3). This was done for the physical
model and the values obtained were used to calculate both Rp and Rq. Rp
was calculated as previously described according to the equation
P ¡ Pc
Rp = :. The Pi used was that pressure which resulted from a
Q
constant flow while the system was in condition 2 (Ps > P0') Rd was -
also calculated as described in the mathematical model. The PQ at the
breakpoint of a curve drawn at constant flow (point B on figure 3) sub-


26
tracted from was used as the pressure drop along the distal segment.
Pq p
R[) was then calculated as Rg = r^ The Rp and Rg calculated by
this method were compared to the known resistances of the small bore
glass tubes which simulated Rp and Rq. The resistances of the glass
tubes had been calibrated previously by measuring the pressure drop across
each tube at several measured flow rates.
In order to test if the relationship between P¡ and PQ in the phys
ical model followed that predicted by the mathematical model in a system
which contained more than one tube, a physical model was built which con
tained three tubes in parallel. This system is analagous to the one pre
sented in figure 4 with the exception that only three tubes were used.
The Starling resistor in each tube traversed a separate plexigls box in
order that the pressure surrounding each Starling resistor could be
varied independently. Rp], Rp and RP3 were simulated with separate
small bore glass tubes so that each could be varied independently of the
others. A constant inflow was provided by means of a finger pump. In
this model the relationship between P¡ and PQ was obtained in exactly the
same manner as described for the one-tube model.
Pj Versus Q,
In order to determine pressure:flow characteristics of a onetube
model, the model was arranged as in figure 1. Inflow pressure, outflow
pressure and flow were measured and recorded as described previously.
Flow was also measured by collecting the outflow for a timed period.
Saline was used as the perfusing fluid. Rp and Rg were again simulated
in the model by small bore glass tubes of various lengths. The diameter
of the tube in the Starling resistor was of such magnitude that its con
tribution to total resistance was negligible.


27
During the construction of a pressurerflow relationship, outflow
pressure was held constant at some value below the hydrostatic pressure
of the water surrounding the Starling resistor. The inflow reservoir
was initially placed below the level of the Starling resistor. It was
then raised a given distance, usually 1 cm, and held there until a stable
flow was attained. The resulting flow and pressures were recorded and
and inflow pressure was plotted against flow. The reservoir was again
raised and the resulting flow measured and plotted against inflow pressure
This procedure was repeated until the desired pressure:flow curve was
obtained. The effects on the pressure:flow curve of changing Rp and Rq,
by substituting various lengths of the small bore glass tubing, and of
changing P$, by varying the level of water in the plexigls box, were all
studied in this model.
The relation between pressure and flow in a model containing three
tubes in parallel was also studied. The model was set up in the same man
ner as it was for obtaining the relation between P¡ and PQ. The only
modification was that a constant inflow pressure was provided by means
of an inflow reservoir. Pressure:flow curves were obtained from this
model in exactly the same manner as that just described for the one-tube
model.
Animals
Fetuses
Pregnant goats were anesthetized with chloralose (50 mg/Kg I.V.)
and sustaining doses (10 mg/Kg I.V.) given hourly. Fetuses (135-1^5 days
gestational age) were delivered by caesarean section onto a warmed table
adjacent to the mother. Care was taken to prevent the fetuses from breath
ing by placing a bag filled with saline over their heads. Colonic temp
erature was monitored and maintained between 37-39C. Caution was taken


28
not to disturb the umbilical circulation. A tracheotomy was performed
and tracheal fluid allowed to drain at atmospheric pressure through a one"
way valve into a beaker. The left carotid artery was isolated and loose
ligatures placed around it. Both femoral arteries were isolated and can-
nulated. A thoracotomy was performed on the left side, removing the
3rd 5th ribs. The left pulmonary artery and the vein draining the
lower lobe of the left lung were dissected free and loose ligatures placed
around them. The blood supply to and from the middle and upper lobes of
the left lung was isolated and ligated. Fetuses were anticoagulated with
heparin (2^00 U/Kg I.V.).
A cannula was introduced into the vein of the lower left lung lobe
via the left atrium and blood directed into a reservoir as indicated in
figure 5> Pulmonary venous pressure (PVP) was varied by raising or low
ering this reservoir. Blood was pumped from the reservoir through a heat-
exchanger into the left femoral artery. The heat exchanger consisted of
a siliconized glass condensing coil over which warm water, regulated at
AlC, was circulated. A cannula was placed in the left carotid artery
and led through a finger pump into the distal end of the left pulmonary
artery, which now perfused only the left lower lobe of the lung. Pulmon
ary artery pressure (PAP) and pulmonary venous pressure were measured
with Statham model 23 PC pressure transducers. PAP and PVP were corrected
for the pressure drop due to the resistance of the cannulas. Pulmonary
arterial and pulmonary venous blood flows were measured with Statham
model FT-QC cannulating flow probes and a Statham model MAOOl electro
magnetic flowmeter. Systemic blood pressure was monitored by means of
the cannula in the right femoral artery. Pressures and flows were recorded
on a Grass model 5C polygraph.


I
1
FIGURE 5. Diagram of surgical preparation of animals.
CA carotid artery, BC brachiocephalic artery, A aorta,
PA pulmonary artery, DA ductus arteriosus, RV right
ventricle, LV left ventricle, UA umbilical artery,
UV umbilical vein, I VC inferior vena cava, SVC superior
vena cava, LLLV vein from left lower lobe, LLV lower
lobe of left lung, HLL middle lobe of left lung,
ULL upper lobe of left lung
. i
I


FINGER
PUMP
HEAT
EXCHANGER
PLACENTA


31
The relationship between PAP and PVP was obtained in exactly the
same manner as in the physical model: (l) the outflow reservoir was
initially lowered below the level of the lung, (2) a constant inflow was
maintained, and (3) the outflow reservoir was slowly raised while PAP
and PVP were being recorded on the Grass polygraph. Simultaneously PAP
was plotted against PVP on a Houston model HR-98 X-Y plotter. Curves
for zero flow were obtained simply by stopping the inflow pump, which
occluded the inflow cannula, and following the same procedure just des
cribed. Normally four curves were drawn; one at zero flow and three
curves at three different constant flow rates.
Rp and Rg were calculated in exactly the same manner described for
the one-tube physical model. The curves obtained from the animals did
not exhibit a sharply defined breakpoint as did the curves from the model.
Figure 6 presents representative curves obtained from an unventilated
fetal animal. The breakpoint for each of the curves obtained from the
animals was arbitrarily defined as the point on each curve which was
raised one mmHg above the baseline for that curve.
In order to determine the effects of ventilation on Rp and Rg, the-
following procedure was carried out on one group of fetuses. A set of
curves was drawn first for the unventilated fetal lung. The animal was
then ventilated with a gas mixture intended not to change the blood gas
values of the fetus. This gas mixture contained O2 and 6% CO2 in N2
and was termed the fetal gas mixture. Animals were ventilated with posi
tive pressure with a peak inspi ratory pressure of 30 CFT1H2O. This was
accomplished by placing a tube, attached to a side arm of the tracheal
cannula, under a 30-cm column of water. Expiratory pressure was kept
equal to atmospheric pressure. Ventilation in each group of experimental


FIGURE 6. Recording of the relation between pulmonary artery
pressure (PAP) and pulmonary venous pressure (PVP) in an
unventilated fetal animal





34
animals was carried out by this method. Another set of curves was ob
tained while the animal was being ventilated with this fetal gas mixture.
The animal was then ventilated with air and another set of curves drawn.
During the construction of each set of curves, pulmonary arterial and
pulmonary venous blood samples were drawn and analyzed for Pq2 PCO2 anc*
pH on a Radiometer blood gas analyzer. Resistances were calculated from
the curves obtained according to the method previously described.
In another group of fetuses the effects on Rp and Rg of changing
blood gases alone was investigated in the following manner. The bronchus
to the left lung was ligated and cut distal to the tie to allow fluid
from the left lung to drain at atmospheric pressure. This allowed venti-
lation of the right lung while the left lung remained unventilated. A
set of curves was obtained from the left lower lobe while both lungs were
in the unventilated fetal state. The right lung was then ventilated with
the fetal gas mixture and a set of curves for the lower left lobe obtained
The right lung was then ventilated with air and another set of curves
drawn for the left lower lobe. Pulmonary arterial and pulmonary venous
blood samples were drawn during the construction of each set of curves-
and again analyzed for Po2> PCO2 anc* P^* Resistances were calculated as
previously described.
The effects of bradykinin on pulmonary vascular resistance were
studied on a final group of fetuses. A set of curves was obtained while
the lungs of the animals were in the unventilated state. Bradykinin
was then infused into the left pulmonary artery (60-240 ng/min) and a set
of curves acquired. The infusion was then stopped and the animals allowed
to stabi1ize; .after which another set of curves was drawn. The animals
were then ventilated with air. The effects of bradykinin during venti-


35
lation with air were studied in the same manner as in the unventilated
state ; that is, sets of curves were collected before, .during and after
the infusion of bradykinin. Pulmonary arterial and pulmonary venous P02
PCO2 ar,d PM were monitored during the construction of each set of curves.
Resistances were calculated as previously described.
Neonates
The effects of hypoxia on the pulmonary circulation of neonatal kids
was investigated in the following manner. Kids were anesthetized with
chloralose (50 mg/Kg I.V.) and placed on a warmed table. Sustaining
doses of chloralose were given hourly. The neonatal animals were pre
pared surgically in exactly the same manner as the fetal animals as
indicated in figure 5- After the chest was opened the kids were main
tained on positive pressure ventilation with air. The relationship
between PAP and PVP was obtained in the kids in the same manner as irr
the fetal animals. Rp and Rg were calculated from this relationship as
previously described.
After surgery was completed a set of curves was obtained while the
kids were being ventilated with air. The animals were then ventilated
with a mixture of 10% O2 in N2 and another set of curves obtained. The
ventilating gas was then changed to 5% O2 in N2 and another set of curves
drawn. Pulmonary arterial and pulmonary venous blood samples were drawn
during the construction of each set of curves and analyzed for P02 P(;02
and pH.


RESULTS
Mathematical Model
P¡ Versus PQ
Figure 3 shows a plot, traced from the original, of the relation
between P¡ and PQ in a one-^tube mathematical model obtained from
program 1 when Rp = 1.0 mmHg-min/ml, RD = 0.5 mmHg*min/ml and Ps =
5.0 mmHg. Three curves were drawn at flows of 0, 20 and 40 ml/min.
For the curve drawn at 20 ml/min the pressure drop across the distal
resistance (PQ/\ Pob) *s ^ mmHg. The pressure drop across the
proximal resistance (P¡ PQ^) is 20 mmHg. Increasing the Ps to 10
mmHg, while holding Rp = 1.0 mmHg-min/ml and Rg = 0.5 mmHg*min/ml
(figure 7), merely increases P¡; the pressure drops across the proxi
mal and distal resistances remain the same. For the curve drawn at
20 ml/min the pressure drop across the distal resistance (PQ/\ Pob)
is still 10 mmHg. Also, the pressure drop across the proximal
resistance is still 20~mmHg, although P¡ is 5 mmHg higher. The only
other difference noted from increasing Ps from 5 to 10 mmHg was that
the breakpoint for each curve shifted to the right.
Figure 8 represents the effects of increasing Rp from 1.0 to 2.0
mmHg.min/ml. Rg was held at 0.5 mmHg'min/ml and Ps was held at 10 mmHg.
In this situation the pressure drop across the proximal resistance, at
a flow of 20 ml/min, doubled from 20 mmHg to 40 mmHg in contrast to
that in figure 7- However, the pressure drop across the distal resis
tance remained 10 mmHg. The breakpoint for each curve remained the
same for the curves of equal flows in figure 7- In figures 3, 7 and 8
36


FIGURE 7. Recording (traced from original) from program 1 of
the relation between P¡ and P0 In a one tube model: effect of
increasing Ps. Rp = 1.0 mmHg'min/ml, R[) = 0.5 mmHg*min/ml,
P$ = 10 mmHg


60 -i


FIGURE 8. Recording (traced from original) from program 1 of
the relation between P¡ and PQ in a one tube model: effect of
increasing Rp. Rp = 2.0 mmHg*min/ml, Rq = 0.5 mmHg*min/ml,
P$ = 10 mmHg


80-1
Q 30 ml/rr.in
60-
B ^
Q*20tn!/fnin ^
pi ,0-
(mm.Hg.)
20-
Q 0 Ql/niin
0 -
*
-20 -10
1
q (m;n.Hg.)


the P0 at the breakpoint for each of the curves drawn during zero flow
(P0^) is equal to Ps.
The relationship between P¡ and PQ in a system containing four
tubes in parallel (program 2) is shown in figure 9- Program 2 was
written (assuming that Rpj = Rp2 = Rp^ =. Rp/j) to investigate the
characteristics of the system when flow was occurring through all
four tubes simultaneously, or when no flow was occurring at all. The
program was written in this manner for the sake of simplicity. The
characteristics of this system when flow was occurring through a
partial number of the tubes were investigated in the subsequent program
(program 3)* In figure 9, Rpj = Rp2 = RP3 = Rp^ = 1.0 mmHg*min/m1,
RD = 0.2 mmHg-min/ml and Ps] = 5, PS2 = 10 PS3 = 15, PS4 = 20 mmHg.
Curves were drawn at 0, bO, 70 and 100 ml/min.
On the curve drawn at zero flow, there is one breakpoint (point A
on figure 9). The value for PQ at this point is equal to the lowest Ps*
On each of the other curves, however, there are four distinct break
points. In the curve obtained at a flow of bQ ml/min in figure 9, these
breakpoints are marked by the letters B, C, D and E. The portion of
this curve up to point B indicates the system is in condition 2: state 1
(Po1 < Ps 1 < PS2 K PS3 < Ps^*) From point B to point C the system is
in condition 2: state 2 (Ps 1 < P0' < Ps2 < pS3 < F*s4) from point C
to point D it is in condition 2: state 3 (PS] < PS2 < Po' < pS3 < PS4);
and from point D to point E the system is operating in accordance with
condition 2: state b (PS] < PS2 < pS3 < P0' < pSi*) Beyond point E
the system is in condition 3 (Ps1 < PS2 < pS3 < pS4 < po')* UP to
point B in figure 9 flow through each of the tubes is occurring in
accordance with condition 2, or the waterfall condition (the Ps of each


FIGURE 9. Recording (traced from original) from program 2 of
the relation between P¡ and PQ .in a four tube model: flow
occurring in all tubes. Rpj = Rp£ = Rp? = Rpi* = 1.0 mmHg*min/ml,
Rg = 0.2 mmHg*min/ml, P^j = 5.0 mmHg, P$2 = 10 mmHg, P5, = 15
mmHg, Pjj^ = 20 mmHg


60
40
(mm.Hg.)
20
sIOOml/min ^
Q = 70 ml/min
Q = 40 ml/min
Q=0 ml/min
T E
10 0
(mm.Hg.)
0
T"
20


44
tube is greater than P0). From point B to point C (condition 2: state
2) tubes 2, 3 and 4 are still in the waterfall condition, but flow
through tube 1 has changed to condition 3 (Ps| < Po')* From C to D
(condition 2: state 3) tubes 3 and 4 are in condition 2, but tube 2
has joined tube 1 in condition 3. From point D to point E (condition 2:
state 4) only tube 4 is still in the waterfall condition; flow through
the remaining three tubes is occurring in accordance with condition 3.
From point E on, flow in all four tubes is in condition 3-
As shown by the dashed line in figure 9, the first breakpoint for
each curve that has a positive flow may be connected by a straight line.
However, this line does not intersect the breakpoint for the curve drawn
at zero flow. Program 2, by means of which figure 9 was obtained,
assumed either that flow was occurring through all four tubes simul
taneously or that flow was zero. Therefore, the condition when flow
was occurring through only one, two or three of the tubes was not
considered. Program 3 was written to observe the relation between
P¡ and P0 when flow was occurring through less than four tubes.
Figure 10 illustrates the results of plotting program 3- For
simplicity this program was written to study the characteristics of
the system only in condition 2: states 1 and 2. In figure 10, Rp =
1.0 mjnHg-min/ml RD = 0.2 mmHg.min/ml and Ps 1 = 5, PS2 = 10, PS3 = 15,
PS2+ = 20 mmHg. As in figure 9, the first breakpoints on the curves
drawn at 40, 80 and 120 ml/min can be connected by a straight line.
Howeyer, the first breakpoints for the curves drawn at 20, 10, 1 and
0 ml/min cannot be connected by a straight line. For all curves the
first breakpoint occurred when Pq1 became greater than Ps1


FIGURE 10. Recording (traced from original) from program 3 of
the relation between P¡ and PQ in a four tube model: flow
occurring in a partial number of tubes. Rpj = Rp£ = RP3 =
Rpi* = 1.0 mmHg*min/ml, Rp = 0.2 mmHg-min/ml, Psj = 5*0 mmHg,
P$2 = 10 mmHg, P^ = 15 mmHg, P$^ = 20 mmHg


60
40 -*
P¡
(mm.Hg.)
20-
0
Q = 120 ml/min
Q = 30 m!/min
Q = 40 ml/min
Q = 20 ml/min
Q = I0 ml/min
Q = I ml/min
Q = 0 ml/mln
i
0
(mm.Hg.)
T"
10
20


P¡ Versus Q
The relationship between P¡ and Q for a one_tube mathematical model
as described in figure 1 is displayed In figure 11. The curves in this
figure were obtained from program four. For curve 1, Rp = 1.0 mmHg-min/
ml, Rg = 0.2 mmHg-min/ml and P$ = 10 mmHg. For curve 2, Rp = 1.0 mmHg*
min/ml, Rp = 0.2 mmHg*min/ml and P$ = 15 mmHg. For curve 3, Rp = 0.5
mmHg'mm/ml, Rd = 0.2 mmHg-min/ml and Ps = 10 mmHg.
In curve 1, no flow occurred until P¡ became greater than Ps,
which was equal to 10 mmHg. Up to this point the Starling resistor is
closed and the system is in condition 1. When P¡ is higher than Ps
flow occurred in accordance with condition 2 (Q = ~ ^S). Point A
Rp
marks the point on curve 1 that P0 became greater than PS. Beyond
this point condition 3 governed flow through the system (Q. = £_|_I_f£)
Rp + Rd
Curve 2 demonstrates the effect of increasing Ps from 10 to 15 mmHg.
On curve 2, no flow occurs until a P¡ of 15 mmHg is reached. Also, the
flow at which the system changes from condition 2 to condition 3 (point
B) has increased, because P0' must now increase to 15 mmHg rather than
10 mmHg for the change to occur. The slope of curve 2 during conditions
2 and 3 is the same as the slope of curve 1 during conditions 2 and 3.
Curve 3 presents the effects of changing only Rp. Neither the pressure
at which flow begins to occur nor the flow at which the system changes
from condition 2 to condition 3 (point C) is different from curve 1.
However, the slope of curve 3 during conditions 2 and 3 is greater than
the slope of curve 1 during conditions 2 and 3*
The relationship between P¡ and Q in a model containing four tubes


FIGURE 11. Recording (traced from original) from program k of
the relation between 0. and P¡ in a one tube model: effect of
decreasing Rp and P$. Curve 1 Rp = 1.0 mmHg'min/ml,
Rg = 0.2 mmHg'min/ml, P$ = 10 mmHg. Curve 2 Rp = 1.0 mmHg'min/ml,
Rg = 0.2 mmHg'min/ml, Ps = 15 mmHg. Curve 3 Rp = 0.5 mmHg*min/ml,
Rg = 0.2 mmHg'min/ml, P$ = 10 mmHg


10 O i


50
in parallel is shown in figure 12. In this figure tube 1 has an Rp^
of 4.0 mmHg-min/ml and a P$] of 10 mmHg; tube 2 has an Rp2 of 4.0
mmHg-min/ml and a P$2 of 15 mmHg; tube 3 has an Rp^ of 4.0 mmHg-min/ml
and a PS3 of 20 mmHg; and tube 4 has an Rp^ of 4.0 mmHg-min/ml and a
P$2j of 25 mmHg. There are four distinct breaks (points A, B, C and D)
on this curve. Up to point A, P¡ has not exceeded the lowest P$ and
no flow takes place because all the Starling resistors are closed.
Between points A and B, P¡ is greater than PS] but less than PS25
therefore,flow is occurring through tube one only. Between points B
and C, P¡ is greater than P$2 but less than P$3 In this region flow
is occurring through tubes 1 and 2. Between points C and D, flow is
occurring through tubes 1, 2 and 3 because P¡ is greater than PS3
but less than PS4- Beyond point D, P¡ is greater than Ps2j and flow
is taking place in all four tubes.
Figure 13 points out the effects of decreasing proximal resistance
without changing Ps values. In this figure curve 1 is the same as in
figure 12. For curve 2, Rp] = 1.0, Rp£ = 2.0, Rp^ = 3.0, Rp^ = 4.0
mmHg-min/ml and P$i = 10, PS2 = 15, PS3 = 20, PsZj = 25 mmHg. On curve
2 there are again four distinct breaks as in curve 1, but the slope of
the linear portion of curve 2 has increased in comparison to the slope
of the same portion of curve 1. Of interest is the fact that the inter
cept of the straight line portion (beyond the last break) of the two
curves is different. Therefore, in this model changing only resistance
changes both the slope and the intercept of the straight line portion
of the pressure:flow curve.
Figure 14 demonstrates the effects of decreasing Ps while holding
Rp constant. Curve 1 in this figure is the same as the curve presented


FIGURE 12. Record!ng.(traced from original) from program 5 of
the relation between Q. and P¡ in a four tube model.
Rp i = Rp2 = Rp-j = Rp/, = 4.0 mmHgmin/ml, Ps] = 10 mmHg,
P$2 = ^5 mmHg, P$^ = 20 mmHg, Ps^ = 25 mmHg


\


FIGURE 13. Record ing.(traced .from original) from program 5 of
the relation between Q. and P¡ in a four tube model: effect of
decreasing Rp. Curve 1 same as figure 12. Curve 2 -
Rp} = 1.0 mmHg'tnin/ml, Rp£ = 2.0 mmHg-min/ml, Rp^ = 3-0 mmHg-min/ml,
Rp/j = 4.0 mmHg-min/ml, P$ ] = 10 mmHg, Ps£ = 15 mmHg, Ps, = 20
mmHg, Ps^ = 25 mmHg


80-
I
80
i
100
vn
Jr-


FIGURE 14. Recording (traced from original) from program 5 of
the relation between Q and P¡ in a four tube model: effect of
decreasing P$. Curve 1 same as figure 12. Curve 2 -




57
in figure 12. For curve 2, Rpj = Rp2 = Rp^ = Rp^ = 4.0 mmHg-min/ml. P$j ,
PS2> PS3 anc* p$4 have values of 5, 10, 15 and 20 mmHg respectively. In
figure 14 the slope of the straight line portion of curve 2 is the same
as that of curve 1; however, the intercept has decreased. Therefore,
changing the P$ values alone changes only the intercept of the straight
line portion of the pressure:flow curve and not the slope.
The question has sometimes arisen as to whether a pressure:flow
curve may have less of a slope (increased resistance) than another in
a family of curves and simultaneously have a lower intercept than the
curve with a lower resistance. Figure 15 shows that this situation is
indeed possible from program 5. For curve 1 in this figure, Rp] = Rp£ =
Rp^ = Rp/j = 1.0 mmHg-min/ml and Ps 1 = 5, PS2 = 1 PS3 = 15, Ps4 = 20
mmHg. Curve 2 has the same values for Ps as curve 1, but in curve 2,
Rpj = 1.0, Rp2 = 2.0, Rp^ = 3-0 and Rp/j = 4.0 mmHg-min/ml. In this
instance curve 2, which has a higher resistance than curve 1, has an
intercept which is less than curve 1.
Physical Model
P¡ Versus PG
Figure 16 illustrates an X-Y recording of the relationship between
P¡ and P0 in a one tube physical model set up as indicated in figure 2.
In figure 16 the glass tubes simulating both Rp and Rd had a resistance
of 0.110 mmHg-min/ml. The depth of water in the box produced a pressure
surrounding the Starling resistor of 10 mmHg. The three curves in figure
16 were drawn on the X-Y recorder at constant flow rates of 0, ~Jb and
111 ml/min. The PQ at the breakpoint on the curve drawn at 0 ml/min
(P0^) should be a measure of P$, and as can be seen in the figure, is
very close to 10 mmHg, which was the pressure produced by the depth of


FIGURE 15. Recording.(traced from original) from program 5 of
the relation between Q. and P¡ in a four tube model: crossing of
the intercept. Curve 1 Rp^ = Rp£ = RP3 = Rpzj = 1.0 mmHg-min/ml,
PSl = 5.0 mmHg, P^ = 10 mmHg, Pg? = 15 mmHg, Ps<4 = 20 mmHg.
Curve 2 Rp^ = 1.0 mmHgTnin/ml, Rp2 = 2.0 mmHg-min/ml,
RP3 = 3.0 mmHgTnin/ml, Rp^ = 4.0 mmHgTnin/ml, P$ values same as
curve 1


so
60
c
E
O
40
20
0.
CURVE I
CURVE 2
40
R
-
0
T-
20
1 1 1 1 1 vn
60 80 ¡00 ^
(mm.Hg.)


60
water in the plexigls box. As in the mathematical model the pressure
drop across the distal resistance is given by PQ^ PGg (or P$ Pob)
for each flow rate. The pressure drop across the proximal resistance
is given by P¡ P0^ (or P¡ P$), where P¡ is the inflow pressure in
the system when the system is in condition 2. Therefore,in figure 16
the pressure drop across the distal resistance at a flow of ]h ml/min
is 6.6 mmHg. The pressure drop across the proximal resistance is jf.h
mmHg.
The effects of increasing Ps upon this relationship are shown
in figure 17- To increase Ps more water was added to the plexigls
chamber until a depth producing a Ps of 15 mmHg was achieved. Rp and
Rp were kept the same as in the previous figure. As noted in the
figure, the pressure drop across the distal resistance at a flow of
~]b ml/min is still 6.7 mmHg and the pressure drop across the proximal
resistance is still 7-3 mmHg. However, the breakpoint for each curve
has been shifted to the right by 5 mmHg when compared to figure 16.
Also the P¡ during condition 2 for each curve has increased 5 mmHg.
By increasing Rp and maintaining Pg at 10 mmHg the curves pre
sented in figure 18 were obtained. In this figure Rp was equal to
0.216 mmHg*min/ml and Ps was held at 10 mmHg as in figure 16. In
figure 18 the breakpoint for each curve occurs at the same point as
in figure 16 and the pressure drop across the distal resistance at a
flow of ~¡k ml/min is still 6.6 mmHg as in figure 16. However, the P¡
during condition 2 for the curve drawn at a flow of 7^ ml/min has
increased by 9.6 mmHg and the pressure drop across the proximal resis
tance has increased to 16.8 mmHg.
The pressure drops across the proximal and distal resistances


FIGURE 16. Recording from the one tube physical model of the
relation between P¡ and PD. Rp = 0.110 mmHg-min/ml, Rp = 0.110
mmHg-min/ml, P$ = 10 mmHg


(mm.Hg.)
62
50i
40
30
Ql~
20
10
Q = 0 ml/rnin
.. P03
< t
~20 To pQ o (mm.Hg.) io 20
1


FIGURE 17. Recording from the one tube physical model of the
relation between P¡ and PQ: effect of increasing Pg.
Rp = 0.110 mmHg*min/ml, R^ = 0.110 mmHg-min/ml, P$ = 15 mmHg


C&Hwuj)
GO
40
*03
'A
i
20
r
-20
-10
T
0
(mm.Hg.)
i
10


FIGURE 18. Recording from the one tube physical model of the
relation between P¡ and PQ: effect of Increasing Rp.
Rp = 0.216 mmHg-mln/ml, Rp = 0.110 mmHg-min/ml, Ps = 10 mmHg


(mm.Hg.)
66


67
obtained from these curves can be used to calculate proximal and distal
resistance simply by dividing them by the flow rate for each curve.
This was done and the values obtained were compared to the previously
calibrated resistance values fQr the glass tubes used to simulate
proximal and distal resistance. The results of this comparison are
displayed in figure 19- The bars labelled C in this figure depict the
calibrated resistances for the three small bore glass tubes used in
this study. The bars labelled P for tubes 1, 2 and 3 indicate the
resistance of these tubes calculated according to the method just
described when each of these tubes was placed in the proximal position
in the model. The bars labelled D are the resistances calculated for
these tubes when they were placed in the distal position. These data
show that there is no significant difference between the known resis
tances of tubes 1, 2 and 3 and the resistances calculated according to
the method just described when the tubes were placed in either the
proximal or distal position in the model.
The relationship between P¡ and PQ in a physical model with three
tubes in parallel is exhibited in figure 20. In these curves Rpj = Rp£
Rp^ = .162 mmHg*min/ml, Rp = .110 mmHg.min/ml and P$] = 6.5, PS2 = 150
mmHg. One curve was drawn at zero flow and another curve was drawn
at a flow rate of 112 ml/min. As shown in the figure there is only one
breakpoint on the curve drawn at zero flow. For the curve drawn at
112 ml/min there are three breakpoints as indicated by the arrows.
Howeyer, the small difference in the slopes of the portions of the
curve between the breaks makes it difficult to visualize the precise
breakpoints. Therefore, a physical model with only two parallel tubes
was used to observe this relationship. The results of this system are


FIGURE 19* Comparison of calibrated resistances of glass tubes
used in the physical model to the resistances calculated while
the tubes were in the proximal or distal position


C Calibrated Resistance
0.2. p Calculated in Proximal Position1
D Calculated in Distal Position
£

re
in
o
s
<
h
(£j
C£
0.!-
0.
TUB!
nh
p
j
TUBE
f
H3>.51
P>.9
P>.2
2
TUTE
5
CN
VO


FIGURE 20. Recording from the three tube physical model of the
relation between P¡ and PQ. Rp^ = Rp£ = Rp^ = 0.162 mmHg-min/ml,
Rd = 0.110 mmHg*min/ml Ps] = 6.5 mmilg, P$2 = 10 mmHg, P$, =
15 mmHg


(mm.Hg.)
71


72
shown in figure 21. For this figure Rpj = Rp2 = 0.162 mmHg-min/ml,
RD = 0.110 mmHg-min/ml, PS] = 10 mmHg and P$2 = 15 mmHg. Curves were
drawn at flows of 0, 40, 110 and 1^2 ml/min. These flow rates were
high enough so that flow was occurring through both tubes at all times.
For the curve drawn at zero flow there is only one breakpoint as pre
dicted by the mathematical model. For each of the other curves there
are two distinct breakpoints, indicated on the curve drawn at A0 ml/min
by the arrows labelled A and B. According to the mathematical model
flow, up to point A, is occurring according to condition 2 in both tubes.
Between point A and point B flow is occurring according to condition 3
(P¡ > P$i < P0) in tube 1, but still according to condition 2 in tube 2
(P¡ > P$2 > P0')- Beyond point B flow is occurring according to condi
tion 3 in both tubes. Also, as predicted by the mathematical model
(figure 9) a line drawn through the first breakpoint of each curve
(indicated by the dashed line on figure 21) does not intersect the
breakpoint of the curve drawn at zero flow.
To investigate the relation between P¡ and PQ in a multitube model
when flow was taking place through only a partial number of tubes, the
three-tube physical model was again employed. As in the mathematical
model this relation was studied only in condition 2: states 1 (P01
PS 1 < PS2 < pS3 < PSA) and 2 (pSl < po < PS2 < PS3 < PS0 in order to
determine the position of the first breakpoint for each curve. Figure
22 demonstrates this relationship. In this figure Rpj = Rp2 = RP3 =
0.216 mmHg-min/ml and Rp = 0.110 mmHg-min/ml. The depth of water in
each box simulated surrounding pressures of P$] = 6 mmHg, P$2 = 10 mmHg
and Ps^ = 1^-2 mmHg. Curves were drawn at 0, 15, 52, 105, 118 and 133
ml/min. As indicated by the dashed line, the breakpoint for the curves


FIGURE 21. Recording from the two tube physical model of the
relation between P¡ and P0: flow occurring in all tubes.
Rpi = Rp2 = 0.162 mmHg*min/ml, Rg = 0.110 mmHg-min/ml,
P51 = 10 mmHg, P$2 = 15 mmHg


I
01 (&HWUJ) 0 d 0I_
-J __ I L_
-ov
L09
H
(tHUJUU)


FIGURE 22. Recording from the three tube physical model of the
relation between P¡ and PG: flow occurring in a partial number
of tubes. Rp | = Rp2 = Rp-3 0.216 mmHg-min/ml, Rp = 0.110
mmHg-min/ml, Ps] = 6.0 mmHg, P$2 = 10 mmHg, Ps^ = 1^.2 mmHg


(mm.Hg.)
76


77
drawn at 105, 118 and 133 ml/min (points A, B and C) can be connected
by a straight line. Howeyer, this line does not intersect the break
point of any of the remaining three curves. Neither can a straight
line be drawn through points D, E and F. Thi_ is exactly what was
predicted by the mathematical model in figure 10.
Pj Versus Q
The relationship between Q and P¡ in a one tube physical model is
shown on figure 23. In this instance Rp = 0.110 mmHg-min/ml and Rd =
0.216 mmHg*min/ml. The water depth in the box simulated a Ps of 10.3
mmHg. Throughout the drawing of the curve P0 was held at 0 mmHg. As
the curve indicates there is no flow until P¡ becomes greater than PS,
after which flow occurs in a linear relationship with P¡ up to point A.
On this portion of the curve, the reciprocal of the slope of the line is
0.111 mmHgmin/ml, which corresponds very well to the resistance of the
glass tube used in the proximal position. This indicates that flow is
occurring in accordance with condition 2 as predicted by the mathematical
model. Beyond point A the reciprocal of the slope of the line is 0.308
mmHg"min/ml, which agrees well with the sum of Rp and Rp, or total
resistance. This indicates that point A is the flow at which P0'
becomes greater than Ps and that beyond point A flow occurs according
to condition 3 as predicted by the mathematical model. In the following
figures the relation between P¡ and Q will be studied only in conditions
1 and 2.
Figure 2h illustrates the effect on the pressure.-flow curve of
increasing Rp. In curve 1, Rp = 0.110 mmHg*min/ml, Rp = 0.110 mmHg*min/
ml and Ps = 10.3 mmHg. In curve 2, Rp = 0.216 mmHg-min/ml and Rp and
PS were the same as in curve 1. The P¡ at which flow begins to occur


FIGURE 23. Recording from the one tube physical model of the
relation between Q. and P¡. Rp = 0.110 mmHgmin/ml, Rq =
0.216 mmHgmin/ml, Pg = 10.3 mmHg


S3 02 (frH'WW) gi 'd 01 5 0
a
(ml/min)


FIGURE 2b. Recording from the one tube physical model of the
relation between Q and P¡: effect of increasing Rp.
Curve 1 Rp = 0.110 mmHg-min/ml, Rg = o.llO mmHg-min/ml,
PS = 10.3 mmHg. Curve 2 Rp = 0.216 mmHg-min/ml, Rq =
0.110 mmHg-min/ml, P5 = 10.3 mmHg


(ml/m¡n)
81


82
is the same for both curves; however, the slope for curve 2 is less
than the slope of curve 1 as predicted by the mathematical model.
Figure 25 presents the effects on the pressure:flow relationship of
increasing only Ps. For both curves 1 and 2, Rp = 0.110 mmHg.min/ml
and Rp = 0.110 mmHg.min/ml. In curve 1, Ps 10.3 mmHg, but in curve 2
Ps = 15.^ mmHg. PD was held at 0 mmHg for both curves. As shown by
the figure, no flow occurred in curve 1 until P¡ became greater than
10.3 mmHg. In curve 2 no flow occurred until P¡ became greater than
15-^ mmHg. However, the slope of both curves is the same after flow
has begun to take place. The behavior of the physical model in this
case is again in accordance with that predicted by the mathematical
model.
The three-tube physical model was used to investigate the relation
ship between Q, and P¡ in a multiple tube system. This relationship is
illustrated in figure 26. For curve 1, the model was arranged so that
Rpj = 0.^36 mmHg.min/ml, Rp2 = 0.162 mmHg-min/ml and Rp^ = 0.110 mmHg.
min/ml. The water level in each box was adjusted so that Ps] = 7-8
mmHg, PS2 = 10.0 mmHg and Ps^ = 12.9 mmHg. Rp was 0.110 mmHg.min/ml
and P0 was held at -5 mmHg throughout the construction of the curve.
Curve 1 exhibits three definite breakpoints as indicated by the arrows
labelled A, B and C. Up to point A no flow occurred. As P¡ increased
beyond point A flow began to occur through tube 1 and between points
A and B flow occurred only through tube 1. At point B flow began to
occur through tube 2 and between points B and C flow was occurring
through tubes 1 and 2. Beyond point C flow was taking place through
all three tubes. As can be seen, the Pj at which flow begins to
occur in each tube corresponds very well with the Ps for each tube.


FIGURE 25. Recording from the one tube physical model of the
relation between Q and P¡: effect of increasing P$.
Curve 1 Rp = 0.110 mmHg-min/ml, Rp = 0.110 mmHg-min/ml,
PS = 10.3 mmHg. Curve 2 Rp = 0.110 mmHg'min/ml, Rp =
0.110 mmHg'min/ml, P$ = 15-^ mmHg




FIGURE 26. Recording from the three tube physical model of the
relation between Q and P¡: effect of increasing Rp.
Curve 1 Rpj = O.A36 mmHg-min/ml, RP2 = 0.162 mmHg-min/ml,
Rp^ = 0.110 mmHg-min/ml, Rp = 0.110 mmHg-min/ml, P$ 1 = 7-8 mmHg,
PS2 = 10 mmHg, P$3 = 12.9 mmHg. Curve 2 Rp| = O.M36
mmHg-min/ml, Rp2 = 0.32^ mmHg-min/ml, Rpo = 0.272 mmHg-min/ml,
Rp = 0.110 mmHg-min/ml, P$, = 7-8 mmHg, P$2 = 10 mmHg,
PS3 = 12.9 mmHg


(ml/rnin)
86


87
Also shown in this figure is the intercept of that portion of curve 1
beyond point C (the straight line portion), indicated by the dashed
line.
Curve 2 in figure 26 indicates the effects of increasing Rp on
the relation between Q and P¡. For curve 2 the values for Ps and Rg
were the same as for curve 1. PG was held constant at -5 mmHg during
the construction of curve 2. However, for curve 2, Rpj = 0.436 mmHg.
min/ml, Rp2 = 0.324 mmHg*min/ml and Rp^ = 0.272 mmHgmin/nil. There
are three distinct breaks on curve 2, each of which occurs at the same
value of P¡ as on curve 1. However, the slope of the straight line
portion of curve 2 is less than that of curve 1. Also the intercept
of curve 2, indicated by the dotted line, is different from that of
curve 1. This figure also affords an example of the phenomenon shown
in figure 15. That is, curve 2 has a greater Rp than curve 1, but also
has a lower intercept.
Figure 27 points out the results of increasing Ps on the pressure:
flow curve. For both curve 1 and 2, Rpj = 0.436 mmHg.min/ml, Rp2 =
0.324 mmHg.min/ml and Rp^ = 0.272 mmHg.min/ml. In each case Rg -
0.110 rnmHg-min/ml and PD was held constant at -5 mmHg throughout the
procedure. For curve 1, the model was arranged so that Ps] = 7.8 mmHg,
PS2 = 10.0 mmHg and P$-j = 12.9 mmHg. For curve 2, Ps] = 10.0 mmHg,
PS2 = 12.9 mmHg and P$3 = 15.0 mmHg. As indicated by the arrows there
are three breakpoints on each curve which correspond to the three Ps
yalues for each curve. The intercept of the straight line portion
(indicated by the dashed line for both curves) of curve 2 is higher
than the intercept of curve 1, but the slope of both curves is the
same. Thus the physical model behaves in the manner predicted by the
/


FIGURE 27. Recording from the three tube physical model of the
relation between $ and P¡:( effect of increasing P$.
Curve 1 same as curve 2 in figure 26. Curve 2 -
Rpj = 0.^36 mmHg*min/ml, Rp£ = 0.324 mmilg-min/ml,
Rp^ = 0.272 mmHg-min/ml, Rg = 0.110 mmHg*min/ml, Psj = 10 mmHg,
P$2 = 12.9 mmHg, PS3 = 15 mmHg
/


(ml/min)
89
I50t
100


Full Text

PAGE 1

3XOPRQDU\ 9DVFXODU 5HVLVWDQFH LQ )HWDO DQG 1HRQDWDO *RDWV E\ 5D\PRQG 'ZLJKW *LOEHUW a $ ',66(57$7,21 35(6(17(' 72 7+( *5$'8$7( &281&,/ 2) 7+( 81,9(56,7< 2) )/25,'$ ,1 3$57,$/ )8/),//0(17 2) 7+( 5(48,5(0(176 )25 7+( '(*5(( 2) '2&725 2) 3+,/2623+< 81,9(56,7< 2) )/25,'$

PAGE 2

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

PAGE 3

7$%/( 2) &217(176 3DJH $&.12:/('*(0(176 L L /,67 2) 7$%/(6 Y /,67 2) ),*85(6 YL $%675$&7 O[ ,1752'8&7,21 0$7(5,$/6 $1' 0(7+2'6 0DWKHPDWLFDO 0RGHO 3c 9HUVXV 3D 3c 9HUVXV 4 3K\VLFDO 0RGHO 3c 9HUVXV 34 3c 9HUVXV 4 $QLPDOV )HWXVHV 1HRQDWHV 5(68/76 0DWKHPDWLFDO 0RGHO 3c 9HUVXV 34 3M 9HUVXV 4a 3K\VLFDO 0RGHO 3c 9HUVXV 34 3c 9HUVXV 4 $QLPDOV )HWXVHV 1HRQDWHV ',6&866,21 0DWKHPDWLFDO DQG 3K\VLFDO 0RGHO 3M 9HUVXV 34 3c 9HUVXV 4 $QLPDOV 6800$5< $1' &21&/86,216 LLL

PAGE 4

$33(1',; $33(1',; %,%/,2*5$3+< 9,7$ LY

PAGE 5

/,67 2) 7$%/(6 7DEOH 3DJH 3f! A& DQFn 3+ nQ SXOPRQDU\ DUWHULDO EORRG LQ IHWDO DQLPDOV ,Q ZKLFK ERWK OXQJV ZHUH XQYHQWLODWHG YHQWLODWHG ZLWK IHWDO JDV DQG YHQWLODWHG ZLWK DLU 3! 3& DQFr S+ nQ SXOPRQDU\ DUWHULDO DQG YHQRXV EORRG LQ IHWDO DQLPDOV LQ ZKLFK ERWK OXQJV ZHUH XQYHQWLODWHG ULJKW OXQJ RQO\ YHQWLODWHG ZLWK IHWDO JDV DQG ULJKW OXQJ RQO\ YHQWLODWHG ZLWK DLU n 3R} A& DQFr 3+ nQ 3XOPRQDU\ DUWHULDO DQG YHQRXV EORRG RI IHWDO DQLPDOV EHIRUH GXULQJ DQG DIWHU LQIXVLRQ RI EUDG\NLQLQ 3} 3&2 DQO 3+ nQ OAr SXOPRQDU\ DUWHULDO DQG YHQRXV EORRG RI QHZO\ YHQWLODWHG DQLPDOV EHIRUH GXULQJ DQG DIWHU LQIXVLRQ RI EUDG\NLQLQ 3! 3& DQFr 3+ nQ OHIW SXOPRQDU\ DUWHULDO EORRG RI QHZERUQ DQLPDOV LQ ZKLFK ERWK OXQJV ZHUH YHQWLODWHG ZLWK DLU b DQG b 2 A 'DWD IURP IHWXVHV LQ WKH XQYHQWLODWHG IHWDO VWDWH )f GXULQJ YHQWLODWLRQ RI ERWK OXQJV ZLWK IHWDO JDV 9)*f DQG ZLWK DLU 9$f 'DWD IURP DQLPDO IURP WDEOH 'DWD IURP YHQWLODWHG DQLPDOV EHIRUH %f GXULQJ 'f DQG DIWHU $f LQIXVLRQ RI EUDG\NLQLQ 'DWD IURP DQLPDO IURP WDEOH 9

PAGE 6

/,67 2) ),*85(6 )LJXUH 3DJH 'LDJUDP RI D RQH WXEH PRGHO FRQWDLQLQJ D 6WDUOLQJ UHVLVn WRU DUUDQJHG WR SURYLGH D FRQVWDQW LQIORZ SUHVVXUH 'LDJUDP RI D RQH WXEH PRGHO FRQWDLQLQJ D 6WDUOLQJ UHVLVn WRU DUUDQJHG WR SURYLGH D FRQVWDQW IORZ OR 5HFRUGLQJ IURP SURJUDP RI WKH UHODWLRQ EHWZHHQ 3SAnf§ DQG 34 LQ D RQH WXEH PRGHO @_ 'LDJUDP RI D IRXU WXEH PRGHO FRQWDLQLQJ D 6WDUOLQJ UHVn LVWRU LQ HDFK WXEH 'LDJUDP RI VXUJLFDO SUHSDUDWLRQ RI DQLPDOV 5HFRUGLQJ RI WKH UHODWLRQ EHWZHHQ SXOPRQDU\ DUWHU\ SUHVVXUH 3$3f DQG SXOPRQDU\ YHQRXV SUHVVXUH 393f LQ DQ XQYHQWLODWHG IHWD DQLPDO 5HFRUGLQJ IURP SURJUDP RI WKH UHODWLRQ EHWZHHQ 3c DQG 34 LQ D RQH WXEH PRGHO HIIHFW RI LQFUHDVLQJ 3 5HFRUGLQJ IURP SURJUDP RI WKH UHODWLRQ EHWZHHQ 3c DQG 3 LQ D RQH WXEH PRGHO HIIHFW RI LQFUHDVLQJ 5S 5HFRUGLQJ IURP SURJUDP RI WKH UHODWLRQ EHWZHHQ 3c DQG 34 LQ D IRXU WXEH PRGHO IORZ RFFXUULQJ LQ DOO WXEHV 5HFRUGLQJ IURP SURJUDP RI WKH UHODWLRQ EHWZHHQ 3c DQG 34 LQ D IRXU WXEH PRGHO IORZ RFFXUULQJ LQ D SDUWLDO QXPEHU RI WXEHV 5HFRUGLQJ IURP SURJUDP RI WKH UHODWLRQ EHWZHHQ 4 DQG 3c LQ D RQH WXEH PRGHO HIIHFW RI GHFUHDVLQJ 5S DQG 3J 5HFRUGLQJ IURP SURJUDP RI WKH UHODWLRQ EHWZHHQ 4 DQG 3c LQ D IRXU WXEH PRGHO 5HFRUGLQJ IURP SURJUDP RI WKH UHODWLRQ EHWZHHQ 4 DQG 3c LQ D IRXU WXEH PRGHO HIIHFW RI GHFUHDVLQJ 5S 9L

PAGE 7

5HFRUGLQJ IURP SURJUDP RI WKH UHODWLRQ EHWZHHQ 4 DQG 3c LQ D IRXU WXEH PRGHO HIIHFW RI GHFUHDVLQJ "6 5HFRUGLQJ IURP SURJUDP RI WKH UHODWLRQ EHWZHHQ 4 DQG 3c LQ D IRXU WXEH PRGHO FURVVLQJ RI WKH LQWHUFHSW 5HFRUGLQJ IURP WKH RQH WXEH SK\VLFDO PRGHO RI WKH UHODWLRQ EHWZHHQ 3c DQG 34 5HFRUGLQJ IURP WKH RQH WXEH SK\VLFDO PRGHO RI WKH UHODWLRQ EHWZHHQ 3c DQG 3' HIIHFW RI LQFUHDVLQJ 36 5HFRUGLQJ IURP WKH RQH WXEH SK\VLFDO PRGHO RI WKH UHODWLRQ EHWZHHQ 3c DQG 34 HIIHFW RI LQFUHDVLQJ 5S &RPSDULVRQ RI FDOLEUDWHG UHVLVWDQFHV RI JODVV WXEHV XVHG LQ WKH SK\VLFDO PRGHO WR WKH UHVLVWDQFHV FDOFXODWHG ZKLOH WKH WXEHV ZHUH LQ WKH SUR[LPDO RU GLVWDO SRVLWLRQ 5HFRUGLQJ IURP WKH WKUHH WXEH SK\VLFDO PRGHO RI WKH UHODWLRQ EHWZHHQ 3c DQG 34 5HFRUGLQJ IURP WKH WZR WXEH SK\VLFDO PRGHO RI WKH UHODWLRQ EHWZHHQ 3c DQG 34 IORZ RFFXUULQJ LQ DOO WXEHV 5HFRUGLQJ IURP WKH WKUHH WXEH SK\VLFDO PRGHO RI WKH UHODWLRQ EHWZHHQ 3c DQG 34 IORZ RFFXUULQJ LQ D SDUWLDO QXPEHU RI WXEHV 5HFRUGLQJ IURP WKH RQH WXEH SK\VLFDO PRGHO RI WKH UHODWLRQ EHWZHHQ 4 DQG 3c 5HFRUGLQJ IURP WKH RQH WXEH SK\VLFDO PRGHO RI WKH UHODWLRQ EHWZHHQ 4 DQG 3c HIIHFW RI LQFUHDVLQJ 5S 5HFRUGLQJ IURP WKH RQH WXEH SK\VLFDO PRGHO RI WKH UHODWLRQ EHWZHHQ 4 DQG 3c HIIHFW RI LQFUHDVLQJ 3 5HFRUGLQJ IURP WKH WKUHH WXEH SK\VLFDO PRGHO RI WKH UHODWLRQ EHWZHHQ 4 DQG 3c HIIHFW RI LQFUHDVLQJ 5S 5HFRUGLQJ IURP WKH WKUHH WXEH SK\VLFDO PRGHO RI WKH UHODWLRQ EHWZHHQ 4 DQG 3c HIIHFW RI LQFUHDVLQJ 3 5HFRUGLQJ RI WKH UHODWLRQ EHWZHHQ 3$3 DQG 393 ,Q D YHQWLODWHG DQLPDO YL L

PAGE 8

&RPSDULVRQ RI SUR[LPDO DQG GLVWDO UHVLVWDQFH DQG VXUURXQGLQJ SUHVVXUH LQ WKH OHIW OXQJ GXULQJ WKH XQYHQWLODWHG IHWDO VWDWH )f GXULQJ YHQWn LODWLRQ RI ERWK OXQJV ZLWK IHWDO JDV 9)*f DQG GXULQJ YHQWLODWLRQ RI ERWK OXQJV ZLWK DLU 9$f 5HODWLRQ EHWZHHQ SUR[LPDO UHVLVWDQFH DQG SXOPRQDU\ DUWHULDO 3 cQ YHQWLODWHG DQLPDOV 5HODWLRQ EHWZHHQ ORJ SUR[LPDO UHVLVWDQFH DQG ORJ SXOPRQDU\ DUWHULDO 3T LQ YHQWLODWHG DQLPDOV 5HODWLRQ EHWZHHQ GLVWDO UHVLVWDQFH DQG SXOPRQDU\ YHQRXV 3 LQ YHQWLODWHG DQLPDOV &RPSDULVRQ RI WRWDO UHVLVWDQFH 7f FDOFXODWHG LQ FRQGLWLRQ WR WKH VXP RI SUR[LPDO DQG GLVWDOA UHVLVWDQFH 3 'f FDOFXODWHG LQ FRQGLWLRQ LQ XQYHQWLODWHG IHWDO DQLPDOV DQLPDOV YHQWLn ODWHG ZLWK IHWDO JDV DQG YHQWLODWHG ZLWK DLU rr &RPSDULVRQ RI SUR[LPDO DQG GLVWDO UHVLVWDQFH DQG VXUURXQGLQJ SUHVVXUH LQ WKH OHIW OXQJ GXULQJ WKH XQYHQWLODWHG IHWDO VWDWH )f GXULQJ YHQWLn ODWLRQ RI WKH ULJKW OXQJ ZLWK IHWDO JDV 9)*f DQG GXULQJ YHQWLODWLRQ RI WKH ULJKW OXQJ ZLWK DLU 9$f 5HODWLRQ EHWZHHQ SUR[LPDO UHVLVWDQFH DQG SXOPRQDU\ DUWHULDO 3 LQ XQYHQWLODWHG DQLPDOV ,OO 5HODWLRQ EHWZHHQ GLVWDO UHVLVWDQFH DQG SXOPRQDU\ YHQRXV 3 LQ XQYHQWLODWHG DQLPDOV r &RPSDULVRQ RI SUR[LPDO DQG GLVWDO UHVLVWDQFH DQG VXUURXQGLQJ SUHVVXUH LQ WKH OHIW OXQJ RI XQYHQWLn ODWHG DQLPDOV EHIRUH %f GXULQJ 'f DQG DIWHU $f LQIXVLRQ RI EUDG\NLQLQ LQWR WKH SXOPRQDU\ DUWHU\ &RPSDULVRQ RI SUR[LPDO DQG GLVWDO UHVLVWDQFH DQG VXUURXQGLQJ SUHVVXUH LQ WKH OHIW OXQJ RI QHZO\ YHQWLODWHG DQLPDOV EHIRUH %f GXULQJ 'f DQG DIWHU $f LQIXVLRQ RI EUDG\NLQLQ LQWR WKH SXOPRQDU\ DUWHU\ &RPSDULVRQ RI SUR[LPDO DQG GLVWDO UHVLVWDQFH DQG VXUURXQGLQJ SUHVVXUH LQ WKH OHIW OXQJ RI QHZERUQ DQLPDOV GXULQJ YHQWLODWLRQ ZLWK DLU $f b 2 LQ 1 f DQG b 2 LQ 1 f \LLL

PAGE 9

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f ZDV FDOFXODWHG DV LQIORZ SUHVVXUH PLQXV WKH SUHVVXUH VXUURXQGLQJ WKH 6WDUOLQJ UHVLVWRU 3Vf GLYLGHG E\ IORZ 'LVWDO UHVLVWDQFH 5Gf ZDV FDOFXODWHG DV VXUURXQGLQJ SUHVVXUH PLQXV RXWn IORZ SUHVVXUH GLYLGHG E\ IORZ 7KLV PHWKRG ZDV XVHG WR DQDO\]H FKDQJHV LQ SXOPRQDU\ YDVFXODU UHVLVWDQFH DIWHU YHQWLODWLRQ RU LQIXVLRQ RI EUDG\ NLQLQ LQ PDWXUH IHWDO JRDWV DQG DIWHU K\SR[LD LQ QHZERUQ JRDWV 'HWHUn PLQDWLRQV RI SUR[LPDO DQG GLVWDO UHVLVWDQFHV ZHUH PDGH IURP PHDVXUHPHQWV RI SXOPRQDU\ DUWHU\ SUHVVXUH DQG SXOPRQDU\ YHQRXV SUHVVXUH ZKLOH SXOPRQDU\ DUWHU\ SUHVVXUH ZDV NHSW FRQVWDQW DQG SXOPRQDU\ YHQRXV SUHVVXUH YDULHG LQ PDWXUH JRDWV YHQWLODWLRQ RI ERWK OXQJV ZLWK D JDV WKDW GLG QRW FKDQJH EORRG JDVHV IHWDO JDVf UHVXOWHG LQ D GHFUHDVH LQ 5S DQG 3V )XUWKHU YHQWLODWLRQ RI ERWK OXQJV ZLWK DLU FDXVHG 5S 5S DQG 3 WR GHFUHDVH 9HQWLODWLRQ RI RQO\ WKH ULJKW OXQJ ZLWK IHWDO JDV GLG QRW UHVXOW LQ DQ\ FKDQJHV LQ 5S 5T RU 3V LQ WKH OHIW OXQJ KRZHYHU YHQWLODWLRQ RI WKH ULJKW OXQJ ZLWK DLU ZDV IROORZHG E\ GHFUHDVHV LQ 5S 5T DQG 3V LQ WKH c;

PAGE 10

OHIW OXQJ ,Q QHZERUQ JRDWV 5S 5J DQG 3V LQFUHDVHG LQ UHVSRQVH WR YHQWLODWLRQ K\SR[LD b cQ 1ff 5S DQG 3V GHFUHDVHG LQ XQYHQWLODWHG IHWXVHV DIWHU ,QIXVLRQ RI EUDG\NOQLQ LQWR WKH SXOPRQDU\ DUWHU\ $IWHU WKH IHWXVHV ZHUH YHQWLODWHG ZLWK DLU EUDG\NLQLQ LQIXVLRQ VWLOO FDXVHG D GHFUHDVH LQ 5S EXW QRW LQ 3V [

PAGE 11

,1752'8&7,21 7KH SXOPRQDU\ FLUFXODWLRQ ZDV VKRZQ WR UHVSRQG WR FKDQJHV LQ EORRG JDVHV ILUVW LQ ZKHQ YRQ (XOHU DQG /LOMHVWUDQG Of GHPRQVWUDWHG WKDW K\SR[LD FDXVHG D ULVH LQ SXOPRQDU\ DUWHU\ SUHVVXUH LQ WKH DGXOW FDW 6XEVHTXHQWO\ LW KDV EHHQ ZHOO FRQILUPHG WKDW WKH SXOPRQDU\ YDVFXODWXUH RI DGXOW OXQJV FRQVWULFWV LQ UHVSRQVH WR GHFUHDVHG 3 ff 7KH DFWLRQ RI WKH GHFUHDVHG 3Re KDV EHHQ VKRZQ WR EH D ORFDO RQH LQ LVRODWHG OXQJ SUHSDUDWLRQV f DV ZHOO DV EHLQJ PHGLDWHG WKURXJK SHULSKHUDO FKHPRUHFHSWRUV f 7KH UHVSRQVH RI IHWDO SXOPRQDU\ YDVFXODWXUH WR K\SR[LD DQG YHQWLODWLRQ LV YHU\ VLPLODU WR WKDW RI DGXOW OXQJV DQG KDV EHHQ UHYLHZHG H[WHQVLYHO\ E\ VHYHUDO DXWKRUV f 9HQWLODWLRQ RI IHWDO OXQJV ZLWK DQ\ JDV FDXVHV D GHFUHDVH LQ SXOn PRQDU\ DUWHU\ SUHVVXUH DQG DQ LQFUHDVH LQ SXOPRQDU\ DUWHU\ IORZ f ,QIODWLRQ RI IHWDO OXQJV ZLWK VDOLQH RU GH[WUDQ FRQWDLQLQJ D ORZ 3 GRHV QRW FDXVH WKH VDPH GHFUHDVH LQ SUHVVXUH DQG LQFUHDVH LQ IORZ EXW UDWKHU UHVXOWV LQ QR FKDQJH RU D GHFUHDVH LQ IORZ f 7KH UHGXFWLRQ RI IHWDO SXOPRQDU\ YDVFXODU UHVLVWDQFH 395f XSRQ YHQWLODWLRQ ZLWK D JDV KDV EHHQ VKRZQ WR EH WKH UHVXOW RI WZR VHSDUDWH FDXVHV f WKH PHFKDQLFDO HYHQWV ZKLFK DFFRPSDQ\ H[SDQVLRQ RI WKH OXQJV ZLWK D JDV DQG f WKH ORFDO HIIHFW RQ WKH SXOPRQDU\ YDVFXODWXUH RI DQ LQFUHDVH LQ 3} RU GHFUHDVH LQ 3& f &DPSEHOO HW DO f KDYH VKRZQ DOVR WKDW FKDQJHV LQ WKH JDV FRPSRVLWLRQ RI EORRG SHUn IXVLQJ XQYHQWLODWHG IHWDO OXQJV ZLOO HOLFLW FKDQJHV LQ 395 7R GDWH QR RQH KDV UHSRUWHG LQ WKH OLWHUDWXUH DQ\ DWWHPSW WR LVRODWH WKH VLWH RI WKHVH FKDQJHV LQ 395 LQ IHWDO OXQJV LQ UHVSRQVH WR YHQWLODWLRQ DQG

PAGE 12

WR FKDQJHV LQ 3 DQG 3&r 'HWHUPLQDWLRQV RI WKH GLVWULEXWLRQ RI YDVFXODU UHVLVWDQFH DQG RI WKH VLWHV VHQVLWLYH WR K\SR[LD DQG K\SHUn FDSQLD KDYH EHHQ PDGH IRU DGXOW OXQJV f +RZHYHU VLPLODU GHWHUPLQDWLRQV KDYH QRW EHHQ PDGH IRU IHWDO RU QHZERUQ OXQJV 7KH HIIHFW RI GUXJV RQ WKH SXOPRQDU\ FLUFXODWLRQ DQG WKHLU UHODWLRQn VKLS WR WKH SXOPRQDU\ YDVFXODU UHVSRQVH WR K\SR[LD KDYH EHHQ VWXGLHG LQ ERWK IHWDO DQG DGXOW DQLPDOV fr 7KH FDWHFKRODPLQHV KDYH EHHQ UHSRUWHG WR FRQVWULFW WKH SXOPRQDU\ YDVFXODWXUH RI IHWDO ODPEV HYHQ ZKHQ JLYHQ LQ VPDOO GRVHV PJNJf f (SLQHSKULQH DOVR FDXVHV YDVFXODU FRQVWULFWLRQ LQ DGXOW OXQJV WKDW KDV EHHQ ORFDOL]HG XVLQJ SXOPRQDU\ DUWHU\ DQG YHLQ ZHGJH SUHVVXUHV WR WKH YHQRXV VHJPHQW RI WKH YDVFXODWXUH f 1RUHSLQHSKULQH LQFUHDVHV SXOPRQDU\ YDVFXODU UHVLVWDQFH LQ ERWK QHRQDWDO DQG DGXOW DQLPDOV Af %DUHU f GHPRQVWUDWHG WKDW QRUHSLQHSKULQH LQFUHDVHG 395 HYHQ LQ FROODSVHG DGXOW OXQJV +\PDQ f FRQFOXGHG WKDW WKH HIIHFW RI QRUHSLQHSKULQH LQ GRJ OXQJV ZDV H[HUWHG RQ DOO YHVVHOV DQG QRW ORFDOL]HG WR RQH VHJPHQW 7KH HIIHFW RI WKH FDWHFKRODPLQHV RQ 395 KDV EHHQ EORFNHG ZLWK SKHQR[\EHQ]DUQLQH SKHQWRODPLQH DQG SURSUDQRORO f 7KH UHVSRQVH RI WKH SXOPRQDU\ YDVFXODWXUH WR K\SR[LD KDV EHHQ VKRZQ E\ VRPH f WR EH DEROLVKHG E\ SKHQR[\EHQ]DUQLQH RU SKHQWRODPLQH KRZHYHU RWKHUV f KDYH LQGLFDWHG WKHVH DJHQWV KDYH QR HIIHFW RQ WKH UHVSRQVH WR K\SR[LD 'HSOHWLRQ RI FDWHFKRODPLQH UHVHUYHV ZLWK UHVHUSLQH RU E\ DGUHQDOHFWRP\ GRHV QRW GHFUHDVH WKH K\SR[LF UHVn SRQVH RI HLWKHU DGXOW RU QHRQDWDO OXQJV f &DVVLQ f VKRZHG WKDW DGUHQDOHFWRP\ GLG QRW DOWHU WKH SXOPRQDU\ FLUFXODWRU\ UHVSRQVH WR DVSK\[LD LQ LPPDWXUH IHWDO ODPEV

PAGE 13

$FHW\OFKROLQH LQLWLDWHV D ODUJH LQFUHDVH LQ EORRG IORZ LQ WKH XQH[SDQGHG OXQJV RI WKH IHWDO ODPE EXW KDV OLWWOH HIIHFW RQ SXOPRQDU\ FLUFXODWLRQ DIWHU YHQWLODWLRQ KDV EHJXQ O$f 6KHSDUG HW DO f VKRZHG WKDW DFHW\OFKROLQH GHFUHDVHG SXOPRQDU\ YDVFXODU UHVLVWDQFH LQ WKH K\SR[LF QHRQDWDO ODPE EXW KDG QR HIIHFW RQ QRQK\SR[LF QHRQDWHV ,Q FRQWUDVW LQ WKH LQWDFW DGXOW GRJ OXQJ DFHW\OFKROLQH KDV EHHQ GHPRQn VWUDWHG WR FRQVWULFW WKH YDVFXODWXUH f +RZHYHU &KX HW DO Af KDV REVHUYHG WKDW DFHW\OFKROLQH GLODWHV WKH SXOPRQDU\ YDVFXODWXUH RI QHZERUQ KXPDQ LQIDQWV 2WKHUV f KDYH VKRZQ WKDW DFHW\OFKROLQH GHFUHDVHVn SXOPRQDU\ YDVFXODU UHVLVWDQFH RI QRUPDO PHQ DQG ZRPHQ DQG LQ LQGLYLGXDOV ZLWK SULPDU\ SXOPRQDU\ K\SHUWHQVLRQ +LVWDPLQH KDV EHHQ VKRZQ WR LQFUHDVH 395 LQ QRUPDO DGXOW OXQJV f DQG LQ FROODSVHG OXQJV f 6RPH HYLGHQFH VXJJHVWV WKLV UHVSRQVH LV ODUJHU LQ WKH YHQRXV VHJPHQW RI WKH YDVFXODWXUH WKDQ LQ WKH DUWHULDO VHJPHQW f %MXUH HW DO f KDV LQGLFDWHG WKDW KLVWDPLQH LQMHFWLRQ UHVXOWV LQ D ODUJH LQFUHDVH LQ SXOPRQDU\ EORRG IORZ f +LVWDPLQH UHOHDVHUV DQG DQWLKLVWDPLQH GUXJV KDYH EHHQ GHPRQn VWUDWHG WR DEROLVK WKH SXOPRQDU\ YDVFXODU SUHVVRU UHVSRQVH WR YHQWLn ODWLRQ K\SR[LD LQ ERWK LVRODWHG DQG LQWDFW DGXOW OXQJV fr %UDG\NLQLQ SURGXFHV D GHFUHDVH LQ 395 LQ LVRODWHG DQG LQWDFW GRJ OXQJV $2 f LQ QRUPDO DGXOW KXPDQ OXQJV f LQ OXQJV RI KXPDQV ZLWK DUWHULDO K\SHUWHQVLRQ SXOPRQDU\ DUWHULDO K\SHUWHQVLRQ DQG HPSK\VHPD f DV ZHOO DV LQ XQYHQWLODWHG IHWDO OXQJV RI WKH ODPE f +RZHYHU +\PDQ $f VXJJHVWHG WKDW EUDG\NLQLQ DFWXDOO\ FDXVHG DQ DFWLYH FRQVWULFWLRQ RI SXOPRQDU\ YLQV ZKLFK ZDV PDVNHG E\ D SDVVL\H GLODWDWLRQ RI WKH DUWHULDO VHJPHQW LQ UHVSRQVH WR WKH LQFUHDVHG FDUGLDF RXWSXW FDXVHG E\ WKH EUDG\NLQLQ %UDG\NLQLQ LV DOVR WKRXJKW E\ VRPH

PAGE 14

f WR EH WKH PHGLDWRU RI WKH GHFUHDVH LQ 395 XSRQ YHQWLODWLRQ RI IHWDO DQLPDOV 1R RQH KDV DWWHPSWHG WR GHPRQVWUDWH WKH VLWHV RI DFWLRQ RI WKHVH GUXJV LQ WKH IHWDO RU QHZERUQ SXOPRQDU\ YDVFXODWXUH 7KHUHIRUH WKH SXUSRVH RI WKH H[SHULPHQWV WR EH SUHVHQWHG KHUH ZDV WR GHWHUPLQH WKH VLWHV RI FKDQJH LQ SXOPRQDU\ YDVFXODWXUH UHVLVWDQFH LQ UHVSRQVH WR Of FKDQJHV LQ WKH 3 DQG 3F WALH EORRG SHUIXVLQJ XQYHQWLODWHG IHWDO OXQJV f WKH PHFKDQLFDO HYHQWV WKDW DFFRPSDQ\ YHQWLODWLRQ RI IHWDO OXQJV f YHQWLODWLRQ RI IHWDO OXQJV ZLWK DLU f K\SR[LD LQ QHZERUQ OXQJV DQG f DQ LQIXVLRQ RI EUDG\NLQLQ LQ IHWDO DQG QHZO\ YHQWLODWHG OXQJV ,W ZDV LPSRVVLEOH WR LQYHVWLJDWH WKH VLWHV RI DFWLRQ RI DOO WKH GUXJV PHQWLRQHG DERYH DW WKH SUHVHQW WLPH 7KHUHIRUH EUDG\NLQLQ ZDV FKRVHQ WR EH VWXGLHG EHFDXVH LW KDV EHHQ VXJJHVWHG DV D SRVVLEOH PHGLDWRU LQ WKH HYHQWV DFFRPSDQ\LQJ YHQWLODWLRQ RI IHWDO OXQJ ,Q RUGHU WR DQDO\]H VHJPHQWDOO\ WKH UHVLVWDQFH LQ WKH SXOPRQDU\ YDVFXODWXUH LW ZDV QHFHVVDU\ WR HPSOR\ D PRGHO RI WKH SXOPRQDU\ FLUFXn ODWLRQ DV GHVFULEHG E\ YDULRXV ZRUNHUV f 7KLV PRGHO LV EDVHG RQ WKH WHQHW WKDW WKH SXOPRQDU\ FLUFXODWLRQ EHKDYHV LQ D PDQQHU VLPLODU WR D V\VWHP RI SDUDOOHO WXEHV FRQWDLQLQJ 6WDUOLQJ UHVLVWRUV $ 6WDUOLQJ UHVLVWRU ZDV ILUVW GHVFULEHG DV D WKLQ ZDOOHG FROODSVLEOH WXEH WUDYHUVLQJ D FKDPEHU LQ ZKLFK WKH SUHVVXUH VXUURXQGLQJ WKH WXEH FDQ EH FRQWUROOHG (YLGHQFH WR VXSSRUW WKLV PRGHO ZDV ILUVW SUHVHQWHG E\ %DQLVWHU DQG 7RUUDQFH LQ f 7KH\ VKRZHG LQ LVRODWHG DGXOW FDW OXQJV WKDW DW D FRQVWDQW LQIORZ SXOPRQDU\ DUWHU\ SUHVVXUH ZDV LQGHSHQGHQW RI SXOn PRQDU\ YHQRXV SUHVVXUH LI SXOPRQDU\ YHQRXV SUHVVXUH ZDV EHORZ WUDFKHDO SUHVVXUH 7KLV ZRUN KDV EHHQ FRQILUPHG E\ RWKHUV f 3HUPXWW HW DO f GHPRQVWUDWHG WKDW DW D FRQVWDQW SXOPRQDU\ DUWHULDO SUHVVXUH

PAGE 15

IORZ LV QRW LQIOXHQFHG E\ FKDQJHV LQ OHIW DWULDO SUHVVXUH LI OHIW DWULDO SUHVVXUH LV EHORZ WUDFKHDO SUHVVXUH 3XOPRQDU\ DUWHULDO SUHVVXUH DW D FRQVWDQW IORZ LV OLQHDUO\ UHODWHG WR WUDFKHDO SUHVVXUH ZLWK D VORSH RI RQH LI WUDFKHDO SUHVVXUH LV DERYH OHIW DWULDO SUHVVXUH rrr :KHQ OHIW DWULDO SUHVVXUH LV ]HUR WKH SUHVVXUH WR ZKLFK SXOPRQDU\ DUWHULDO SUHVVXUH IDOOV ZKHQ IORZ LV VWRSSHG LV HTXDO WR WUDFKHDO SUHVVXUH LI WUDFKHDO SUHVVXUH LV DERYH PP+J ,I WUDFKHDO SUHVVXUH LV OHVV WKDQ PP+J WKH SXOPRQDU\ DUWHULDO SUHVVXUH DW ]HUR IORZ UHPDLQV PP+J UDWKHU WKDQ IDOOLQJ WR ]HUR f 5HFHQWO\ 3HUPXWW HW DO f KDV JLYHQ HYLGHQFH WKDW SXOPRQDU\ FDSLOODULHV DUH LQGLVWHQVLEOH $OVR $EUDKDP DQG &DOGLQL KDYH IRXQG WKDW WKH SXOPRQDU\ EORRG YROXPH LV OLQHDUO\ UHODWHG WR WKH VORSH RI WKH SUHVVXUHIORZ FXUYH VXJJHVWLQJ WR KLP WKDW UHVLVWDQFH LV FRQVWDQW DORQJ WKH VWUDLJKW OLQH SRUWLRQ RI WKH SUHVVXUHIORZ FXUYH f $ QHZ PHWKRG ZLOO EH SUHVHQWHG LQ WKLV SUHVHQW VWXG\ XWLOL]LQJ WKLV FRQFHSW RI WKH SXOPRQDU\ YDUFXODWXUH FRQWDLQLQJ 6WDUOLQJ UHVLVWRUV WKDW DOORZHG UHVLVWDQFH WR EH FDOFXODWHG LQ WZR VHJPHQWV RI WKH SXOn PRQDU\ YDVFXODWXUH 5HVLVWDQFH ZDV FDOFXODWHG LQ WKDW VHJPHQW SUR[LPDO WR WKH 6WDUOLQJ UHVLVWRUV DQG DOVR LQ WKH VHJPHQW GLVWDO WR WKH 6WDUOLQJ UHVLVWRUV 7KH UHVLVWDQFH LQ WKHVH WZR VHJPHQWV ZDV XVHG WKHQ WR GHWHUn PLQH WKH VLWHV RI FKDQJH LQ SXOPRQDU\ YDVFXODU UHVLVWDQFH LQ HDFK RI WKH FRQGLWLRQV PHQWLRQHG SUHYLRXVO\

PAGE 16

0$7(5,$/6 $1' 0(7+2'6 )LJXUH LV D GLDJUDPPDWLF UHSUHVHQWDWLRQ RI WKH EDVLF PRGHO XVHG LQ WKHVH H[SHULPHQWV 7KLV PRGHO KDV EHHQ GHVFULEHG E\ RWKHUV SUHYLRXVO\ Af $ FRQVWDQW LQIORZ SUHVVXUH LV PDLQWDLQHG LQ WKLV PRGHO E\ PHDQV RI D UHVHUYRLU ZKLFK FDQ EH UDLVHG RU ORZHUHG ,QIORZ SUHVVXUH 3Lf IORZ 4f DQG RXWIORZ SUHVVXUH 34f FDQ EH PHDVXUHG DW WKH SRLQWV LQGLFDWHG LQ WKH ILJXUH 7KH 6WDUOLQJ UHVLVWRU LV GLDJUDPPHG DV D FROODSVLEOH WXEH WUDYHUVLQJ D SOH[LJO£V FKDPEHU ILOOHG ZLWK ZDWHU 7KH SUHVVXUH WHQGLQJ WR FORVH WKH 6WDUOLQJ UHVLVWRU 3f LV WKH K\GURVWDWLF SUHVVXUH RI WKH ZDWHU VXUURXQGLQJ WKH 6WDUOLQJ UHVLVWRU 7KH UHVLVWDQFH IURP WKH SRLQW DW ZKLFK 3c LV PHDVXUHG WR WKH HQG RI WKH 6WDUOLQJ UHVLVWRU LV GHVLJQDWHG 5S RU SUR[LPDO UHVLVWDQFH 7KH UHVLVWDQFH IURP WKH HQG RI WKH 6WDUOLQJ UHVLVWRU WR WKH SRLQW DW ZKLFK 34 LV PHDVXUHG LV GHQRWHG E\ 5J RU GLVWDO UHVLVWDQFH 34n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

PAGE 17

),*85( 'LDJUDP RI D RQH WXEH PRGHO FRQWDLQL UHVLVWRU DUUDQJHG WR SURYLGH D FRQVWDQW LQIORZ 4 IORZ 5S SUR[LPDO UHVLVWDQFH 5T GLVWDO 3c LQIORZ SUHVVXUH 34 RXWIORZ SUHVVXUH 34 LPPHGLDWHO\ SUR[LPDO WR GLVWDO UHVLVWDQFH QJ D 6WDUOLQJ SUHVVXUH UHVVWDQFH SUHVVXUH

PAGE 18

RR

PAGE 19

),*85( 'LDJUDP RI D RQH WXEH PRGHO FRQWDLQLQJ D 6WDUOLQJ UHVLVWRU DUUDQJHG WR SURYLGH D FRQVWDQW IORZ 4 IORZ 5S SUR[LPDO UHVLVWDQFH 5T GLVWDO UHVLVWDQFH 3$3 LQIORZ SUHVVXUH 393 RXWIORZ SUHVVXUH 393 SUHVVXUH LPPHGLDWHO\ SUR[LPDO WR GLVWDO UHVLVWDQFH I W

PAGE 20

:$7(5 /(9(/ 4 3$3 393n 6 ),1*(5 3803 -$ 67$5/,1* 5(6,6725

PAGE 21

WKH IROORZLQJ VHWV &RQGLWLRQ &RQGLWLRQ &RQGLWLRQ RI FRQGLWLRQV cI 3L 36 4 LI Sc SV Sn LI 3c 36 Sn 4 3L 3V 53 3" a 3R 5S 5J 7KURXJKRXW WKH VHFWLRQ RQ PHWKRGRORJ\ WKH DERYH FRQGLWLRQV RU HTXLYDOHQW FRQGLWLRQV ZLOO DOZD\V EH UHIHUUHG WR E\ WKH QXPEHUV LQGLFDWHG ,Q FRQGLWLRQ WKH WRWDO UHVLVWDQFH 5M 5S 5Jf RI WKH V\VWHP FDQ EH FDOFXODWHG E\ WKH HTXDWLRQ 5\ f§ _Q FRQGLWLRQ 5S FDQ EH 4 U 3 r f SF FDOFXODWHG IURP WKH HTXDWLRQ 5S f§ UT PD\ EH REWDLQHG LQ VHYn HUDO ZD\V 5S FDQ EH VXEWUDFWHG IURP 5M WR REWDLQ D YDOXH IRU 5J RU LW PD\ EH FDOFXODWHG IURP WKH HTXDWLRQ 5J ,Q RUGHU WR FDOFXODWH 5S DQG 5T LQ YLYR LW LV QHFHVVDU\ WR REWDLQ YDOXHV IRU 3c 3V 3R! 3Rn DQG 4 0HDVXUHV RI 3c 34 DQG 4 DUH HDVLO\ REWDLQDEOH KRZHYHU PHWKRGV KDG WR EH GHYLVHG WR REWDLQ YDOXHV IRU 3 DQG 3n 7KHVH PHWKRGV ZHUH GHULYHG WKURXJK IXUWKHU PDWKHPDWLFDO FRQVLGn HUDWLRQV RI WKH FKDUDFWHULVWLFV RI D V\VWHP VXFK DV WKDW SUHVHQWHG LQ ILJXUHV DQG )RU SXUSRVHV RI FODULW\ WKH VHFWLRQ RQ PHWKRGRORJ\ ZLOO EH GLYLGHG LQWR WKUHH SDUWV 7KH ILUVW SDUW ZLOO GHDO ZLWK WKH WKHRUHWLn FDO DQG PDWKHPDWLFDO DVSHFWV RI WKLV V\VWHP 6HFRQGO\ WKH DSSOLFDWLRQ RI WKHVH PDWKHPDWLFDO DVSHFWV WR D SK\VLFDO PRGHO ZLOO EH FRQVLGHUHG /DVWO\ WKH XVH RI WKHVH FRQFHSWV LQ YLYR WR DQDO\]H VHJPHQWDOO\ SXOPRQDU\ YDVFXODU UHVLVWDQFH ZLOO EH FRYHUHG

PAGE 22

0DWKHPDWLFDO 0RGHO 3c 9HUVXV 34 ,QLWLDOO\ LW ZDV QHFHVVDU\ WR REVHUYH WKH UHODWLRQVKLS EHWZHHQ 3c DQG 3R LQ D V\VWHP VXFK DV WKDW LQGLFDWHG LQ ILJXUH (TXDWLRQV GHVn FULELQJ WKLV V\VWHP ZHUH SURJUDPPHG LQWR D +HZOHWW 3DFNDUG PRGHO $ FDOFXODWRU DQG GHVLUHG UHODWLRQVKLSV ZHUH UHFRUGHG RQ D +HZOHWW 3DFNDUG PRGHO +5 ;< SORWWHU $ SURJUDP ZDV ZULWWHQ WR HYDOXDWH WKLV UHODWLRQn VKLS EDVHG RQ WKH IROORZLQJ UHDVRQLQJ 7KH DFWXDO SURJUDP LV JLYHQ LQ $SSHQGL[ DV SURJUDP *LYHQ 4 LV FRQVWDQW 4LQ 4RXW 3R 45' 3 &RQGLWLRQ LI 4 WKHQ 3c 3V LQ FRQGLWLRQ RU 3c 3n LQ FRQGLWLRQ &RQGLWLRQ LI 3V 3 WKHQ 3c 45S 3V &RQGLWLRQ f LI 3V 3Rn WKHQ 3c 45S 3Rn 7KH SURJUDP ZDV JLYHQ DQ LQLWLDO 34 7KH FDOFXODWRU ZDV SURJUDPPHG WR FDOFXODWH 3n DFFRUGLQJ WR WKH HTXDWLRQ JLYHQ ,W QH[W FRPSDUHG 3R WR WKH JLYHQ 3V FDOFXODWHG WKH DSSURSULDWH 3c DQG SORWWHG 3c DJDLQVW 3R RQ WKH ;< UHFRUGHU 7KH FDOFXODWRU ZDV SURJUDPPHG WR LQFUHDVH 34 E\ D JLYHQ LQWHUYDO DQG H[HFXWH WKH VDPH SURFHGXUH MXVW GHVFULEHG 7KLV F\FOH ZDV UHSHDWHG DXWRPDWLFDOO\ XQWLO WKH GHVLUHG FXUYH ZDV REWDLQHG DQG WKH SURJUDP PDQXDOO\ VWRSSHG 7\SLFDO FXUYHV REWDLQHG IURP WKLV SURJUDP IRU VHYHUDO GLIIHUHQW IORZV DUH VKRZQ LQ ILJXUH 7KHVH FXUYHV DUH WUDFHG IURP WKH RULJLQDO FXUYHV REWDLQHG IURP WKH ;< SORWWHU

PAGE 23

),*85( 5HFRUGLQJ WUDFHG IURP RULJLQDOf IURP SURJUDP RI WKH UHODWLRQ EHWZHHQ 3c DQG 34 LQ D RQH WXEH PRGH@ 5S PP+JYQLQPO 5T PP+JrPLQPO 3V r PP+J

PAGE 24

Q 3c PP+Jf 4} POPLQ 4} POPLQ % 4r POPLQ N PP+Jf

PAGE 25

$FFRUGLQJ WR WKLV PRGHO ZKHQ 4 LV ]HUR 3c 3 LQ FRQGLWLRQ EXW 3c 3n LQ FRQGLWLRQ $W DQ\ FRQVWDQW IORZ RU ]HUR IORZf 3c LV LQGHn SHQGHQW RI 3 DV ORQJ DV 3f LV OHVV WKDQ 3 :KHQHYHU 3f EHFRPHV JUHDWHU WKDQ 3 34 ZLOO LQIOXHQFH 3c LQ D RQH WR RQH UHODWLRQVKLS ,Q RWKHU ZRUGV 3f 3 LV WKH ERXQGDU\ EHWZHHQ FRQGLWLRQ DQG FRQGLWLRQ m $W ]HUR IORZ WKH 34 ZKLFK EHJLQV WR LQIOXHQFH 3c SRLQW $ RQ ILJXUH f LV HTXDO WR 3 VLQFH 3n 34 DW ]HUR IORZ 7KHUHIRUH WKH 34 DW SRLQW $ PD\ EH WDNHQ DV D PHDVXUH RI 3 $W DQ\ FRQVWDQW IORZ 3n LV JUHDWHU WKDQ 34 GXH WR WKH UHVLVWDQFH DORQJ WKH GLVWDO VHJPHQW :KHQ 34 MXVW EHJLQV WR LQIOXHQFH 3c SRLQW % RQ ILJXUH f 3Rn LV HTXDO WR 3 7KHUHn IRUH DW SRLQW % WKH SUHVVXUH GURS DORQJ WKH GLVWDO VHJPHQW LV 3 PLQXV WKH RXWIORZ SUHVVXUH DW SRLQW % 34Jf 'LVWDO UHVLVWDQFH PD\ EH FDOFXn ODWHG DV WKLV SUHVVXUH GURS GLYLGHG E\ IORZ 5S f§A f 7KH 3V XVHG IRU WKLV FDOFXODWLRQ LV WKH YDOXH RI 3 DW SRLQW $ 3Af RQ WKH ]HUR IORZ FXUYH GHVFULEHG DERYH 7KH FRUUHFW HTXDWLRQ IRU FDOFXODWLQJ 5S LV WKHQ 5S 7KLV VDPH YDOXH IRU 3M PD\ EH XVHG WR FDOFXODWH 5S ,I D FRQVWDQW IORZ LV PDLQWDLQHG VXFK WKDW WKH V\VWHP LV LQ FRQGLWLRQ S f B ST 3V 3ff WKHQ 5S f§cf§ $JDLQ WKH FRUUHFW HTXDWLRQ LV DFWXDOO\ 4 US ‘3L SrIW 4 ,W ZDV QHFHVVDU\ WR REVHUYH WKH UHODWLRQVKLS EHWZHHQ 3c DQG 3R LQ D PRGHO FRQVLVWLQJ RI PRUH WKDQ RQH WXEH )LJXUH LV D GLDJUDPPDWLF UHSUHn VHQWDWLRQ RI D V\VWHP FRQWDLQLQJ IRXU WXEHV LQ SDUDOOHO 7KH WXEHV ZHUH QRW VWDFNHG YHUWLFDOO\ EXW ZHUH DOO LQ WKH VDPH KRUL]RQWDO SODQH (DFK WXEH KDV D 6WDUOLQJ UHVLVWRU WUDYHUVLQJ D VHSDUDWH SOH[LJO£V ER[ (DFK

PAGE 26

),*85( 'LDJUDP RI D IRXU WXEH PRGHO FRQWDLQLQJ D 6WDUOLQJ UHVLVWRU LQ HDFK WXEH 4 IORZ 5S SUR[LPDO UHVLVWDQFH 5T GLVWDO UHVLVWDQFH 3 SUHVVXUH VXUURXQGLQJ WKH 6WDUOLQJ UHVLVWRU 3c LQIORZ SUHVVXUH 34 RXWIORZ SUHVVXUH 3n SUHVVXUH LPPHGLDWHO\ SUR[LPDO WR GLVWDO UHVLVWDQFH L ,

PAGE 27

4 SL f3 5 3 53 U"} 8ZPZYD’f§a M::::::S 3_ ;Z$:$YM:Y9:::9S 3" ,Y$9999 09$9::WHS 3" IO:-:9:W Ir' 8 67$5/,1* 5(6,6725

PAGE 28

ER[ PD\ EH ILOOHG ZLWK GLIIHUHQW DPRXQWV RI ZDWHU DQG LQ WKLV PDQQHU IRU HDFK 6WDUOLQJ UHVLVWRU FDQ EH YDULHG LQGHSHQGHQWO\ 5SM GHVLJQDWHV WKH UHVLVWDQFH IURP WKH SRLQW DW ZKLFK 3c LV PHDVXUHG WR WKH HQG RI WKH 6WDUOLQJ UHVLVWRU LQ WXEH 7KH VDPH GHVFULSWLRQ DSSOLHV WR 5Se! 5SM f D 2 DQG 5SS 7KH UHPDLQGHU RI WKH V\PEROV XVHG IRU WKLV PRGHO DUH HTXLYDOHQW WR WKRVH GHVFULEHG IRU ILJXUH $ SURJUDP ZDV ZULWWHQ IRU WKLV PRGHO DFFRUGLQJ WR WKH IROORZLQJ HTXDn WLRQV 7KH DFWXDO SURJUDP LV JLYHQ LQ $SSHQGL[ DV SURJUDP *LYHQ 4 LV FRQVWDQW 4LQ 4O 4 A 4 4RXW Sn 45G 3R 36 3 36 36 DQG DOO DUH FRQVWDQW 5SM 5S 5SM 5S DQG DUH UHSUHVHQWHG E\ 5 &RQGLWLRQ 6WDWH LI 34n 3V@ 3V 36 36,r WKHQ 4@ A 4r 3L 3 T SL aSL A 5 DQG 4 AA 3c VROYLQJ IRU 3M 3 45 36 36 S6A S6 n

PAGE 29

7KLV HTXDWLRQ LV YDOLG RQO\ LI WKH 3c REWDLQHG IURP LW LV JUHDWHU WKDQ 3A WKDW LV LI IORZ LV RFFXUULQJ WKURXJK DOO IRXU WXEHV )RU VLPSOLFLW\ LQ WKLV SURJUDP LW ZDV DVVXPHG WKDW WKH RQO\ WLPH 3c 3V ZDV ZKHQ 7KHUHIRUH LQ WKLV VWDWH DQG WKH IROORZLQJ VWDWHV LI WKH FDOFXODWHG 3c ZDV OHVV WKDQ 3VA} IORZ ZDV DVVXPHG WR EH ]HUR ,Q WKLV VWDWH 3c 36@ ZKHQ 6WDWH LI 3V@ 3n 36 36 S6 WKHQ  /-/,R, }LB 36 W /LBI6O 3L 36/ 5 5 5 5 6ROYLQJ IRU 3M S 5 3S 3V S6 S6 $JDLQ LI WKH FDOFXODWHG 3c LV OHVV WKDQ 3V WKLV HTXDf§ WLRQ LV QRW YDOLG ,Q WKLV VWDWH 3c 3n ZKHQ 6WDWH LI 36@ 36 SRn S6 36 WKHQ 4 W/3Jn "O -9 SL a 36 SL a 36 5 5 5 5 6ROYLQJ IRU 3c B 5 3R 36 36 Sn L ,Q WKLV VWDWH LI WKHQ 3c 3n 6WDWH N LI 3@ 3V 36 3Rn S6 WKHQ W.U ISn 3RO 5 5 5 5 6ROYLQJ IRU 3M

PAGE 30

f B 45 3Rn 3VE Q ,Q WKLV VWDWH LI 4 WKHQ 3 3n &RQGLWLRQ LI 36 L 36 S6 36 3Tn 6ROYLQJ IRU 3c R B 45 A3R S 7KLV HTXDWLRQ LV DOZD\V YDOLG $V LQ SURJUDP WKH FDOFXODWRU ZDV JLYHQ DQ LQLWLDO 34 ZLWK ZKLFK LW FDOFXODWHG 34n DFFRUGLQJ WR WKH JLYHQ HTXDWLRQ ,W WKHQ PDGH WKH DSSURSULDWH FRPSDULVRQV DQG FDOFXODWHG WKH FRUUHFW 3c ZKLFK LW SORWWHG DJDLQVW WKH RULJLQDO 34 7KH SURJUDP ZDV VHW XS VR WKDW WKH FDOFXODWRU LQFUHDVHG 34 E\ D JLYHQ LQWHUYDO DQG FDOFXODWHG D QHZ 3c ZKLFK ZDV SORWWHG DJDLQVW WKH VHFRQG 34 7KLV F\FOH ZDV UHSHDWHG XQWLO WKH SURJUDP ZDUL PDQXDOO\ VWRSSHG /HDGLQJ IURP SURJUDP LW ZDV QHFHVVDU\ WR LQYHVWLJDWH WKH UHODWLRQ VK7S!EHWZHHQ 3c DQG 3R LQ FRQGLWLRQ VWDWHV DQG ZKHQ 4 \HW WKA UHVXOWDQW 3c 3V WKDW LV ZKHQ IORZ ZDV RFFXUULQJ WKURXJK RQO\ D SIIIWULDO QXPEHU RI WKH WXEHV 7KH IROORZLQJ SURJUDP ZDV ZULWWHQ WR LQYHVn WLJDWH WKLV UHODWLRQVKLS 5HIHU WR ILJXUH E IRU QRPHQFODWXUH ,Q WKLV SURJUDP WKH FDOFXODWRU ZDV DOVR JLYHQ DQ LQLWLDO 34 ZLWK ZKLFK LW FDOFXn ODWHG WKH FRUUHFW 3c DQG SORWWHG LW DJDLQVW 34 ,W WKHQ UDLVHG 34 E\ DB JL9HK LQFUHPHQW DQG FDOFXODWHG D QHZ 3c 7KLV F\FOH ZDV UHSHDWHG XQWLO WKH SURJUDP ZDV PDQXDOO\ VWRSSHG 7KLV SURJUDP LV JLYHQ LQ $SSHQGL[ DV

PAGE 31

SURJUDP *LYHQ 4 LV FRQVWDQW 4LQ 4O 4 4 4Lr 4RXW 3Rn 4n5G 3R 36O 36 36 36 &RQGLWLRQ 6WDWH LI 3n 36@ 3V 3V S6} WKHQ 45 36 36 36 3VW LI 3c @ 36I} WKHQ B 45 3VL 36 36 Nc A LI 3c 3VAM WKHQ G 36 S6 n LI 36! WKHQ Sc 45 S6@ 3cM LV YDOLG RQO\ LI IORZ LV RFFXUULQJ WKURXJK DOO IRXU WXEHV ,I WKH JLYHQ IORZ GRHV QRW JHQHUDWH D 3c KJ7HUa WKDQ 3VLM WKHQ WKH 6WDUOLQJ UHVLVWRU LQ WXEH IRXU ZLOO EH FORVHG ,I QR IORZ LV RFFXUULQJ WKURXJK WXEH WKHQ 3L EH YDOLG LI IORZ LV RFFXUULQJ WKURXJK WKH UHn PDLQLQJ WKUHH WXEHV ,I WKH JLYHQ IORZ GRHV QRW JHQHUDWH D 3 KLJKHU WKDQ 36! WKHQ WKH 6WDUOLQJ UHVLVWRU LQ WXEH ZLOO EH FORVHG ,Q WKLV FDVH 3cA ZLOO EH YDOLG LI IORZ LV RFFXUULQJ WKURXJK WKH UHPDLQLQJ WZR WXEHV $JDLQ LI WKH JLYHQ IORZ GRHV QRW JHQHUDWH D 3c KLJKHU WKDQ 36}

PAGE 32

WKHQ QR IORZ ZLOO RFFXU WKURXJK WXEH RU 3cA ZLOO WKHQ EH YDOLG IRU DQ\ IORZ ZKLFK JHQHUDWHV D 3c OHVV WKDQ 3r 7KH VDPH UHDVRQLQJ DSSOLHV WR VWDWH 6WDWH LI 3V@ 3R "6 36 3V=M WKHQ Q B 45 36 3VAL 3VLr SRf 3 n c7 3 369 WKHQ B 45 3V 36 3Rn Y? LI 3c 36} WKHQ B 45 36 3Rn 3 LI 3c 3r WKHQ 3L 45 3f 3 9HUVXV 4 ,W ZDV DOVR LQWHUHVWLQJ WR PH WR VWXG\ WKH UHODWLRQVKLS EHWZHHQ 4 DQG 3c LQ D PRGHO VLPLODU WR WKH RQH SUHVHQWHG LQ ILJXUH 7KHUHIRUH D SURJUDP ZDV ZULWWHQ WR GHVFULEH WKLV UHODWLRQVKLS ,Q WKLV SURJUDP 3\ ZDV WKH FRQWUROOHG YDULDEOH DQG 4 ZDV WKH GHSHQGHQW YDULDEOH 7KH SURn JUDP ZDV GHVLJQHG WR XWLOL]H DQ LQLWLDO JLYHQ 3c WR FDOFXODWH WKH DSSUR f f SULDWH 4 DQG SORW 3c DV D IXQFWLRQ 4 7KH FRPSXWHU ZDV SURJUDPPHG WR LQFUHDVH 3c E\ D JLYHQ LQWHUYDO DQG UHSHDW WKH LQLWLDO SURFHVV 7KLV FRXOG EH UHSHDWHG XQWLO WKH GHVLUHG FXUYH ZDV REWDLQHG 7KH SURJUDP WR FDOFXODWH 4 ZDV EDVHG RQ WKH IROORZLQJ UHODWLRQVKLSV 7KH DFWXDO SURJUDP LV JLYHQ LQ $SSHQGL[ DV SURJUDP *LYHQ 34 LV FRQVWDQW 3n 45 3

PAGE 33

&RQGLWLRQ LI 3c 3 WKHQ 4 &RQGLWLRQ LI 3c 3 3f WKHQ 3" 3 5S &RQGLWLRQ cI 3c 3 3r WKHQ / 3" 3Rn 5S 5T 7KH UHODWLRQVKLS EHWZHHQ IORZ DQG LQIORZ SUHVVXUH ZDV DOVR VWXGLHG LQ D PRGHO FRQWDLQLQJ IRXU WXEHV VXFK DV WKDW SUHVHQWHG LQ ILJXUH $V LQ WKH RQH WXEH PRGHO WKH SURJUDP ZDV GHVLJQHG WR FDOFXODWH 4 IURP D JLYHQ 3c DQG SORW 3c DJDLQVW 4 7KH 3c ZDV WKHQ LQFUHDVHG D JLYHQ LQFUHn PHQW DQG 4 DJDLQ FDOFXODWHG DQG SORWWHG DJDLQVW 3c 7KLV F\FOH ZDV UHn SHDWHG XQWLO WKH GHVLUHG FXUYH ZDV REWDLQHG 7KH FDOFXODWLRQ RI 4 ZDVf§ FDUULHG RXW DFFRUGLQJ WR WKH IROORZLQJ UHODWLRQVKLSV 7KLV SURJUDP LV JLYHQ LQ $SSHQGL[ DV SURJUDP *LYHQ 34 LV FRQVWDQW 3Rn 36 36 36 36 &RQGLWLRQ LI 3c 3@ 36e 36 36 WKHQ 4 &RQGLWLRQ 6WDWH LI 3V@ WKHQ 6WDWH LI 3JM WKHQ 3c 36 S6 36 3M 36 5S 36 3c 36 36  3M 36 3M 36 53 53

PAGE 34

6WDWH LI 3V@ 3 36 3c 36 WKHQ $ SL S6O 3L I6 SM SVL WKHQ 4 5S@ 5S] 5S 6WDWH LI 3VM 3 36 3V 3L WKHQ  3L 36n rc 3L a 3} (O 53O 53 53 5SLr &RQGLWLRQ ZDV QRW LQFOXGHG LQ WKLV SURJUDP IRU WKH VDNH RI VLPn SOLFLW\ 7KHUHIRUH FDUH ZDV WDNHQ VR WKDW 34n QHYHU EHFDPH JUHDWHU WKDQ 36@ GXULQJ WKH FRQVWUXFWLRQ RI WKH FXUYHV IURP WKLV SURJUDP 7KLV SURn JUDP ZDV XVHG WR VWXG\ WKH HIIHFWV RI FKDQJLQJ 3 YDOXHV ZKLOH KROGLQJ 5S YDOXHV FRQVWDQW DQG YLFH YHUVD 7KH UHVXOW RI FKDQJLQJ ERWK 3 DQG 5S YDOXHV VLPXOWDQHRXVO\ ZDV DOVR VWXGLHG 3K\VLFDO 0RGHO 3 9HUVXV 34 ,Q RUGHU WR WHVW WKH PDWKHPDWLFDO PRGHO SUHVHQWHG DERYH DQG DOVR WR GHWHUPLQH LI YDOXHV IRU WKH GHVLUHG SDUDPHWHUV FRXOG EH REWDLQHG DFFXUDWHO\ D SK\VLFDO PRGHO ZDV EXLOW 7R REWDLQ SUHVVXUHIORZ FXUYHV IURP WKH SK\Vn LFDO PRGHO DQ LQIORZ UHVHUYRLU DV GLDJUDPPHG LQ ILJXUH ZDV XWLOL]HG WR PDLQWDLQ D FRQVWDQW LQIORZ SUHVVXUH +RZHYHU LQ RUGHU WR REWDLQ WKH UHODWLRQVKLS EHWZHHQ LQIORZ SUHVVXUH DQG RXWIORZ SUHVVXUH WKH PRGHO ZDV FRQVWUXFWHG DV LQ ILJXUH LQ RUGHU WR PDLQWDLQ D FRQVWDQW LQIORZ UDWH $V LQ WKH PDWKHPDWLFDO PRGHO WKH LQLWLDO PHDVXUHPHQWV ZHUH PDGH LQ D RQH WXEH V\VWHP LQ WKH SK\VLFDO PRGHO ,Q RUGHU WR GHWHUPLQH WKH UHODn WLRQVKLS EHWZHHQ 3c DQG 3' WKH SK\VLFDO PRGHO ZDV DUUDQJHG DV LQGLFDWHG LQ ILJXUH 5S DQG 5J ZHUH VLPXODWHG E\ VPDOO ERUH JODVV WXEHV RI YDUn LRXV OHQJWKV 7KH GLDPHWHU RI WKH 6WDUOLQJ UHVLVWRU ZDV RI VXFK PDJQLn WXGH WKDW LWV FRQWULEXWLRQ WR WRWDO UHVLVWDQFH ZDV QHJOLJLEOH 7KH

PAGE 35

6WDUOLQJ UHVLVWRU ZDV PDGH E\ SODFLQJ WZR SRO\HWK\OHQH VKHHWV WRJHWKHU DQG KHDW VHDOLQJ WZR VWULSV FP DSDUW 7KH WXEH WKXV REWDLQHG ZDV WULPPHG DQG FXW WR WKH GHVLUHG OHQJWK FPf 'XULQJ WKLV SURFHGXUH LQIORZ SUHVVXUH DQG RXWIORZ SUHVVXUH ZHUH PHDVXUHG ZLWK 6WDWKDP PRGHO 3& SUHVVXUH WUDQVGXFHUV )ORZ ZDV PHDVXUHG XWLOL]LQJ D 6WDWKDP PRGHO )74& FDQQXODWLQJ IORZ SUREH DQG D 6WDWKDP PRGHO 0A22O HOHFWURPDJQHWLF IORZPHWHU 3UHVVXUHV DQG IORZV ZHUH UHFRUGHG RQ D *UDVV PRGHO & SRO\n JUDSK ,Q DGGLWLRQ 3c ZDV SORWWHG DJDLQVW 34 GXULQJ WKH SURFHGXUH E\ PHDQV RI D +RXVWRQ PRGHO +5 ;< SORWWHU 6DOLQH ZDV XVHG DV WKH SHLf§ IXVLQJ IOXLG 7KH UHODWLRQVKLS EHWZHHQ 3c DQG 3T DW DQ\ FRQVWDQW IORZ ZDV REWDLQHG LQ WKH IROORZLQJ PDQQHU f WKH RXWIORZ WXEH ZDV ORZHUHG VR WKDW 3n ZDV OHVV WKDQ 3 f D FRQVWDQW IORZ ZDV PDLQWDLQHG E\ WKH ILQJHU SXPS f WKH RXWIORZ WXEH ZDV WKHQ UDLVHG VORZO\ ZKLOH 3c ZDV EHLQJ SORWWHG DJDLQVW 34 RQ WKH ;< UHFRUGHU 7KLV VDPH SURFHGXUH ZDV FDUULHG RXW WR REWDLQ WKH UHODWLRQVKLS EHWZHHQ 3c DQG 34 DW ]HUR IORZn 'XULQJ WKLV FRQGLWLRQ IORZ LQ WKH UHYHUVH GLUHFWLRQ ZDV SUHYHQWHG E\ WKH ILQJHU SXPS ZKLFK RFFOXGHG WKH LQIORZ WXEH $FFRUGLQJ WR WKH PDWKHPDWLFDO PRGHO SUHVHQWHG SUHYLRXVO\ WKH 34 DW WKH EUHDNSRLQW RI WKH FXUYH GUDZQ GXULQJ ]HUR IORZ PD\ EH WDNHQ DV D PHDVXUH RI 3 SRLQW $ RQ ILJXUH f 7KLV ZDV GRQH IRU WKH SK\VLFDO PRGHO DQG WKH YDOXHV REWDLQHG ZHUH XVHG WR FDOFXODWH ERWK 5S DQG 5T 5S ZDV FDOFXODWHG DV SUHYLRXVO\ GHVFULEHG DFFRUGLQJ WR WKH HTXDWLRQ 3 c 3F 5S f§ 7KH 3L XVHG ZDV WKDW SUHVVXUH ZKLFK UHVXOWHG IURP D 4 FRQVWDQW IORZ ZKLOH WKH V\VWHP ZDV LQ FRQGLWLRQ 3V 3nf} 5G ZDV DOVR FDOFXODWHG DV GHVFULEHG LQ WKH PDWKHPDWLFDO PRGHO 7KH 34 DW WKH EUHDNSRLQW RI D FXUYH GUDZQ DW FRQVWDQW IORZ SRLQW % RQ ILJXUH f VXE

PAGE 36

WUDFWHG IURP ZDV XVHG DV WKH SUHVVXUH GURS DORQJ WKH GLVWDO VHJPHQW 3T B S 5>f ZDV WKHQ FDOFXODWHG DV 5J Uf§A 7KH 5S DQG 5J FDOFXODWHG E\ WKLV PHWKRG ZHUH FRPSDUHG WR WKH NQRZQ UHVLVWDQFHV RI WKH VPDOO ERUH JODVV WXEHV ZKLFK VLPXODWHG 5S DQG 5T 7KH UHVLVWDQFHV RI WKH JODVV WXEHV KDG EHHQ FDOLEUDWHG SUHYLRXVO\ E\ PHDVXULQJ WKH SUHVVXUH GURS DFURVV HDFK WXEH DW VHYHUDO PHDVXUHG IORZ UDWHV ,Q RUGHU WR WHVW LI WKH UHODWLRQVKLS EHWZHHQ 3c DQG 34 LQ WKH SK\Vn LFDO PRGHO IROORZHG WKDW SUHGLFWHG E\ WKH PDWKHPDWLFDO PRGHO LQ D V\VWHP ZKLFK FRQWDLQHG PRUH WKDQ RQH WXEH D SK\VLFDO PRGHO ZDV EXLOW ZKLFK FRQn WDLQHG WKUHH WXEHV LQ SDUDOOHO 7KLV V\VWHP LV DQDODJRXV WR WKH RQH SUHn VHQWHG LQ ILJXUH ZLWK WKH H[FHSWLRQ WKDW RQO\ WKUHH WXEHV ZHUH XVHG 7KH 6WDUOLQJ UHVLVWRU LQ HDFK WXEH WUDYHUVHG D VHSDUDWH SOH[LJO£V ER[ LQ RUGHU WKDW WKH SUHVVXUH VXUURXQGLQJ HDFK 6WDUOLQJ UHVLVWRU FRXOG EHf§ YDULHG LQGHSHQGHQWO\ 5S@ 5S DQG 53 ZHUH VLPXODWHG ZLWK VHSDUDWH VPDOO ERUH JODVV WXEHV VR WKDW HDFK FRXOG EH YDULHG LQGHSHQGHQWO\ RI WKH RWKHUV $ FRQVWDQW LQIORZ ZDV SURYLGHG E\ PHDQV RI D ILQJHU SXPS ,Q WKLV PRGHO WKH UHODWLRQVKLS EHWZHHQ 3c DQG 34 ZDV REWDLQHG LQ H[DFWO\ WKH VDPH PDQQHU DV GHVFULEHG IRU WKH RQHWXEH PRGHO 3M 9HUVXV 4 ,Q RUGHU WR GHWHUPLQH SUHVVXUHIORZ FKDUDFWHULVWLFV RI D RQHfWXEH PRGHO WKH PRGHO ZDV DUUDQJHG DV LQ ILJXUH ,QIORZ SUHVVXUH RXWIORZ SUHVVXUH DQG IORZ ZHUH PHDVXUHG DQG UHFRUGHG DV GHVFULEHG SUHYLRXVO\ )ORZ ZDV DOVR PHDVXUHG E\ FROOHFWLQJ WKH RXWIORZ IRU D WLPHG SHULRG 6DOLQH ZDV XVHG DV WKH SHUIXVLQJ IOXLG 5S DQG 5J ZHUH DJDLQ VLPXODWHG LQ WKH PRGHO E\ VPDOO ERUH JODVV WXEHV RI YDULRXV OHQJWKV 7KH GLDPHWHU RI WKH WXEH LQ WKH 6WDUOLQJ UHVLVWRU ZDV RI VXFK PDJQLWXGH WKDW LWV FRQn WULEXWLRQ WR WRWDO UHVLVWDQFH ZDV QHJOLJLEOH

PAGE 37

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£V ER[ ZHUH DOO VWXGLHG LQ WKLV PRGHO 7KH UHODWLRQ EHWZHHQ SUHVVXUH DQG IORZ LQ D PRGHO FRQWDLQLQJ WKUHH WXEHV LQ SDUDOOHO ZDV DOVR VWXGLHG 7KH PRGHO ZDV VHW XS LQ WKH VDPH PDQn QHU DV LW ZDV IRU REWDLQLQJ WKH UHODWLRQ EHWZHHQ 3c DQG 34 7KH RQO\ PRGLILFDWLRQ ZDV WKDW D FRQVWDQW LQIORZ SUHVVXUH ZDV SURYLGHG E\ PHDQV RI DQ LQIORZ UHVHUYRLU 3UHVVXUHIORZ FXUYHV ZHUH REWDLQHG IURP WKLV PRGHO LQ H[DFWO\ WKH VDPH PDQQHU DV WKDW MXVW GHVFULEHG IRU WKH RQHWXEH PRGHO $QLPDOV )HWXVHV 3UHJQDQW JRDWV ZHUH DQHVWKHWL]HG ZLWK FKORUDORVH PJ.J ,9f DQG VXVWDLQLQJ GRVHV PJ.J ,9f JLYHQ KRXUO\ )HWXVHV A GD\V JHVWDWLRQDO DJHf ZHUH GHOLYHUHG E\ FDHVDUHDQ VHFWLRQ RQWR D ZDUPHG WDEOH DGMDFHQW WR WKH PRWKHU &DUH ZDV WDNHQ WR SUHYHQW WKH IHWXVHV IURP EUHDWK LQJ E\ SODFLQJ D EDJ ILOOHG ZLWK VDOLQH RYHU WKHLU KHDGV &RORQLF WHPSn HUDWXUH ZDV PRQLWRUHG DQG PDLQWDLQHG EHWZHHQ r& &DXWLRQ ZDV WDNHQ

PAGE 38

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f $ FDQQXOD ZDV LQWURGXFHG LQWR WKH YHLQ RI WKH ORZHU OHIW OXQJ OREH YLD WKH OHIW DWULXP DQG EORRG GLUHFWHG LQWR D UHVHUYRLU DV LQGLFDWHG LQ ILJXUH 3XOPRQDU\ YHQRXV SUHVVXUH 393f ZDV YDULHG E\ UDLVLQJ RU ORZn HULQJ WKLV UHVHUYRLU %ORRG ZDV SXPSHG IURP WKH UHVHUYRLU WKURXJK D KHDW H[FKDQJHU LQWR WKH OHIW IHPRUDO DUWHU\ 7KH KHDW H[FKDQJHU FRQVLVWHG RI D VLOLFRQL]HG JODVV FRQGHQVLQJ FRLO RYHU ZKLFK ZDUP ZDWHU UHJXODWHG DW $Or& ZDV FLUFXODWHG $ FDQQXOD ZDV SODFHG LQ WKH OHIW FDURWLG DUWHU\ DQG OHG WKURXJK D ILQJHU SXPS LQWR WKH GLVWDO HQG RI WKH OHIW SXOPRQDU\ DUWHU\ ZKLFK QRZ SHUIXVHG RQO\ WKH OHIW ORZHU OREH RI WKH OXQJ 3XOPRQn DU\ DUWHU\ SUHVVXUH 3$3f DQG SXOPRQDU\ YHQRXV SUHVVXUH ZHUH PHDVXUHG ZLWK 6WDWKDP PRGHO 3& SUHVVXUH WUDQVGXFHUV 3$3 DQG 393 ZHUH FRUUHFWHG IRU WKH SUHVVXUH GURS GXH WR WKH UHVLVWDQFH RI WKH FDQQXODV 3XOPRQDU\ DUWHULDO DQG SXOPRQDU\ YHQRXV EORRG IORZV ZHUH PHDVXUHG ZLWK 6WDWKDP PRGHO )74& FDQQXODWLQJ IORZ SUREHV DQG D 6WDWKDP PRGHO 0$22O HOHFWURn PDJQHWLF IORZPHWHU 6\VWHPLF EORRG SUHVVXUH ZDV PRQLWRUHG E\ PHDQV RI WKH FDQQXOD LQ WKH ULJKW IHPRUDO DUWHU\ 3UHVVXUHV DQG IORZV ZHUH UHFRUGHG RQ D *UDVV PRGHO & SRO\JUDSK

PAGE 39

, ),*85( 'LDJUDP RI VXUJLFDO SUHSDUDWLRQ RI DQLPDOV &$ FDURWLG DUWHU\ %& EUDFKLRFHSKDOLF DUWHU\ $ DRUWD 3$ SXOPRQDU\ DUWHU\ '$ GXFWXV DUWHULRVXV 59 ULJKW YHQWULFOH /9 OHIW YHQWULFOH 8$ XPELOLFDO DUWHU\ 89 XPELOLFDO YHLQ 9& LQIHULRU YHQD FDYD 69& VXSHULRU YHQD FDYD ///9 YHLQ IURP OHIW ORZHU OREH //9 ORZHU OREH RI OHIW OXQJ +// PLGGOH OREH RI OHIW OXQJ 8// XSSHU OREH RI OHIW OXQJ L ,

PAGE 40

),1*(5 3803 +($7 (;&+$1*(5 3/$&(17$

PAGE 41

7KH UHODWLRQVKLS EHWZHHQ 3$3 DQG 393 ZDV REWDLQHG LQ H[DFWO\ WKH VDPH PDQQHU DV LQ WKH SK\VLFDO PRGHO Of WKH RXWIORZ UHVHUYRLU ZDV LQLWLDOO\ ORZHUHG EHORZ WKH OHYHO RI WKH OXQJ f D FRQVWDQW LQIORZ ZDV PDLQWDLQHG DQG f WKH RXWIORZ UHVHUYRLU ZDV VORZO\ UDLVHG ZKLOH 3$3 DQG 393 ZHUH EHLQJ UHFRUGHG RQ WKH *UDVV SRO\JUDSK 6LPXOWDQHRXVO\ 3$3 ZDV SORWWHG DJDLQVW 393 RQ D +RXVWRQ PRGHO +5 ;< SORWWHU &XUYHV IRU ]HUR IORZ ZHUH REWDLQHG VLPSO\ E\ VWRSSLQJ WKH LQIORZ SXPS ZKLFK RFFOXGHG WKH LQIORZ FDQQXOD DQG IROORZLQJ WKH VDPH SURFHGXUH MXVW GHVn FULEHG 1RUPDOO\ IRXU FXUYHV ZHUH GUDZQ RQH DW ]HUR IORZ DQG WKUHHf§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b &2 LQ 1 DQG ZDV WHUPHG WKH IHWDO JDV PL[WXUH $QLPDOV ZHUH YHQWLODWHG ZLWK SRVLn WLYH SUHVVXUH ZLWK D SHDN LQVSL UDWRU\ SUHVVXUH RI &)7+2 7KLV ZDV DFFRPSOLVKHG E\ SODFLQJ D WXEH DWWDFKHG WR D VLGH DUP RI WKH WUDFKHDO FDQQXOD XQGHU D FP FROXPQ RI ZDWHU ([SLUDWRU\ SUHVVXUH ZDV NHSW HTXDO WR DWPRVSKHULF SUHVVXUH 9HQWLODWLRQ LQ HDFK JURXS RI H[SHULPHQWDO

PAGE 42

),*85( 5HFRUGLQJ RI WKH UHODWLRQ EHWZHHQ SXOPRQDU\ DUWHU\ SUHVVXUH 3$3f DQG SXOPRQDU\ YHQRXV SUHVVXUH 393f LQ DQ XQYHQWLODWHG IHWDO DQLPDO

PAGE 43



PAGE 44

DQLPDOV ZDV FDUULHG RXW E\ WKLV PHWKRG $QRWKHU VHW RI FXUYHV ZDV REn WDLQHG ZKLOH WKH DQLPDO ZDV EHLQJ YHQWLODWHG ZLWK WKLV IHWDO JDV PL[WXUH 7KH DQLPDO ZDV WKHQ YHQWLODWHG ZLWK DLU DQG DQRWKHU VHW RI FXUYHV GUDZQ 'XULQJ WKH FRQVWUXFWLRQ RI HDFK VHW RI FXUYHV SXOPRQDU\ DUWHULDO DQG SXOPRQDU\ YHQRXV EORRG VDPSOHV ZHUH GUDZQ DQG DQDO\]HG IRU 3T} 3&2 DQFr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r 3Ar 5HVLVWDQFHV ZHUH FDOFXODWHG DV SUHYLRXVO\ GHVFULEHG 7KH HIIHFWV RI EUDG\NLQLQ RQ SXOPRQDU\ YDVFXODU UHVLVWDQFH ZHUH VWXGLHG RQ D ILQDO JURXS RI IHWXVHV $ VHW RI FXUYHV ZDV REWDLQHG ZKLOH WKH OXQJV RI WKH DQLPDOV ZHUH LQ WKH XQYHQWLODWHG VWDWH %UDG\NLQLQ ZDV WKHQ LQIXVHG LQWR WKH OHIW SXOPRQDU\ DUWHU\ QJPLQf DQG D VHW RI FXUYHV DFTXLUHG 7KH LQIXVLRQ ZDV WKHQ VWRSSHG DQG WKH DQLPDOV DOORZHG WR VWDELL]H DIWHU ZKLFK DQRWKHU VHW RI FXUYHV ZDV GUDZQ 7KH DQLPDOV ZHUH WKHQ YHQWLODWHG ZLWK DLU 7KH HIIHFWV RI EUDG\NLQLQ GXULQJ YHQWL

PAGE 45

ODWLRQ ZLWK DLU ZHUH VWXGLHG LQ WKH VDPH PDQQHU DV LQ WKH XQYHQWLODWHG VWDWH WKDW LV VHWV RI FXUYHV ZHUH FROOHFWHG EHIRUH GXULQJ DQG DIWHU WKH LQIXVLRQ RI EUDG\NLQLQ 3XOPRQDU\ DUWHULDO DQG SXOPRQDU\ YHQRXV 3} 3&2 DUG 30 ZHUH PRQLWRUHG GXULQJ WKH FRQVWUXFWLRQ RI HDFK VHW RI FXUYHV 5HVLVWDQFHV ZHUH FDOFXODWHG DV SUHYLRXVO\ GHVFULEHG 1HRQDWHV 7KH HIIHFWV RI K\SR[LD RQ WKH SXOPRQDU\ FLUFXODWLRQ RI QHRQDWDO NLGV ZDV LQYHVWLJDWHG LQ WKH IROORZLQJ PDQQHU .LGV ZHUH DQHVWKHWL]HG ZLWK FKORUDORVH PJ.J ,9f DQG SODFHG RQ D ZDUPHG WDEOH 6XVWDLQLQJ GRVHV RI FKORUDORVH ZHUH JLYHQ KRXUO\ 7KH QHRQDWDO DQLPDOV ZHUH SUHn SDUHG VXUJLFDOO\ LQ H[DFWO\ WKH VDPH PDQQHU DV WKH IHWDO DQLPDOV DV LQGLFDWHG LQ ILJXUH $IWHU WKH FKHVW ZDV RSHQHG WKH NLGV ZHUH PDLQn WDLQHG RQ SRVLWLYH SUHVVXUH YHQWLODWLRQ ZLWK DLU 7KH UHODWLRQVKLS EHWZHHQ 3$3 DQG 393 ZDV REWDLQHG LQ WKH NLGV LQ WKH VDPH PDQQHU DV LUU WKH IHWDO DQLPDOV 5S DQG 5J ZHUH FDOFXODWHG IURP WKLV UHODWLRQVKLS DV SUHYLRXVO\ GHVFULEHG $IWHU VXUJHU\ ZDV FRPSOHWHG D VHW RI FXUYHV ZDV REWDLQHG ZKLOH WKH NLGV ZHUH EHLQJ YHQWLODWHG ZLWK DLU 7KH DQLPDOV ZHUH WKHQ YHQWLODWHG ZLWK D PL[WXUH RI b 2 LQ 1 DQG DQRWKHU VHW RI FXUYHV REWDLQHG 7KH YHQWLODWLQJ JDV ZDV WKHQ FKDQJHG WR b 2 LQ 1 DQG DQRWKHU VHW RI FXUYHV GUDZQ 3XOPRQDU\ DUWHULDO DQG SXOPRQDU\ YHQRXV EORRG VDPSOHV ZHUH GUDZQ GXULQJ WKH FRQVWUXFWLRQ RI HDFK VHW RI FXUYHV DQG DQDO\]HG IRU 3} 3 DQG S+

PAGE 46

5(68/76 0DWKHPDWLFDO 0RGHO 3c 9HUVXV 34 )LJXUH VKRZV D SORW WUDFHG IURP WKH RULJLQDO RI WKH UHODWLRQ EHWZHHQ 3c DQG 34 LQ D RQHAWXEH PDWKHPDWLFDO PRGHO REWDLQHG IURP SURJUDP ZKHQ 5S PP+JPLQPO 5' PP+JrPLQPO DQG 3V PP+J 7KUHH FXUYHV ZHUH GUDZQ DW IORZV RI DQG POPLQ )RU WKH FXUYH GUDZQ DW POPLQ WKH SUHVVXUH GURS DFURVV WKH GLVWDO UHVLVWDQFH 34? f 3REf rV A PP+J 7KH SUHVVXUH GURS DFURVV WKH SUR[LPDO UHVLVWDQFH 3c 34Af LV PP+J ,QFUHDVLQJ WKH 3V WR PP+J ZKLOH KROGLQJ 5S PP+JPLQPO DQG 5J PP+JrPLQPO ILJXUH f PHUHO\ LQFUHDVHV 3c WKH SUHVVXUH GURSV DFURVV WKH SUR[Ln PDO DQG GLVWDO UHVLVWDQFHV UHPDLQ WKH VDPH )RU WKH FXUYH GUDZQ DW POPLQ WKH SUHVVXUH GURS DFURVV WKH GLVWDO UHVLVWDQFH 34? 3REf LV VWLOO PP+J $OVR WKH SUHVVXUH GURS DFURVV WKH SUR[LPDO UHVLVWDQFH LV VWLOO aPP+J DOWKRXJK 3c LV PP+J KLJKHU 7KH RQO\ RWKHU GLIIHUHQFH QRWHG IURP LQFUHDVLQJ 3V IURP WR PP+J ZDV WKDW WKH EUHDNSRLQW IRU HDFK FXUYH VKLIWHG WR WKH ULJKW )LJXUH UHSUHVHQWV WKH HIIHFWV RI LQFUHDVLQJ 5S IURP WR PP+JPLQPO 5J ZDV KHOG DW PP+JnPLQPO DQG 3V ZDV KHOG DW PP+J ,Q WKLV VLWXDWLRQ WKH SUHVVXUH GURS DFURVV WKH SUR[LPDO UHVLVWDQFH DW D IORZ RI POPLQ GRXEOHG IURP PP+J WR PP+J LQ FRQWUDVW WR WKDW LQ ILJXUH +RZHYHU WKH SUHVVXUH GURS DFURVV WKH GLVWDO UHVLVn WDQFH UHPDLQHG PP+J 7KH EUHDNSRLQW IRU HDFK FXUYH UHPDLQHG WKH VDPH IRU WKH FXUYHV RI HTXDO IORZV LQ ILJXUH ,Q ILJXUHV DQG

PAGE 47

),*85( 5HFRUGLQJ WUDFHG IURP RULJLQDOf IURP SURJUDP RI WKH UHODWLRQ EHWZHHQ 3c DQG 3 ,Q D RQH WXEH PRGHO HIIHFW RI LQFUHDVLQJ 3V 5S PP+JnPLQPO 5>f PP+JrPLQPO 3 PP+J

PAGE 48

L

PAGE 49

),*85( 5HFRUGLQJ WUDFHG IURP RULJLQDOf IURP SURJUDP RI WKH UHODWLRQ EHWZHHQ 3c DQG 34 LQ D RQH WXEH PRGHO HIIHFW RI LQFUHDVLQJ 5S 5S PP+JrPLQPO 5T PP+JrPLQPO 3 PP+J

PAGE 50

4 m POUULQ % A 4rWQIQLQ A SL PP+Jf 4} 4OQLLQ r • T PQ+Jf

PAGE 51

WKH 3 DW WKH EUHDNSRLQW IRU HDFK RI WKH FXUYHV GUDZQ GXULQJ ]HUR IORZ 3Af LV HTXDO WR 3V 7KH UHODWLRQVKLS EHWZHHQ 3c DQG 34 LQ D V\VWHP FRQWDLQLQJ IRXU WXEHV LQ SDUDOOHO SURJUDP f LV VKRZQ LQ ILJXUH 3URJUDP ZDV ZULWWHQ DVVXPLQJ WKDW 5SM 5S 5SA 5SMf WR LQYHVWLJDWH WKH FKDUDFWHULVWLFV RI WKH V\VWHP ZKHQ IORZ ZDV RFFXUULQJ WKURXJK DOO IRXU WXEHV VLPXOWDQHRXVO\ RU ZKHQ QR IORZ ZDV RFFXUULQJ DW DOO 7KH SURJUDP ZDV ZULWWHQ LQ WKLV PDQQHU IRU WKH VDNH RI VLPSOLFLW\ 7KH FKDUDFWHULVWLFV RI WKLV V\VWHP ZKHQ IORZ ZDV RFFXUULQJ WKURXJK D SDUWLDO QXPEHU RI WKH WXEHV ZHUH LQYHVWLJDWHG LQ WKH VXEVHTXHQW SURJUDP SURJUDP fr ,Q ILJXUH 5SM 5S 53 5SA PP+JrPLQP 5' PP+JPLQPO DQG 3V@ 36 } 36 36 PP+J &XUYHV ZHUH GUDZQ DW E2 DQG POPLQ 2Q WKH FXUYH GUDZQ DW ]HUR IORZ WKHUH LV RQH EUHDNSRLQW SRLQW $ RQ ILJXUH f 7KH YDOXH IRU 34 DW WKLV SRLQW LV HTXDO WR WKH ORZHVW 3Vr 2Q HDFK RI WKH RWKHU FXUYHV KRZHYHU WKHUH DUH IRXU GLVWLQFW EUHDNn SRLQWV ,Q WKH FXUYH REWDLQHG DW D IORZ RI E4 POPLQ LQ ILJXUH WKHVH EUHDNSRLQWV DUH PDUNHG E\ WKH OHWWHUV % & DQG ( 7KH SRUWLRQ RI WKLV FXUYH XS WR SRLQW % LQGLFDWHV WKH V\VWHP LV LQ FRQGLWLRQ VWDWH 3R 3V 36 36 3VArf f )URP SRLQW % WR SRLQW & WKH V\VWHP LV LQ FRQGLWLRQ VWDWH 3V 3n 3V S6 )rVf IURP SRLQW & WR SRLQW LW LV LQ FRQGLWLRQ VWDWH 36@ 36 3Rn S6 36f DQG IURP SRLQW WR SRLQW ( WKH V\VWHP LV RSHUDWLQJ LQ DFFRUGDQFH ZLWK FRQGLWLRQ VWDWH E 36@ 36 S6 3n S6Lrf f %H\RQG SRLQW ( WKH V\VWHP LV LQ FRQGLWLRQ 3V 36 S6 S6 SRnfr 83 WR SRLQW % LQ ILJXUH IORZ WKURXJK HDFK RI WKH WXEHV LV RFFXUULQJ LQ DFFRUGDQFH ZLWK FRQGLWLRQ RU WKH ZDWHUIDOO FRQGLWLRQ WKH 3V RI HDFK

PAGE 52

),*85( 5HFRUGLQJ WUDFHG IURP RULJLQDOf IURP SURJUDP RI WKH UHODWLRQ EHWZHHQ 3c DQG 34 LQ D IRXU WXEH PRGHO IORZ RFFXUULQJ LQ DOO WXEHV 5SM 5Se 5S" 5SLr PP+JrPLQPO 5J PP+JrPLQPO 3AM PP+J 3 PP+J 3 PP+J 3MMA PP+J

PAGE 53

PP+Jf £V,22POPLQ A 4 POPLQ 4 POPLQ 4 POPLQ 7 ( PP+Jf 7

PAGE 54

WXEH LV JUHDWHU WKDQ 3ff )URP SRLQW % WR SRLQW & FRQGLWLRQ VWDWH f WXEHV DQG DUH VWLOO LQ WKH ZDWHUIDOO FRQGLWLRQ EXW IORZ WKURXJK WXEH KDV FKDQJHG WR FRQGLWLRQ 3V_ 3Rnfr )URP & WR FRQGLWLRQ VWDWH f WXEHV DQG DUH LQ FRQGLWLRQ EXW WXEH KDV MRLQHG WXEH LQ FRQGLWLRQ )URP SRLQW WR SRLQW ( FRQGLWLRQ VWDWH f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n WDQHRXVO\ RU WKDW IORZ ZDV ]HUR 7KHUHIRUH WKH FRQGLWLRQ ZKHQ IORZ ZDV RFFXUULQJ WKURXJK RQO\ RQH WZR RU WKUHH RI WKH WXEHV ZDV QRW FRQVLGHUHG 3URJUDP ZDV ZULWWHQ WR REVHUYH WKH UHODWLRQ EHWZHHQ 3c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f

PAGE 55

),*85( 5HFRUGLQJ WUDFHG IURP RULJLQDOf IURP SURJUDP RI WKH UHODWLRQ EHWZHHQ 3c DQG 34 LQ D IRXU WXEH PRGHO IORZ RFFXUULQJ LQ D SDUWLDO QXPEHU RI WXEHV 5SM 5Se 53 5SLr PP+JrPLQPO 5S PP+JPLQPO 3VM r PP+J 3 PP+J 3A PP+J 3A PP+J

PAGE 56

r 3c PP+Jf 4 POPLQ 4 PPLQ 4 POPLQ 4 POPLQ 4 POPLQ 4 POPLQ 4 POPOQ L PP+Jf 7

PAGE 57

3c 9HUVXV 4 7KH UHODWLRQVKLS EHWZHHQ 3c DQG 4 IRU D RQHBWXEH PDWKHPDWLFDO PRGHO DV GHVFULEHG LQ ILJXUH LV GLVSOD\HG ,Q ILJXUH 7KH FXUYHV LQ WKLV ILJXUH ZHUH REWDLQHG IURP SURJUDP IRXU )RU FXUYH 5S PP+JPLQ PO 5J PP+JPLQPO DQG 3 PP+J )RU FXUYH 5S PP+Jr PLQPO 5S PP+JrPLQPO DQG 3 PP+J )RU FXUYH 5S PP+JnPPPO 5G PP+JPLQPO DQG 3V PP+J ,Q FXUYH QR IORZ RFFXUUHG XQWLO 3c EHFDPH JUHDWHU WKDQ 3V ZKLFK ZDV HTXDO WR PP+J 8S WR WKLV SRLQW WKH 6WDUOLQJ UHVLVWRU LV FORVHG DQG WKH V\VWHP LV LQ FRQGLWLRQ :KHQ 3c LV KLJKHU WKDQ 3V IORZ RFFXUUHG LQ DFFRUGDQFH ZLWK FRQGLWLRQ 4 a A6f 3RLQW $ 5S PDUNV WKH SRLQW RQ FXUYH WKDW 3f EHFDPH JUHDWHU WKDQ 36 %H\RQG WKLV SRLQW FRQGLWLRQ JRYHUQHG IORZ WKURXJK WKH V\VWHP 4 eB_B,BIef f 5S 5G &XUYH GHPRQVWUDWHV WKH HIIHFW RI LQFUHDVLQJ 3V IURP WR PP+J 2Q FXUYH QR IORZ RFFXUV XQWLO D 3c RI PP+J LV UHDFKHG $OVR WKH IORZ DW ZKLFK WKH V\VWHP FKDQJHV IURP FRQGLWLRQ WR FRQGLWLRQ SRLQW %f KDV LQFUHDVHG EHFDXVH 3n PXVW QRZ LQFUHDVH WR PP+J UDWKHU WKDQ PP+J IRU WKH FKDQJH WR RFFXU 7KH VORSH RI FXUYH GXULQJ FRQGLWLRQV DQG LV WKH VDPH DV WKH VORSH RI FXUYH GXULQJ FRQGLWLRQV DQG &XUYH SUHVHQWV WKH HIIHFWV RI FKDQJLQJ RQO\ 5S 1HLWKHU WKH SUHVVXUH DW ZKLFK IORZ EHJLQV WR RFFXU QRU WKH IORZ DW ZKLFK WKH V\VWHP FKDQJHV IURP FRQGLWLRQ WR FRQGLWLRQ SRLQW &f LV GLIIHUHQW IURP FXUYH +RZHYHU WKH VORSH RI FXUYH GXULQJ FRQGLWLRQV DQG LV JUHDWHU WKDQ WKH VORSH RI FXUYH GXULQJ FRQGLWLRQV DQG r 7KH UHODWLRQVKLS EHWZHHQ 3c DQG 4 LQ D PRGHO FRQWDLQLQJ IRXU WXEHV

PAGE 58

),*85( 5HFRUGLQJ WUDFHG IURP RULJLQDOf IURP SURJUDP N RI WKH UHODWLRQ EHWZHHQ DQG 3c LQ D RQH WXEH PRGHO HIIHFW RI GHFUHDVLQJ 5S DQG 3 &XUYH 5S PP+JnPLQPO 5J PP+JnPLQPO 3 PP+J &XUYH 5S PP+JnPLQPO 5J PP+JnPLQPO 3V PP+J &XUYH 5S PP+JrPLQPO 5J PP+JnPLQPO 3 PP+J

PAGE 59

2 f§L

PAGE 60

LQ SDUDOOHO LV VKRZQ LQ ILJXUH ,Q WKLV ILJXUH WXEH KDV DQ 5SA RI PP+JPLQPO DQG D 3@ RI PP+J WXEH KDV DQ 5S RI PP+JPLQPO DQG D 3 RI PP+J WXEH KDV DQ 5SA RI PP+JPLQPO DQG D 36 RI PP+J DQG WXEH KDV DQ 5SA RI PP+JPLQPO DQG D 3M RI PP+J 7KHUH DUH IRXU GLVWLQFW EUHDNV SRLQWV $ % & DQG 'f RQ WKLV FXUYH 8S WR SRLQW $ 3c KDV QRW H[FHHGHG WKH ORZHVW 3 DQG QR IORZ WDNHV SODFH EHFDXVH DOO WKH 6WDUOLQJ UHVLVWRUV DUH FORVHG %HWZHHQ SRLQWV $ DQG % 3c LV JUHDWHU WKDQ 36@ EXW OHVV WKDQ 36 WKHUHIRUHIORZ LV RFFXUULQJ WKURXJK WXEH RQH RQO\ %HWZHHQ SRLQWV % DQG & 3c LV JUHDWHU WKDQ 3 EXW OHVV WKDQ 3m ,Q WKLV UHJLRQ IORZ LV RFFXUULQJ WKURXJK WXEHV DQG %HWZHHQ SRLQWV & DQG IORZ LV RFFXUULQJ WKURXJK WXEHV DQG EHFDXVH 3c LV JUHDWHU WKDQ 36 EXW OHVV WKDQ 36 %H\RQG SRLQW 3c LV JUHDWHU WKDQ 3VM DQG IORZ LV WDNLQJ SODFH LQ DOO IRXU WXEHV )LJXUH SRLQWV RXW WKH HIIHFWV RI GHFUHDVLQJ SUR[LPDO UHVLVWDQFH ZLWKRXW FKDQJLQJ 3V YDOXHV ,Q WKLV ILJXUH FXUYH LV WKH VDPH DV LQ ILJXUH )RU FXUYH 5S@ 5Se 5SA 5SA PP+JPLQPO DQG 3L 36 36 3V=M PP+J 2Q FXUYH WKHUH DUH DJDLQ IRXU GLVWLQFW EUHDNV DV LQ FXUYH EXW WKH VORSH RI WKH OLQHDU SRUWLRQ RI FXUYH KDV LQFUHDVHG LQ FRPSDULVRQ WR WKH VORSH RI WKH VDPH SRUWLRQ RI FXUYH 2I LQWHUHVW LV WKH IDFW WKDW WKH LQWHUn FHSW RI WKH VWUDLJKW OLQH SRUWLRQ EH\RQG WKH ODVW EUHDNf RI WKH WZR FXUYHV LV GLIIHUHQW 7KHUHIRUH LQ WKLV PRGHO FKDQJLQJ RQO\ UHVLVWDQFH FKDQJHV ERWK WKH VORSH DQG WKH LQWHUFHSW RI WKH VWUDLJKW OLQH SRUWLRQ RI WKH SUHVVXUHIORZ FXUYH )LJXUH GHPRQVWUDWHV WKH HIIHFWV RI GHFUHDVLQJ 3V ZKLOH KROGLQJ 5S FRQVWDQW &XUYH LQ WKLV ILJXUH LV WKH VDPH DV WKH FXUYH SUHVHQWHG

PAGE 61

),*85( 5HFRUGQJWUDFHG IURP RULJLQDOf IURP SURJUDP RI WKH UHODWLRQ EHWZHHQ 4 DQG 3c LQ D IRXU WXEH PRGHO 5S L 5S 5SM 5S PP+JfPLQPO 3V@ PP+J 3 A PP+J 3A PP+J 3VA PP+J

PAGE 62

?

PAGE 63

),*85( 5HFRUG LQJWUDFHG IURP RULJLQDOf IURP SURJUDP RI WKH UHODWLRQ EHWZHHQ 4 DQG 3c LQ D IRXU WXEH PRGHO HIIHFW RI GHFUHDVLQJ 5S &XUYH VDPH DV ILJXUH &XUYH 5S` PP+JnWQLQPO 5Se PP+JPLQPO 5SA PP+JPLQPO 5SM PP+JPLQPO 3 @ PP+J 3Ve PP+J 3V PP+J 3VA PP+J

PAGE 64

f, fL YQ -U

PAGE 65

),*85( 5HFRUGLQJ WUDFHG IURP RULJLQDOf IURP SURJUDP RI WKH UHODWLRQ EHWZHHQ 4 DQG 3c LQ D IRXU WXEH PRGHO HIIHFW RI GHFUHDVLQJ 3 &XUYH VDPH DV ILJXUH &XUYH

PAGE 67

LQ ILJXUH )RU FXUYH 5SM 5S 5SA 5SA PP+JPLQPO 3M 36! 36 DQFr S KDYH YDOXHV RI DQG PP+J UHVSHFWLYHO\ ,Q ILJXUH WKH VORSH RI WKH VWUDLJKW OLQH SRUWLRQ RI FXUYH LV WKH VDPH DV WKDW RI FXUYH KRZHYHU WKH LQWHUFHSW KDV GHFUHDVHG 7KHUHIRUH FKDQJLQJ WKH 3 YDOXHV DORQH FKDQJHV RQO\ WKH LQWHUFHSW RI WKH VWUDLJKW OLQH SRUWLRQ RI WKH SUHVVXUHIORZ FXUYH DQG QRW WKH VORSH 7KH TXHVWLRQ KDV VRPHWLPHV DULVHQ DV WR ZKHWKHU D SUHVVXUHIORZ FXUYH PD\ KDYH OHVV RI D VORSH LQFUHDVHG UHVLVWDQFHf WKDQ DQRWKHU LQ D IDPLO\ RI FXUYHV DQG VLPXOWDQHRXVO\ KDYH D ORZHU LQWHUFHSW WKDQ WKH FXUYH ZLWK D ORZHU UHVLVWDQFH )LJXUH VKRZV WKDW WKLV VLWXDWLRQ LV LQGHHG SRVVLEOH IURP SURJUDP )RU FXUYH LQ WKLV ILJXUH 5S@ 5Se 5SA 5SM PP+JPLQPO DQG 3V 36 r} 36 3V PP+J &XUYH KDV WKH VDPH YDOXHV IRU 3V DV FXUYH EXW LQ FXUYH 5SM 5S 5SA DQG 5SM PP+JPLQPO ,Q WKLV LQVWDQFH FXUYH ZKLFK KDV D KLJKHU UHVLVWDQFH WKDQ FXUYH KDV DQ LQWHUFHSW ZKLFK LV OHVV WKDQ FXUYH 3K\VLFDO 0RGHO 3c 9HUVXV 3* )LJXUH LOOXVWUDWHV DQ ;< UHFRUGLQJ RI WKH UHODWLRQVKLS EHWZHHQ 3c DQG 3 LQ D RQH WXEH SK\VLFDO PRGHO VHW XS DV LQGLFDWHG LQ ILJXUH ,Q ILJXUH WKH JODVV WXEHV VLPXODWLQJ ERWK 5S DQG 5G KDG D UHVLVWDQFH RI PP+JPLQPO 7KH GHSWK RI ZDWHU LQ WKH ER[ SURGXFHG D SUHVVXUH VXUURXQGLQJ WKH 6WDUOLQJ UHVLVWRU RI PP+J 7KH WKUHH FXUYHV LQ ILJXUH ZHUH GUDZQ RQ WKH ;< UHFRUGHU DW FRQVWDQW IORZ UDWHV RI a-E DQG POPLQ 7KH 34 DW WKH EUHDNSRLQW RQ WKH FXUYH GUDZQ DW POPLQ 3Af VKRXOG EH D PHDVXUH RI 3 DQG DV FDQ EH VHHQ LQ WKH ILJXUH LV YHU\ FORVH WR PP+J ZKLFK ZDV WKH SUHVVXUH SURGXFHG E\ WKH GHSWK RI

PAGE 68

),*85( 5HFRUGLQJWUDFHG IURP RULJLQDOf IURP SURJUDP RI WKH UHODWLRQ EHWZHHQ 4 DQG 3c LQ D IRXU WXEH PRGHO FURVVLQJ RI WKH LQWHUFHSW &XUYH 5SA 5Se 53 5S]M PP+JPLQPO 36O PP+J 3A PP+J 3J" PP+J 3V PP+J &XUYH 5SA PP+J7QLQPO 5S PP+JPLQPO 53 PP+J7QLQPO 5SA PP+J7QLQPO 3 YDOXHV VDPH DV FXUYH

PAGE 69

VR F ( ‘2 &859( &859( 5 7 YQ c A PP+Jf

PAGE 70

ZDWHU LQ WKH SOH[LJO£V ER[ $V LQ WKH PDWKHPDWLFDO PRGHO WKH SUHVVXUH GURS DFURVV WKH GLVWDO UHVLVWDQFH LV JLYHQ E\ 34A 3*J RU 3 3REf IRU HDFK IORZ UDWH 7KH SUHVVXUH GURS DFURVV WKH SUR[LPDO UHVLVWDQFH LV JLYHQ E\ 3c 3A RU 3c 3f ZKHUH 3c LV WKH LQIORZ SUHVVXUH LQ WKH V\VWHP ZKHQ WKH V\VWHP LV LQ FRQGLWLRQ 7KHUHIRUHLQ ILJXUH WKH SUHVVXUH GURS DFURVV WKH GLVWDO UHVLVWDQFH DW D IORZ RI @K POPLQ LV PP+J 7KH SUHVVXUH GURS DFURVV WKH SUR[LPDO UHVLVWDQFH LV MIK PP+J 7KH HIIHFWV RI LQFUHDVLQJ 3V XSRQ WKLV UHODWLRQVKLS DUH VKRZQ LQ ILJXUH 7R LQFUHDVH 3V PRUH ZDWHU ZDV DGGHG WR WKH SOH[LJO£V FKDPEHU XQWLO D GHSWK SURGXFLQJ D 3V RI PP+J ZDV DFKLHYHG 5S DQG 5S ZHUH NHSW WKH VDPH DV LQ WKH SUHYLRXV ILJXUH $V QRWHG LQ WKH ILJXUH WKH SUHVVXUH GURS DFURVV WKH GLVWDO UHVLVWDQFH DW D IORZ RI a@E POPLQ LV VWLOO PP+J DQG WKH SUHVVXUH GURS DFURVV WKH SUR[LPDO UHVLVWDQFH LV VWLOO PP+J +RZHYHU WKH EUHDNSRLQW IRU HDFK FXUYH KDV EHHQ VKLIWHG WR WKH ULJKW E\ PP+J ZKHQ FRPSDUHG WR ILJXUH $OVR WKH 3c GXULQJ FRQGLWLRQ IRU HDFK FXUYH KDV LQFUHDVHG PP+J %\ LQFUHDVLQJ 5S DQG PDLQWDLQLQJ 3J DW PP+J WKH FXUYHV SUHn VHQWHG LQ ILJXUH ZHUH REWDLQHG ,Q WKLV ILJXUH 5S ZDV HTXDO WR PP+JrPLQPO DQG 3V ZDV KHOG DW PP+J DV LQ ILJXUH ,Q ILJXUH WKH EUHDNSRLQW IRU HDFK FXUYH RFFXUV DW WKH VDPH SRLQW DV LQ ILJXUH DQG WKH SUHVVXUH GURS DFURVV WKH GLVWDO UHVLVWDQFH DW D IORZ RI acN POPLQ LV VWLOO PP+J DV LQ ILJXUH +RZHYHU WKH 3c GXULQJ FRQGLWLRQ IRU WKH FXUYH GUDZQ DW D IORZ RI A POPLQ KDV LQFUHDVHG E\ PP+J DQG WKH SUHVVXUH GURS DFURVV WKH SUR[LPDO UHVLVn WDQFH KDV LQFUHDVHG WR PP+J 7KH SUHVVXUH GURSV DFURVV WKH SUR[LPDO DQG GLVWDO UHVLVWDQFHV

PAGE 71

),*85( 5HFRUGLQJ IURP WKH RQH WXEH SK\VLFDO PRGHO RI WKH UHODWLRQ EHWZHHQ 3c DQG 3' 5S PP+JPLQPO 5S PP+JPLQPO 3 PP+J

PAGE 72

PP+Jf L 4Oa 4 POUQLQ 3 W a 7R S4 R PP+Jf LR

PAGE 73

),*85( 5HFRUGLQJ IURP WKH RQH WXEH SK\VLFDO PRGHO RI WKH UHODWLRQ EHWZHHQ 3c DQG 34 HIIHFW RI LQFUHDVLQJ 3J 5S PP+JrPLQPO 5A PP+JPLQPO 3 PP+J

PAGE 74

&t+ZXMf *2 r n$ f§Lf§ ff§U 7 PP+Jf L

PAGE 75

),*85( 5HFRUGLQJ IURP WKH RQH WXEH SK\VLFDO PRGHO RI WKH UHODWLRQ EHWZHHQ 3c DQG 34 HIIHFW RI ,QFUHDVLQJ 5S 5S PP+JPOQPO 5S PP+JPLQPO 3V PP+J

PAGE 76

PP+Jf

PAGE 77

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n WDQFHV RI WXEHV DQG DQG WKH UHVLVWDQFHV FDOFXODWHG DFFRUGLQJ WR WKH PHWKRG MXVW GHVFULEHG ZKHQ WKH WXEHV ZHUH SODFHG LQ HLWKHU WKH SUR[LPDO RU GLVWDO SRVLWLRQ LQ WKH PRGHO 7KH UHODWLRQVKLS EHWZHHQ 3c DQG 34 LQ D SK\VLFDO PRGHO ZLWK WKUHH WXEHV LQ SDUDOOHO LV H[KLELWHG LQ ILJXUH ,Q WKHVH FXUYHV 5SM 5Se 5SA PP+JrPLQPO 5S PP+JPLQPO DQG 3@ 36 m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

PAGE 78

),*85( r &RPSDULVRQ RI FDOLEUDWHG UHVLVWDQFHV RI JODVV WXEHV XVHG LQ WKH SK\VLFDO PRGHO WR WKH UHVLVWDQFHV FDOFXODWHG ZKLOH WKH WXEHV ZHUH LQ WKH SUR[LPDO RU GLVWDO SRVLWLRQ

PAGE 79

& f§ &DOLEUDWHG 5HVLVWDQFH r Sf§ &DOFXODWHG LQ 3UR[LPDO 3RVLWLRQ 'f§ &DOFXODWHG LQ 'LVWDO 3RVLWLRQ e UH LQ R V K eM &e 78% QK S M 78%( I +!f§ ‘3! f3! 787( &1 92

PAGE 80

),*85( 5HFRUGLQJ IURP WKH WKUHH WXEH SK\VLFDO PRGHO RI WKH UHODWLRQ EHWZHHQ 3c DQG 34 5SA 5Se 5SA PP+JPLQPO 5G PP+JrPLQPO 3V@ PPLOJ 3 PP+J 3 PP+J

PAGE 81

PP+Jf

PAGE 82

VKRZQ LQ ILJXUH )RU WKLV ILJXUH 5SM 5S PP+JPLQPO 5' PP+JPLQPO 36@ PP+J DQG 3 PP+J &XUYHV ZHUH GUDZQ DW IORZV RI DQG A POPLQ 7KHVH IORZ UDWHV ZHUH KLJK HQRXJK VR WKDW IORZ ZDV RFFXUULQJ WKURXJK ERWK WXEHV DW DOO WLPHV )RU WKH FXUYH GUDZQ DW ]HUR IORZ WKHUH LV RQO\ RQH EUHDNSRLQW DV SUHn GLFWHG E\ WKH PDWKHPDWLFDO PRGHO )RU HDFK RI WKH RWKHU FXUYHV WKHUH DUH WZR GLVWLQFW EUHDNSRLQWV LQGLFDWHG RQ WKH FXUYH GUDZQ DW $ POPLQ E\ WKH DUURZV ODEHOOHG $ DQG % $FFRUGLQJ WR WKH PDWKHPDWLFDO PRGHO IORZ XS WR SRLQW $ LV RFFXUULQJ DFFRUGLQJ WR FRQGLWLRQ LQ ERWK WXEHV %HWZHHQ SRLQW $ DQG SRLQW % IORZ LV RFFXUULQJ DFFRUGLQJ WR FRQGLWLRQ 3c 3L 3ff LQ WXEH EXW VWLOO DFFRUGLQJ WR FRQGLWLRQ LQ WXEH 3c 3 3nf %H\RQG SRLQW % IORZ LV RFFXUULQJ DFFRUGLQJ WR FRQGLn WLRQ LQ ERWK WXEHV $OVR DV SUHGLFWHG E\ WKH PDWKHPDWLFDO PRGHO ILJXUH f D OLQH GUDZQ WKURXJK WKH ILUVW EUHDNSRLQW RI HDFK FXUYH LQGLFDWHG E\ WKH GDVKHG OLQH RQ ILJXUH f GRHV QRW LQWHUVHFW WKH EUHDNSRLQW RI WKH FXUYH GUDZQ DW ]HUR IORZ 7R LQYHVWLJDWH WKH UHODWLRQ EHWZHHQ 3c DQG 34 LQ D PXOWLWXEH PRGHO ZKHQ IORZ ZDV WDNLQJ SODFH WKURXJK RQO\ D SDUWLDO QXPEHU RI WXEHV WKH WKUHHWXEH SK\VLFDO PRGHO ZDV DJDLQ HPSOR\HG $V LQ WKH PDWKHPDWLFDO PRGHO WKLV UHODWLRQ ZDV VWXGLHG RQO\ LQ FRQGLWLRQ VWDWHV 3 36 36 S6 36$f DQG S6O SRf 36 36 36 LQ RUGHU WR GHWHUPLQH WKH SRVLWLRQ RI WKH ILUVW EUHDNSRLQW IRU HDFK FXUYH )LJXUH GHPRQVWUDWHV WKLV UHODWLRQVKLS ,Q WKLV ILJXUH 5SM 5S 53 PP+JPLQPO DQG 5S PP+JPLQPO 7KH GHSWK RI ZDWHU LQ HDFK ER[ VLPXODWHG VXUURXQGLQJ SUHVVXUHV RI 3@ PP+J 3 PP+J DQG 3VA A PP+J &XUYHV ZHUH GUDZQ DW DQG POPLQ $V LQGLFDWHG E\ WKH GDVKHG OLQH WKH EUHDNSRLQW IRU WKH FXUYHV

PAGE 83

),*85( 5HFRUGLQJ IURP WKH WZR WXEH SK\VLFDO PRGHO RI WKH UHODWLRQ EHWZHHQ 3c DQG 3 IORZ RFFXUULQJ LQ DOO WXEHV 5SL 5S PP+JrPLQPO 5J PP+JPLQPO 3 PP+J 3 PP+J

PAGE 84

, t+:8-f rG ,B -f§f§ BB f§/B RY / + W+8-88f

PAGE 85

),*85( 5HFRUGLQJ IURP WKH WKUHH WXEH SK\VLFDO PRGHO RI WKH UHODWLRQ EHWZHHQ 3c DQG 3* IORZ RFFXUULQJ LQ D SDUWLDO QXPEHU RI WXEHV 5S 5S 5S PP+JPLQPO 5S PP+JPLQPO 3V@ PP+J 3 PP+J 3VA A PP+J

PAGE 86

PP+Jf

PAGE 87

GUDZQ DW DQG POPLQ SRLQWV $ % DQG &f FDQ EH FRQQHFWHG E\ D VWUDLJKW OLQH +RZH\HU WKLV OLQH GRHV QRW LQWHUVHFW WKH EUHDNn SRLQW RI DQ\ RI WKH UHPDLQLQJ WKUHH FXUYHV 1HLWKHU FDQ D VWUDLJKW OLQH EH GUDZQ WKURXJK SRLQWV ( DQG ) 7KLB LV H[DFWO\ ZKDW ZDV SUHGLFWHG E\ WKH PDWKHPDWLFDO PRGHO LQ ILJXUH 3M 9HUVXV 4 7KH UHODWLRQVKLS EHWZHHQ 4 DQG 3c LQ D RQH WXEH SK\VLFDO PRGHO LV VKRZQ RQ ILJXUH ,Q WKLV LQVWDQFH 5S PP+JPLQPO DQG 5G PP+JrPLQPO 7KH ZDWHU GHSWK LQ WKH ER[ VLPXODWHG D 3V RI PP+J 7KURXJKRXW WKH GUDZLQJ RI WKH FXUYH 3 ZDV KHOG DW PP+J $V WKH FXUYH LQGLFDWHV WKHUH LV QR IORZ XQWLO 3c EHFRPHV JUHDWHU WKDQ 36 DIWHU ZKLFK IORZ RFFXUV LQ D OLQHDU UHODWLRQVKLS ZLWK 3c XS WR SRLQW $ 2Q WKLV SRUWLRQ RI WKH FXUYH WKH UHFLSURFDO RI WKH VORSH RI WKH OLQH LV PP+JfPLQPO ZKLFK FRUUHVSRQGV YHU\ ZHOO WR WKH UHVLVWDQFH RI WKH JODVV WXEH XVHG LQ WKH SUR[LPDO SRVLWLRQ 7KLV LQGLFDWHV WKDW IORZ LV RFFXUULQJ LQ DFFRUGDQFH ZLWK FRQGLWLRQ DV SUHGLFWHG E\ WKH PDWKHPDWLFDO PRGHO %H\RQG SRLQW $ WKH UHFLSURFDO RI WKH VORSH RI WKH OLQH LV PP+JPLQPO ZKLFK DJUHHV ZHOO ZLWK WKH VXP RI 5S DQG 5S RU WRWDO UHVLVWDQFH 7KLV LQGLFDWHV WKDW SRLQW $ LV WKH IORZ DW ZKLFK 3n EHFRPHV JUHDWHU WKDQ 3V DQG WKDW EH\RQG SRLQW $ IORZ RFFXUV DFFRUGLQJ WR FRQGLWLRQ DV SUHGLFWHG E\ WKH PDWKHPDWLFDO PRGHO ,Q WKH IROORZLQJ ILJXUHV WKH UHODWLRQ EHWZHHQ 3c DQG 4 ZLOO EH VWXGLHG RQO\ LQ FRQGLWLRQV DQG )LJXUH K LOOXVWUDWHV WKH HIIHFW RQ WKH SUHVVXUHIORZ FXUYH RI LQFUHDVLQJ 5S ,Q FXUYH 5S PP+JrPLQPO 5S PP+JrPLQ PO DQG 3V PP+J ,Q FXUYH 5S PP+JPLQPO DQG 5S DQG 36 ZHUH WKH VDPH DV LQ FXUYH 7KH 3c DW ZKLFK IORZ EHJLQV WR RFFXU

PAGE 88

),*85( 5HFRUGLQJ IURP WKH RQH WXEH SK\VLFDO PRGHO RI WKH UHODWLRQ EHWZHHQ 4 DQG 3c 5S PP+JfPLQPO 5T PP+JfPLQPO 3J PP+J

PAGE 89

6 IU+n::f JL nG D POPLQf

PAGE 90

),*85( E 5HFRUGLQJ IURP WKH RQH WXEH SK\VLFDO PRGHO RI WKH UHODWLRQ EHWZHHQ 4 DQG 3c HIIHFW RI LQFUHDVLQJ 5S &XUYH 5S PP+JPLQPO 5J ROO2 PP+JPLQPO 36 PP+J &XUYH 5S PP+JPLQPO 5T PP+JPLQPO 3 PP+J

PAGE 91

POPcQf

PAGE 92

LV WKH VDPH IRU ERWK FXUYHV KRZHYHU WKH VORSH IRU FXUYH LV OHVV WKDQ WKH VORSH RI FXUYH DV SUHGLFWHG E\ WKH PDWKHPDWLFDO PRGHO )LJXUH SUHVHQWV WKH HIIHFWV RQ WKH SUHVVXUHIORZ UHODWLRQVKLS RI LQFUHDVLQJ RQO\ 3V )RU ERWK FXUYHV DQG 5S PP+JPLQPO DQG 5S PP+JPLQPO ,Q FXUYH 3V f§ PP+J EXW LQ FXUYH 3V A PP+J 3' ZDV KHOG DW PP+J IRU ERWK FXUYHV $V VKRZQ E\ WKH ILJXUH QR IORZ RFFXUUHG LQ FXUYH XQWLO 3c EHFDPH JUHDWHU WKDQ PP+J ,Q FXUYH QR IORZ RFFXUUHG XQWLO 3c EHFDPH JUHDWHU WKDQ A PP+J +RZHYHU WKH VORSH RI ERWK FXUYHV LV WKH VDPH DIWHU IORZ KDV EHJXQ WR WDNH SODFH 7KH EHKDYLRU RI WKH SK\VLFDO PRGHO LQ WKLV FDVH LV DJDLQ LQ DFFRUGDQFH ZLWK WKDW SUHGLFWHG E\ WKH PDWKHPDWLFDO PRGHO 7KH WKUHHWXEH SK\VLFDO PRGHO ZDV XVHG WR LQYHVWLJDWH WKH UHODWLRQn VKLS EHWZHHQ 4 DQG 3c LQ D PXOWLSOH WXEH V\VWHP 7KLV UHODWLRQVKLS LV LOOXVWUDWHG LQ ILJXUH )RU FXUYH WKH PRGHO ZDV DUUDQJHG VR WKDW 5SM A PP+JPLQPO 5S PP+JPLQPO DQG 5SA PP+J PLQPO 7KH ZDWHU OHYHO LQ HDFK ER[ ZDV DGMXVWHG VR WKDW 3V@ PP+J 36 PP+J DQG 3VA PP+J 5S ZDV PP+JPLQPO DQG 3 ZDV KHOG DW PP+J WKURXJKRXW WKH FRQVWUXFWLRQ RI WKH FXUYH &XUYH H[KLELWV WKUHH GHILQLWH EUHDNSRLQWV DV LQGLFDWHG E\ WKH DUURZV ODEHOOHG $ % DQG & 8S WR SRLQW $ QR IORZ RFFXUUHG $V 3c LQFUHDVHG EH\RQG SRLQW $ IORZ EHJDQ WR RFFXU WKURXJK WXEH DQG EHWZHHQ SRLQWV $ DQG % IORZ RFFXUUHG RQO\ WKURXJK WXEH $W SRLQW % IORZ EHJDQ WR RFFXU WKURXJK WXEH DQG EHWZHHQ SRLQWV % DQG & IORZ ZDV RFFXUULQJ WKURXJK WXEHV DQG %H\RQG SRLQW & IORZ ZDV WDNLQJ SODFH WKURXJK DOO WKUHH WXEHV $V FDQ EH VHHQ WKH 3M DW ZKLFK IORZ EHJLQV WR RFFXU LQ HDFK WXEH FRUUHVSRQGV YHU\ ZHOO ZLWK WKH 3V IRU HDFK WXEH

PAGE 93

),*85( 5HFRUGLQJ IURP WKH RQH WXEH SK\VLFDO PRGHO RI WKH UHODWLRQ EHWZHHQ 4 DQG 3c HIIHFW RI LQFUHDVLQJ 3 &XUYH 5S PP+JPLQPO 5S PP+JPLQPO 36 PP+J &XUYH 5S PP+JnPLQPO 5S PP+JnPLQPO 3 A PP+J

PAGE 95

),*85( 5HFRUGLQJ IURP WKH WKUHH WXEH SK\VLFDO PRGHO RI WKH UHODWLRQ EHWZHHQ 4 DQG 3c HIIHFW RI LQFUHDVLQJ 5S &XUYH 5SM 2$ PP+JPLQPO 53 PP+JPLQPO 5SA PP+JPLQPO 5S PP+JPLQPO 3 PP+J 36 PP+J 3 PP+J &XUYH 5S_ 20 PP+JPLQPO 5S A PP+JPLQPO 5SR PP+JPLQPO 5S PP+JPLQPO 3 PP+J 3 PP+J 36 PP+J

PAGE 96

POUQLQf

PAGE 97

$OVR VKRZQ LQ WKLV ILJXUH LV WKH LQWHUFHSW RI WKDW SRUWLRQ RI FXUYH EH\RQG SRLQW & WKH VWUDLJKW OLQH SRUWLRQf LQGLFDWHG E\ WKH GDVKHG OLQH &XUYH LQ ILJXUH LQGLFDWHV WKH HIIHFWV RI LQFUHDVLQJ 5S RQ WKH UHODWLRQ EHWZHHQ 4 DQG 3c )RU FXUYH WKH YDOXHV IRU 3V DQG 5J ZHUH WKH VDPH DV IRU FXUYH 3* ZDV KHOG FRQVWDQW DW PP+J GXULQJ WKH FRQVWUXFWLRQ RI FXUYH +RZHYHU IRU FXUYH 5SM PP+J PLQPO 5S PP+JrPLQPO DQG 5SA PP+JfPLQQLO 7KHUH DUH WKUHH GLVWLQFW EUHDNV RQ FXUYH HDFK RI ZKLFK RFFXUV DW WKH VDPH YDOXH RI 3c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f RI FXUYH LV KLJKHU WKDQ WKH LQWHUFHSW RI FXUYH EXW WKH VORSH RI ERWK FXUYHV LV WKH VDPH 7KXV WKH SK\VLFDO PRGHO EHKDYHV LQ WKH PDQQHU SUHGLFWHG E\ WKH

PAGE 98

),*85( 5HFRUGLQJ IURP WKH WKUHH WXEH SK\VLFDO PRGHO RI WKH UHODWLRQ EHWZHHQ DQG 3c HIIHFW RI LQFUHDVLQJ 3 &XUYH VDPH DV FXUYH LQ ILJXUH &XUYH 5SM A PP+JrPLQPO 5Se PPLOJPLQPO 5SA PP+JPLQPO 5J PP+JrPLQPO 3VM PP+J 3 PP+J 36 PP+J

PAGE 99

POPLQf ,W

PAGE 100

PD WKHPD WLFD PRGHO $QLPDOV )HWXVHV 7KH UHODWLRQVKLS EHWZHHQ SXOPRQDU\ DUWHU\ SUHVVXUH 3$3f DQG SXOPRQDU\ \HQRXV SUHVVXUH 393f LQ DQ XQYHQWLODWHG IHWDO OXQJ KDV DOUHDG\ EHHQ VKRZQ LQ ILJXUH 7KLV VDPH UHODWLRQVKLS LQ D IHWXV YHQWLODWHG ZLWK DLU LV SUHVHQWHG LQ ILJXUH 7KH LQWHUPLWWHQW ORRSV LQ HDFK FXUYH GHPRQVWUDWH WKH HIIHFW RI SRVLWLYH SUHVVXUH LQIODWLRQ RQ 3$3 DQG 393 7KHVH ORRSV ZHUH GLVUHJDUGHG LQ REWDLQLQJ WKH YDOXHV QHFHVVDU\ WR FDOFXODWH 5S DQG 5S 2QO\ WKH SRUWLRQV RI HDFK FXUYH GXULQJ HQG H[SLUDWLRQ ZHUH XVHG WR REWDLQ WKHVH YDOXHV _Q WKH XQYHQWLODWHG OXQJ WKH WUDFKHD ZDV RSHQ WR DWPRVSKHULF SUHVVXUH 7KHUHn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f.JPLQPO 8SRQ VXEVWLWXWLQJ DLU IRU WKH IHWDO JDV PL[WXUH ERWK SUR[LPDO DQG GLVWDO IHOO VLJQLILn FDQWO\ WR DQG PP+J f .J LQ L QPO UHVSHFWLYHO\ ,Q WKH XQYHQWL ODWHG OXQJ 3V DYHUDJHG PP+J 8SRQ YHQWLODWLRQ ZLWK WKH IHWDO JDV PL[WXUH 3V IHOO VLJQLILFDQWO\ WR PP+J )XUWKHU YHQWLODWLRQ ZLWK

PAGE 101

),*85( YHQW L DWHG 5HFRUGLQJ RI WKH UHODWLRQ EHWZHHQ 3$3 DQG 393 LQ D DQLPDO

PAGE 102

f%+f:8-f R G 9G PPLQn PLPLQ PWPLQ ?6! WR

PAGE 103

DLU DJDLQ GHFUHDVHG S VLJQLILFDQWO\ WR PP+J 7KH D\HUDJH YDOXHV IRU 3T! 3&2 DQFr 3A n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r )LJXUH LOOXVWUDWHV WKH UHODWLRQ EHWZHHQ 5S DQG SXOPRQDU\ DUWHULDO 3 LQ YHQWLODWHG DQLPDOV 1R UHODWLRQ ZDV IRXQG LQ WKLV VHULHV RI DQLPDOV EHWZHHQ 5S DQG 3F&! RU S+ $FFRUGLQJ WR ILJXUH 5S GHFUHDVHV PDUNHGO\ DV 3 LQFUHDVHV XS WR DSSUR[LPDWHO\  PP+J :LWK LQFUHDVHV LQ 3 DER\H L} PP+J 5S UHPDLQV FRQVWDQW 7KH GDWD LQ ILJXUH ZHUH UHSORWWHG DV ORJ 5S YHUVXV ORJ 3 DV VKRZQ LQ ILJXUH $ VLJQLILFDQW UHJUHVVLRQ OLQH U 3 f ZDV GUDZQ WKURXJK WKH GDWD SRLQWV LQ ILJXUH DFFRUGLQJ WR WKH HTXDWLRQ ORJ 5S ORJ 3R )LJXUH LQGLFDWHV WKH UHODWLRQVKLS EHWZHHQ 5S DQG SXOPRQDU\ YHQRXV 3f 1r UHODWLRQ FRXOG EH REWDLQHG IRU 5J DQG 3&2 RU S+r 5S GHFUHDVHV ZLWK DQ LQFUHDVH LQ SXOPRQDU\ YHQRXV 3 83 WR DJDLQ DERXW PP+J 5S VHHPV WR UHPDLQ FRQVWDQW LI WKH 3R LV KLJKHU WKDQ 2 PP+J $FFRUGLQJ WR WKH HTXDWLRQV SUHVHQWHG LQ WKH ILUVW SDUW RI 0DWHULDOV DQG 0HWKRGV WKH WRWDO UHVLVWDQFH RI WKH YDVFXODWXUH 5\f VKRXOG EH HTXDO WR 5S DQG 5S ,I IORZ LV RFFXUULQJ DFFRUGLQJ WR FRQGLWLRQ 3L 36 3nf Ir7 FDQ DVR EH FDOFXODWHG DFFRUGLQJ WR WKH HTXDWLRQ

PAGE 104

),*85( &RPSDULVRQ RI SUR[LPDO DQG GLVWDO UHVLVWDQFH DQG VXUURXQGLQJ SUHVVXUH LQ WKH OHIW OXQJ GXULQJ WKH XQYHQWLODWHG IHWDO VWDWH )f GXULQJ YHQWLODWLRQ RI ERWK OXQJV ZLWK IHWDO JDV 9)*f DQG GXULQJ YHQWLODWLRQ RI ERWK OXQJV ZLWK DLU 9$f %DUV DUH WKH DYHUDJH RQH VWDQGDUG HUURU IRU DQLPDOV

PAGE 105

5(6,67$1&( QP+J.J POQUDOf 6855281',1* 35(6685( PP+Df

PAGE 106

7$%/( 3T 3IQ DQG S+ LQ /HIW 3XOPRQDU\ $UWHULDO %ORRG LQ )HWDO $QLPDOV LQ :Q" FK %RWK /XQJV ZHUH 8QYHQW L DWHG 9HQWLODWHG ZLWK )HWDO *DV DQG 9HQWLODWHG ZLWK $LU 38/021$5< $57(5< 3 3& S+ )(7$/ fr f f 9(17,/$7(' :,7+ )(7$/ *$6 f f f 9(17,/$7(' :,7+ $,5 f f f UDQJH

PAGE 107

),*85( 5HODWLRQ EHWZHHQ SUR[LPDO DUWHULDO 3 !Q YHQWLODWHG DQLPDOV UHVLVWDQFH DQG SXOPRQDU\

PAGE 108

R 2 9(17,/$7(' /n/nHV R Y 7 R f§U f§Lf§ 62 3T PP+Jf H R R R k 2 7 7 62 &2

PAGE 109

),*85( 5HODWLRQ EHWZHHQ ORJ SUR[LPDO UHVLVWDQFH DQG ORJ SXOPRQDU\ DUWHULDO 3 LQ YHQWLODWHG DQLPDOV

PAGE 110

2KnXMXMf

PAGE 111

),*85( 5HODWLRQ EHWZHHQ GLVWDO UHVLVWDQFH DQG SXOPRQDU\ YHQRXV 3 LQ YHQWLODWHG DQLPDOV

PAGE 112

PP+Jf R f§ ',67$/ 5(6,6O $1&( PP+J .J PLQPOf S S f§ f§ $ 2} 0 m5 L } , } }f§f§f§2 7!B 2 R R R RR 2 R &B R R 2 2 UR R R R P ] + Ua + P R RRR URUc2‘WrpR R WZ [ R

PAGE 113

W ZDV FDOFXODWHG ,Q WKLV JURXS RI DQLPDOV DFFRUGLQJ WR WKLV HTXDWLRQ 7KLV ZDV GRQH E\ WDNLQJ D SRLQW RQ WKH FXUYH RI 3$3 YHUVXV 393 ZKHUH 393 ZDV LQIOXHQFLQJ 3$3 LQ D RQH WR RQH UHODWLRQ LQVHUW LQ ILJXUH f 5W ZDV WKHQ FDOFXODWHG DV 3$3 PLQXV 393 DW WKDW SRLQW GLYLGHG E\ WKH IORZ IRU WKDW FXUYH 3$3393 UW a7a 7KH YDOXH IRU 5M REWDLQHG E\ WKLV PHWKRG ZDV FRPSDUHG WR WKH VXP RI 5S DQG 5S REWDLQHG SUHYLRXVO\ 7KLV FRPSDULVRQ LV SUHVHQWHG LQ ILJXUH %DUV ODEHOOHG 7 DUH WKH FDOFXODWHG WRWDO UHVLVWDQFH IRU DQLPDOV LQ WKH IHWDO XQYHQWLODWHGf VWDWH YHQWLODWHG ZLWK IHWDO JDV PL[WXUH DQG YHQWLODWHG ZLWK DLU %DUV ODEHOOHG 3 LQGLFDWH WKH VXP RI 5S DQG 5S REWDLQHG SUHYLRXVO\ IRU WKH DQLPDOV LQ HDFK RI WKH WKUHH VWDWHV $V LQGLFDWHG LQ WKH ILJXUH WKHUH LV QR GLIIHUHQFH LQ WKH FDOFXODWHG WRWDO UHVLVWDQFH DQG WKDW REWDLQHG E\ DGGLQJ WKH SUR[LPDO DQG GLVWDO UHVcVWDQFHV 7KH HIIHFWV RQ 5S 5S DQG 3 RI FKDQJHV LQ EORRG JDVHV LQ XQYHQWLn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f.JPLQPO EHIRUH YHQWLODWLRQ ZLWK WKH IHWDO JDV DQG PP+Jf.JPLQPO GXULQJ YHQWLODWLRQ ZLWK WKH IHWDO

PAGE 114

),*85( &RPSDULVRQ RI WRWDO UHVLVWDQFH 7f FDOFXODWHG LQ FRQGLWLRQ WR WKH VXP RI SUR[LPDO DQG GLVWDO UHVLVWDQFH 3 'f FDOFXODWHG LQ FRQGLWLRQ LQ XQYHQWLODWHG IHWDO DQLPDOV DQLPDOV YHQWLODWHG ZLWK IHWDO JDV DQG YHQWLODWHG ZLWK DLU

PAGE 115

)HWDO 9HQWLODWHG ZLWK )HWDO *DV /3!6f§ 9HQWLODWHG ZLWK $LU U 7 7 3' Af§3 f§O

PAGE 116

),*85( A &RPSDULVRQ RI SUR[LPDO DQG GLVWDO UHVLVWDQFH DQG VXUURXQGLQJ SUHVVXUH LQ WKH OHIW OXQJ GXULQJ WKH XQYHQWLODWHG IHWDO VWDWH )f GXULQJ YHQWLODWLRQ RI WKH ULJKW OXQJ ZLWK IHWDO JDV 9)*f DQG GXULQJ YHQWLODWLRQ RI WKH ULJKW OXQJ ZLWK DLU 9$f %DUV DUH WKH DYHUDJH RQH VWDQGDUG HUURU IRU DQLPDOV IRU EDUV ) DQLPDOV IRU EDUV 9)* DQG DQLPDOV IRU EDUV 9$

PAGE 117

5(6,67$1&( PP+J .JrLDLQPOf 352;,0$/ 5(6,67$1&( ',67$/ 5(6,67$1&( 6855281',1* 35(6685( 2 6855281',1* 35(6685( WUDUD.Jf

PAGE 118

JDV 5J ZDV A PP+Jf.JPLQPO EHIRUH DQG PP+Jf.JPLQPO GXULQJ YHQWLODWLRQ ZLWK IHWDO JDV DYHUDJHG PP+J LQ WKH XQYHQWLODWHG VWDWH DQG PP+J GXULQJ YHQWLODWLRQ RI WKH ULJKW OXQJ ZLWK IHWDO JDV :KHQ WKH ULJKW OXQJ ZDV YHQWLODWHG ZLWK DLU 5S GHFUHDVHG VLJQLILFDQWO\ WR PP+Jf.JPLQPO /LNHZLVH 3V GHFUHDVHG VLJQLILFDQWO\ WR PP+J 7KH DYHUDJH YDOXH DQG WKH UDQJHV IRU 3T! 3& DQFr nQ ERWK OHIW SXOPRQDU\ DUWHULDO DQG OHIW SXOPRQDU\ YHQRXV EORRG GXULQJ HDFK RI WKHVH WKUHH VWDWHVDUH JLYHQ LQ 7DEOH 9HQWLODWLRQ RI WKH ULJKW OXQJ ZLWK IHWDM JDV GLG QRW DOWHU SXOPRQDU\ DUWHULDO RU YHQRXV 3 RU 3Fr +RZHYHU ERWK SXOPRQDU\ DUWHULDO DQG YHQRXV S+ ZHUH ORZHU WKDQ LQ WKH XQYHQWLODWHG VWDWH 9HQWLODWLRQ RI WKH ULJKW OXQJ ZLWK DLU LQFUHDVHG 3T DQG GHFUHDVHG 3T nQ ERWK SXOPRQDU\ DUWHULDO DQG YHQRXV EORRG 7KH S+ ZDV LQFUHDVHG DERYH WKH SUHYLRXV VWDWH EXW ZDV QRW KLJKHU WKDQ LQ WKH XQYHQWLODWHG VWDWH )LJXUH GHPRQVWUDWHV WKH UHODWLRQ EHWZHHQ 5S DQG SXOPRQDU\ DUWHULDO 3D LQ WKH XQYHQWLODWHG OXQJ 7KH GDWD IRU WKLV UHODWLRQ ZHUH REWDLQHG IURP WKH JURXS RI IHWXVHV LQ ZKLFK RQO\ WKH ULJKW OXQJ ZDV YHQWLODWHG ILJXUH r DQG IURP WKH ILUVW JURXS RI IHWXVHV ILJXUH f EHIRUH ERWK OXQJV ZHUH YHQWLODWHG 9DOXHV IRU 5S REWDLQHG EHIRUH DGPLQLVWUDWLRQ RI WKH GUXJ LQ WKH QH[W VHULHV RI IHWXVHV ILJXUH f LQ ZKLFK EUDG\NLQLQ ZDV VWXGLHG ZHUH DOVR LQFOXGHG LQ ILJXUH $V LQ WKH YHQWLODWHG OXQJ 5S GURSV UDSLGO\ DV 3T LQFUHDVHV XS WR rr PP+J $V 3D&! LQFUHDVHV DERYH rW PP+J 5S UHPDLQV UHODWLYHO\ FRQVWDQW 'LVWDO UHVLVWDQFH DQG SXOPRQDU\ YHQRXV 3 ZHUH UHODWHG DV GHSLFWHG LQ ILJXUH 'DWD IRU WKLV UHODWLRQ ZHUH REWDLQHG LQ WKH VDPH PDQQHU DV LQ ILJXUH $V VKRZQ LQ WKLV ILJXUH 5J ZDV LQFUHDVHG DW YDOXHV IRU

PAGE 119

7$%/( 3S" 3PR DQG S+ n Q /HIW 3XOPRQDU\ $UWHULDO DQG 9HQRXV %ORRG LQ )HWDO $QLPDOV ,Q :KLFK %RWK /XQJV ZHUH 8QYHQW L DWHG 5LJKW /XQJ 2QO\ 9HQWLODWHG ZLWK )HWD *DV DQG 5LJKW /XQJ 2QO\ 9HQWLDWHG ZLWK $LU 38/021$5< $57(5< 38/021$5< 9(,1 3 3& 3+ S 3& S+ %27+ /81*6 819(17 /$7(' fr f f f f f 5,*+7 /81* 9(17,/$7(' :,7+ )(7$/ *$6 f f f f f f 5,*+7 /81* 9(17,/$7(' :,7+ $,5 f f f f f f UDQJH

PAGE 120

),*85( 5HODWLRQ EHWZHHQ SUR[LPDO DUWHULDO 3 cQ XQYHQWLODWHG DQLPDOV UHVLVWDQFH DQG SXOPRQDU\

PAGE 121

PP+Jf Urf§ UR R R 2M RO 352;,0$/ 5(6,67$1&( UR RM PP+J.JPLQPOf A FML r f§M M R H -f f§

PAGE 122

),*85( YHQRXV 3 5HODWLRQ EHWZHHQ GLVWDO LQ XQYHQWLODWHG DQLPDOV UHVLVWDQFH DQG SXOPRQDU\

PAGE 123

PP+Jf M! R ‘ ',67$/ 5(6,67$1&( 2 R &' O 6 6 k R 4 &2 R PP+J.JPOQPOf 3 FR 2 UR L D k k R H m

PAGE 124

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f DQG 3 3 f VLJQLILFDQWO\ 5S GHFUHDVHG IURP D YDOXH RI $ PP+J.JPLQPO WR PP+Jf.JPLQPO 3 IHOO IURP PP+J WR PP+J $IWHU WKH LQIXVLRQ RI EUDG\NLQLQ ZDV VWRSSHG ERWK 5S DQG 3 UHWXUQHG WR SUHn LQIXVLRQ OHYHOV 5S LQFUHDVHG WR PP+Jf.JPLQPO DQG 3 LQFUHDVHG WR PP+J $OWKRXJK 5J GHFUHDVHG IURP WR PP+Jf.JPLQPO GXULQJ WKH LQIXVLRQ RI EUDG\NLQLQ WKH GHFUHDVH ZDV QRW VLJQLILFDQW $OVR 5J RQO\ LQFUHDVHG WR D YDOXH RI A PP+Jf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f WR GHFUHDVH

PAGE 125

),*85( &RPSDULVRQ RI SUR[LPDO DQG GLVWDO UHVLVWDQFH DQG VXUURXQGLQJ SUHVVXUH LQ WKH OHIW OXQJ RI XQYHQWLODWHG DQLPDOV EHIRUH %f GXULQJ 'f DQG DIWHU $f LQIXVLRQ RI EUDG\NLQLQ LQWR WKH SXOPRQDU\ DUWHU\ %DUV DUH WKH DYHUDJH  RQH VWDQGn DUG HUURU IRU DQLPDOV

PAGE 126

5(6,67$1&( PP+J.JPcQPOf 352;L"$/ 5(6,67$1&( ',67$/ 5(6,67$1&( 6855281',1* 35(6685( 6855281',1* 35(6685( PP+Jf

PAGE 127

7$%/( 3If 3HR" DQG S+ LQ /HIW 3XOPRQDU\ $UWHULDO DQG 9HQRXV %ORRG RI )HWDO $QLPDOV %HIRUH 'XULQJ DQG $IWHU ,QIXVLRQ RI %UDG\NLQLQ 38/021$5< $57(5< 38/021$5< 9(,1 S U S U& S+ 3 3& 3+ %()25( %5$'<.,1,1 fr f f f f f '85,1* %5$'<.,1,1 rr f f f f f f $)7(5 %5$'<.,1,1 f f f f f f r UDQJH

PAGE 128

),*85( &RPSDULVRQ RI SUR[LPDO DQG GLVWDO UHVLVWDQFH DQG VXUURXQGLQJ SUHVVXUH LQ WKH OHIW OXQJ RI QHZO\ YHQWLODWHG DQLPDOV EHIRUH %f GXULQJ 'f DQG DIWHU $f LQIXVLRQ RI EUDG\NLQLQ LQWR WKH SXOPRQDU\ DUWHU\ %DUV DUH WKH DYHUDJH L RQH VWDQGDUG HUURU IRU DQLPDOV

PAGE 129

5(6,67$1&( PP+J.J POQPOf 352;,0$/ 5(6,67$1&( ',67$/ 5(6,67$1&( 6855281',1* 35(6685( 6855281',1* 35(6685( PP+Jf

PAGE 130

7$%/( 3S" 3JR" DQG S+ ,Q /HIW 3XOPRQDU\ $UWHULDO DQG 9HQRXV %ORRG RI 1HZO\ 9HQWLODWHG $QLPDOV %HIRUH 'XULQJ DQG $IWHU ,QIXVLRQ RI %UDG\NLQLQ 38/021$5< $57(5< 38/021$5< 9(,1 3 S & S+ &0 2 &/ 3& S+ %()25( %5$'<.,1,1 fr f f f f f '85,1* %5$'<.,1,1 f f f f f f $)7(5 %5$'<.,1,1 f f f f f f UDQJH

PAGE 131

VLJQLILFDQWO\ IDOOLQJ IURP WR PP+Jf.JPLQPO $IWHU WKH LQIXVLRQ ZDV VWRSSHG 5S UHWXUQHG WR D YDOXH RI PP+Jf.JPLQPO ZKLFK ZDV QRW VLJQLILFDQWO\ GLIIHUHQW IURP WKH SUHLQIXVLRQ OHYHO 36 GHFUHDVHG GXULQJ WKH LQIXVLRQ RI EUDG\NLQLQ EXW QRW VLJQLILFDQWO\ %HIRUH LQIXVLRQ 36 DYHUDJHG PP+J GXULQJ LQIXVLRQ LWV PHDQ ZDV PP+J DQG DIWHU LQIXVLRQ LW LQFUHDVHG WR PP+J 5S DFWXDOO\ LQFUHDVHG VOLJKWO\ GXULQJ LQIXVLRQ RI WKH GUXJ IURP WR PP+Jf.JPLQPO 5J LQFUHDVHG HYHQ IXUWKHU DIWHU FHVVDWLRQ RI LQIXVLRQ WR D YDOXH RI PP+J!.Jr PLQPO +RZHYHU QRQH RI WKH FKDQJHV LQ 5J ZHUH VWDWLVWLFDOO\ VLJQLILn FDQW 7DEOH SUHVHQWV YDOXHV IRU WKH SXOPRQDU\ DUWHULDO DQG YHQRXV EORRG JDVHV DQG S+ LQ HDFK RI WKH WKUHH VWDWHV 1HRQDWHV ,Q D ILQDO JURXS RI DQLPDOV WKH HIIHFW RI K\SR[LD RQ 5S 5J DQG 3 ZDV VWXGLHG LQ QHRQDWDO DQLPDOV )LJXUH LQGLFDWHV WKH UHVXOWV RI WKLV VWXG\ %DUV ODEHOOHG $ LQGLFDWH PHDQ YDOXHV RI 5S 5J DQG 3 IRU DQLPDOV YHQWLODWHG ZLWK DLU %DUV ODEHOOHG LQGLFDWH YDOXHV IRU DQLPDOV YHQWLODWHG ZLWK b LQ 1 %DUV ODEHOOHG GHQRWH YDOXHV IRU DQLPDOV YHQWLODWHG ZLWK LQ 1 3UR[LPDO UHVLVWDQFH LQFUHDVHG EXW QRW VLJQLILFDQWO\ IURP WR PP+Jf.JPLQPO DIWHU FKDQJLQJ WKH YHQWLODWLQJ JDV IURP DLU WR b 2 LQ 1 6XEVWLWXWLRQ RI b LQ 1 DV WKH YHQWLODWLQJ JDV FDXVHG 5S WR LQFUHDVH HYHQ IXUWKHU WR PP+Jf.JrPLQPO 7KLV YDOXH ZDV VLJQLILFDQWO\ JUHDWHU 3 f WKDQ WKDW GXULQJ YHQWLODWLRQ ZLWK DLU 5J IROORZHG WKH VDPH SDWWHUQ DV 5S ,W LQFUHDVHG IURP WR PP+J.JfPLQPO GXULQJ YHQWLODWLRQ ZLWK b 2 DQG LQFUHDVHG WR PP+Jf.JPLQPO GXULQJ YHQWLODWLRQ ZLWK b 2 5J ZDV VLJQLILFDQWO\ KLJKHU 3 f GXULQJ YHQWLODWLRQ ZLWK b 2 LQ 1 WKDQ GXULQJ YHQWLODWLRQ ZLWK DLU 3

PAGE 132

),*85( &RPSDULVRQ RI SUR[LPDO DQG GLVWDO UHVLVWDQFH DQG VXUURXQGLQJ SUHVVXUH LQ WKH OHIW OXQJ RI QHZERUQ DQLPDOV GXULQJ YHQWLODWLRQ ZLWK DLU $f b 2 LQ 1 f DQG b 2 LQ 1 f %DUV DUH WKH DYHUDJH RQH VWDQGDUG HUURU LQ DQLPDOV IRU EDUV $ DQG DQLPDOV IRU EDUV DQG

PAGE 133

5(6,67$1&( PP+J.JPcQPOf 35&A--$/ 5(6,67$1&( ',67$/ 5(6,67$1&( 6855281',1* 3+(668I U7Q 7 )7 c ,, $ 9HQWLODWHG ZLWK $LU ,2 9QDHG YLIK ,b L 9HQWLDWHG ZLWK b LQ 1 ILQ / $ 7 U/ 7 /S!F, /3!/S&/3 !3 3 f 3 ,' X 1! 6855281',1* 35(6685( PUD+Jf

PAGE 134

7$%/( 3SR} 3FR DQG S+ LQ /HIW 3XOPRQDU\ $UWHULDO %ORRG RI 1HZERUQ $QLPDOV LQ :KLFK %RWK /XQJV ZHUH 9HQW L DWHG ZLWK $LU b r DQG b 38/021$5< $57(5< 3 3& 3+ 9(17,/$7(' :,7+ $,5 fr f f 9(17,/$7(' :,7+ b ,1 1 f f f 9(17,/$7(' :,7+ b ,1 1 f +f f UDQJH

PAGE 135

URVH VLJQLILFDQWO\ 3 f IURP WR PP+J XSRQ VXEVWLWXWLRQ RI b 2 IRU DLU DV WKH YHQWLODWLQJ JDV 9HQWLODWLRQ ZLWK b 2 LQ 1 FDXVHG 3V WR LQFUHDVH WR PP+J ZKLFK ZDV DOVR VLJQLILFDQWO\ JUHDWHU 3 f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n VLWH WR WKH FKDQJHV HGHPD VKRXOG FDXVH HGHPD ZDV QRW WKRXJKW WR EH D VHULRXV SUREOHP LQ WKH LQWHUSUHWDWLRQ RI WKH GDWD SUHVHQWHG KHUH

PAGE 136

',6&866,21 0DWKHPDWLFDO DQG 3K\VLFDO 0RGHO 3c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n PRQDU\ YDVFXODU V\VWHP KDV EHHQ VXJJHVWHG WR FRQWDLQ 6WDUOLQJ UHVLVWRUV +rrf VXFK D FRQFHSW ZDV XVHG WR REWDLQ D YDOXH IRU WKH SUHVVXUH DW D SRLQW ZLWKLQ WKH V\VWHP )LJXUHV DQG LQGLFDWH WKHRUHWLFDOO\ KRZ WKH SXOPRQDU\ FLUFXn ODWLRQ ZRXOG EHKDYH LI LW FRXOG EH FRPSDUHG WR D PRGHO VXFK DV SUHVHQWHG LQ ILJXUH :KHQ IORZ LV RFFXUULQJ LQ FRQGLWLRQ 3c 3 3nf WKH IXQFWLRQ RI WKH 6WDUOLQJ UHVLVWRU LV WR FRQWURO WKH SUHVVXUH ZLWKLQ WKH FROODSVLEOH WXEH DFWLQJ DV WKH 6WDUOLQJ UHVLVWRU HTXDO WR WKH SUHVVXUH WHQGLQJ WR FORVH LW 3Jf ,Q WKH SK\VLFDO PRGHO WKH SUHVVXUH WHQGLQJ WR FORVH WKH 6WDUOLQJ UHVLVWRU ZDV VLPXODWHG E\ WKH K\GURVWDWLF SUHVVXUH RI WKH ZDWHU VXUURXQGLQJ WKH 6WDUOLQJ UHVLVWRU ,I WKH VXUURXQGLQJ SUHVVXUH

PAGE 137

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n WLRQ EHWZHHQ LQIORZ SUHVVXUH DQG RXWIORZ SUHVVXUH LV REVHUYHG ZKLOH RXWIORZ SUHVVXUH LV VORZO\ UDLVHG WKH SUHVVXUH QHHGHG WR RSHQ WKH 6WDUOLQJ UHVLVWRU FDQ EH REWDLQHG 7KH RXWIORZ SUHVVXUH DW ZKLFK LQIORZ SUHVVXUH EHJLQV WR EH LQIOXHQFHG E\ FKDQJHV LQ WKH RXWIORZ SUHVVXUH LQGLFDWHV WKH SUHVVXUH QHHGHG WR RSHQ WKH 6WDUOLQJ UHVLVWRU 7KH SRLQW ODEHOOHG 3*A LQ ILJXUH LQGLFDWHV WKLV SUHVVXUHf )LJXUHV DQG VKRZ WKDW WKLV SRLQW 3RDf LV HTXDO WR WKH SUHVVXUH WHQGLQJ WR FORVH WKH 6WDUOLQJ UHVLVWRU )LJXUH LQGLFDWHV WKDW WKH UHVLVWDQFH SUR[LPDO DQG GLVWDO WR WKH 6WDUOLQJ UHVLVWRU FDQ EH FDOFXn ODWHG DFFXUDWHO\ DFFRUGLQJ WR WKH WKHRUHWLFDO HTXDWLRQV JLYHQ E\ WKH PDWKHPDWLFDO PRGHO 7KHUH ZDV QR VKDUS EUHDNSRLQW LQ WKH UHODWLRQ EHWZHHQ 393 DQG 3$3 LQ WKH DQLPDO ILJXUH f DV ZDV GHPRQVWUDWHG E\ WKH PDWKHPDWLFDO RU SK\VLFDO RQH WXEH PRGHO 7KHUHIRUH LW VHHPHG QHFHVVDU\ WR DWWHPSW WR H[SODLQ WKH EHKDYLRU RI WKH SXOPRQDU\ FLUFXODWLRQ LQ WKH DQLPDO RQ WKH EDVLV RI WKH PRGHO )LJXUH GHPRQVWUDWHV KRZ WKH RQH WXEH PRGHO ZDV

PAGE 138

PRGLILHG WR H[SODLQ WKLV EHKDYLRU 6LPSO\ E\ DGGLQJ D QXPEHU RI WXEHV LQ SDUDOOHO DOO RI ZKLFK KDYH WKH VDPH UHVLVWDQFH LQ ILJXUH DQG DOORZLQJ WKH 6WDUOLQJ UHVLVWRU LQ HDFK WXEH WR KDYH D GLIIHUHQW 3V FXUYHV VLPLODU WR WKH RQHV REWDLQHG IURP WKH DQLPDO FRXOG EH GUDZQ ,Q ILJXUH WKHUH DUH IRXU GLVWLQFW EUHDNSRLQWV RQ HDFK FXUYH EHFDXVH WKHUH ZHUH RQO\ IRXU WXEHV +RZHYHU LI D ODUJHU QXPEHU RI WXEHV ZHUH DGGHG LQ SDUDOOHO WKHQ D GLVWLQFW EUHDNSRLQW ZRXOG QRW EH YLVLEOH DQG D VPRRWK FXUYH ZRXOG UHVXOW VLPLODU WR WKH RQHV GHPRQVWUDWHG E\ WKH DQLPDOV LQ ILJXUH 3c 9HUVXV 4 6LQFH WKH UHODWLRQ EHWZHHQ SUHVVXUH DQG IORZ KDV EHHQ XVHG RIWHQ WR DVVHVV WKH VWDWH RI WKH SXOPRQDU\ YDVFXODU EHG DQG VLQFH WKH FKDUDFWHUn LVWLFV RI WKLV UHODWLRQVKLS KDYH EHHQ ZHOO GHPRQVWUDWHG f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n VWUDWHG WR EH FXUYLOLQHDU UDWKHU WKDQ OLQHDU )LJXUH LOOXVWUDWHV KRZ WKH WKHRUHWLFDO PRGHO FDQ EH DGMXVWHG WR SURGXFH D FXUYLOLQHDU SUHVVXUHIORZ UHODWLRQ ,I IRXU WXEHV DUH DUUDQJHG LQ SDUDOOHO ZLWK HDFK 6WDUOLQJ UHVLVWRU KDYLQJ D GLIIHUHQW 3V WKHQ WKH UHODWLRQ

PAGE 139

GHPRQVWUDWHV D FXUYHG SRUWLRQ IURP SRLQW $ WR SRLQW 'f DQG D OLQHDU SRUWLRQ EH\RQG SRLQW 'f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f WR H[KLELW FULWLFDO FORVXUH WKDW LV FHVVDWLRQ RI IORZ ZKLOH WKHUH LV VWLOO D SUHVVXUH JUDGLHQW EHWZHHQ SXOPRQDU\ DUWHU\ DQG OHIW DWULXP 7KH LQWHUFHSW RI WKH SUHVVXUHFIORZ FXUYH KDV EHHQ XVHG DV D PHDVXUH RI WKLV FULWLFDO FORVLQJ SUHVVXUH DQG KDV DOVR EHHQ XVHG WR DVVHVV WKH VWDWH RI WRQXV RI WKH SXOPRQDU\ EHG f &DVVLQ f KDV SUHVHQWHG SUHVVXUH IORZ FXUYHV ZKLFK VKRZ DQ LQFUHDVH LQ UHVLVWDQFH \HW WKH LQWHUFHSW LV OHVV WKDQ WKH LQWHUFHSW RI WKH FRQWURO FXUYHV 7KHVH GDWD DUH GLIILFXOW WR H[SODLQ LI WKH LQWHUFHSW LV DQ LQGLFDWRU RI WKH WRQXV RI WKH YDVFXn ODWXUH +RZHYHU ILJXUH LQGLFDWHV WKDW LQ FHUWDLQ LQVWDQFHV WKH PRGHO SUHVHQWHG LQ WKLV VWXG\ ZRXOG SUHGLFW D GHFUHDVHG LQWHUFHSW ZLWK RQO\ DQ LQFUHDVH LQ UHVLVWDQFH )LJXUH VKRZV WKDW WKH DFWLRQV RI WKH SK\VLFDO PRGHO FRUUHVSRQG WR WKRVH SUHGLFWHG E\ WKH PDWKHPDWLFDO PRGHO LQ ILJXUH r 3HUPXWW f KDV LQGLFDWHG WKDW WKH LQWHUFHSW RI WKH SUHVVXUHIORZ FXUYH LV HTXLYDOHQW WR WKH PHDQ FULWLFDO FORVLQJ SUHVVXUH +H LQGLFDWHV WKDW WKH LQWHUFHSW LV WKH PHDQ RI DOO WKH YDOXHV IRU 3 RI WKH YHVVHOV

PAGE 140

EHLQJ SHUIXVHG 7KH PRGHO SUHVHQWHG LQ WKLV VWXG\ GRHV QRW LQGLFDWH WKDW WKH LQWHUFHSW RI WKH SUHVVXUHUIORZ FXUYH LV WKH DULWKPHWLF PHDQ RI DOO WKH 3 YDOXHV EXW WKDW WKH LQWHUFHSW LV LQIOXHQFHG DOVR E\ UHVLVWDQFH )RU D V\VWHP RI WKUHH WXEHV WKH LQWHUFHSW RQ WKH DEVFLVVD RI WKH SUHVVXUHIORZ FXUYH LV HTXDO WR WKH H[SUHVVLRQ 36L5Sf53f S653Of53f S65SMf53f f:M775SS 5S_f 5SAf 53f 5Sf 7KLV H[SUHVVLRQ ZDV REWDLQHG VLPSO\ E\ VROYLQJ WKH HTXDWLRQ IRU D VWUDLJKW OLQH ; f§ < D ZKHUH P LV VORSH DQG D LV WKH LQWHUFHSW RI WKH DEVFLVVD $FFRUGLQJ WR WKH H[SUHVVLRQ JLYHQ DERYH WKH LQWHUFHSW LV LQIOXHQFHG QRW RQO\ E\ 3 EXW DOVR E\ UHVLVWDQFH &OHDUO\ D FKDQJH LQ UHVLVWDQFH DORQH ZRXOG FKDQJH WKH LQWHUFHSW DV VHHQ LQ ILJXUHV DQG 7KH LQWHUFHSW PD\ EH WKRXJKW RI DV D ZHLJKWHG PHDQ RI DOO WKH YDOXHV IRU S6 7KH FXUYHG SRUWLRQ RI WKH SUHVVXUHIORZ FXUYH ILJXUH f FDQ EH H[SODLQHG E\ FRQVLGHULQJ WKH HYHQWV WKDW RFFXU DW HDFK EUHDNSRLQW $V 3c LQFUHDVHV QR IORZ RFFXUV XQWLO 3c EHFRPHV JUHDWHU WKDQ WKH ORZHVW 36 SRLQW $f $W SRLQW % 3c KDV EHFRPH JUHDWHU WKDQ ERWK 3M DQG 3 DQG IORZ EHJLQV WR RFFXU LQ WZR WXEHV LQVWHDG RI RQH %\ DGGLQJ DQRWKHU WXEH LQ SDUDOOHO ZLWK WKH ILUVW 5S GHFUHDVHV DQG WKH VORSH RI WKH SUHVVXUHIORZ FXUYH LQFUHDVHV 7KHVH VDPH HYHQWV WDNH SODFH DW SRLQWV & DQG %H\RQG IORZ LV RFFXUULQJ LQ DOO WXEHV DQG WKH UHODWLRQ EHWZHHQ 3c DQG EHFRPHV OLQHDU VLQFH UHVLVWDQFH LV FRQVWDQW 7KLV SKHQRPHQRQ LV LQYROYHG LQ WKH EHKDYLRU RI WKH UHODWLRQ EHWZHHQ 3c DQG 3 VKRZQ LQ ILJXUHV DQG ,

PAGE 141

7KH GDVKHG OLQH LQ ILJXUH FRQQHFWV WKH ILUVW EUHDNSRLQW RI HDFK FXUYH EXW GRHV QRW LQWHUVHFW WKH EUHDNSRLQW RI WKH ]HUR IORZ FXUYH )RU DOO WKH FXUYHV LQ ILJXUH IORZ LV RFFXUULQJ WKURXJK DOO WKH WXEHV )LJXUH GHPRQVWUDWHV VRPH FXUYHV REWDLQHG ZKHQ IORZ ZDV RFFXUULQJ WKURXJK RQO\ D SDUWLDO QXPEHU RI WXEHV 7KH GDVKHG OLQH LQ ILJXUH FRQQHFWV WKH ILUVW EUHDNSRLQW RI HDFK FXUYH DQG H[KLELWV D FXUYHG SRUWLRQ DQG D OLQHDU SRUWLRQ 7KH YDOXH ZKLFK 3c DVVXPHV DW D JLYHQ IORZ UDWH LV GHSHQGHQW XSRQ WZR IDFWRUV SUR[LPDO UHVLVWDQFH DQG 3 $V ORQJ DV 5S DQG 3 DUH FRQVWDQW WKH ILUVW EUHDNSRLQW RI HDFK FXUYH ZLOO IRUP D VWUDLJKW OLQH 7KLV LV WKH FDVH LQ ILJXUH IRU WKH FXUYHV GUDZQ DW A DQG POPLQ EHFDXVH LQ HDFK FXUYH IORZ LV SURFHHGLQJ WKURXJK DOO WXEHV +RZHYHU IRU WKH FXUYH GUDZQ DW POPLQ IORZ LV RFFXUULQJ WKURXJK RQO\ WKUHH RI WKH IRXU WXEHV VLQFH 3c 36r 5HPRYLQJ RQH WXEH IURP WKH SDUDOOHO FLUFXLW LQFUHDVHV 5S EXW 3V LV GHFUHDVHG 7KH 3V UHIHUUHG WR KHUH LV WKH ZHLJKWHG PHDQ 3 RU WKH LQWHUFHSW RI WKH VWUDLJKW OLQH SRUWLRQ RI WKH SUHVVXUHIORZ FXUYH $W DQ\ FRQVWDQW IORZ UDWH DQ LQFUHDVH LQ 5S ZRXOG LQFUHDVH 3c EXW D GHFUHDVH LQ 3V ZRXOG GHFUHDVH 3c 7KH UHVXOW RI WKHVH WZR IDFWRUV LV WKDW WKH 3c IRU WKH FXUYH GUDZQ DW POPLQ LQ ILJXUH LV ORZHU WKDQ LW ZRXOG EH LI IORZ FRXOG RFFXU LQ DOO IRXU WXEHV 7KH ILUVW EUHDN RQ DOO FXUYHV RFFXUV ZKHQ 3* EHFRPHV JUHDWHU WKDQ 3V@ DQG RFFXUV DW WKH VDPH 34 UHJDUGOHVV RI ZKDW 5S RU WKH ZHLJKWHG PHDQ 3 DUH 7KH EUHDNSRLQW RI WKH POPLQ FXUYH GRHV QRW IDOO RQ D VWUDLJKW OLQH ZLWK WKH FXUYHV RI A DQG POPLQ RQO\ EHFDXVH WKH 3c LV ORZHU WKDQ LW ZRXOG EH LI IORZ FRXOG RFFXU WKURXJK DOO IRXU WXEHV DV LQ WKH RWKHU FXUYHV

PAGE 142

$QLPDOV %HIRUH WKH UHVXOWV REWDLQHG IURP WKH DQLPDOV DUH GLVFXVVHG LW LV QHFHVVDU\ WR FRQVLGHU ZKDW FRQVWLWXWHV 3 3V ZDV WHUPHG VXUURXQGLQJ SUHVVXUH EHFDXVH LQ WKH SK\VLFDO PRGHO ILJXUHV DQG $f LW ZDV VLPXODWHG E\ WKH K\GURVWDWLF SUHVVXUH RI WKH ZDWHU VXUURXQGLQJ WKH 6WDUOLQJ UHVLVWRU +RZHYHU DQ\ IRUFH ZKLFK WHQGV WR FORVH WKH 6WDUOLQJ UHVLVWRU ZRXOG FRQWULEXWH WR 3 ,Q WKH DQLPDO 3V LV SUREDEO\ QRW PDGH XS RI VLPSO\ D K\GURVWDWLF SUHVVXUH VXUURXQGLQJ YHVVHOV ,W LV SUREDEO\ D FRPELQDWLRQ RI LQWHUVWLWLDO SUHVVXUH DOYHRODU SUHVVXUH VPRRWK PXVFOH WRQH DQG RWKHU IRUFHV 6HYHUDO LQYHVWLJDWRUV KDYH UHSRUWHG YDOXHV IRU WKH LQWHUVWLWLDO SUHVVXUH LQ WKH OXQJ f )RU DGXOW FORVHG FKHVW DQLPDOV WKH YDOXHV UHSRUWHG DUH DURXQG a6 PP+J $OO RI WKH DQLPDOV WKDW ZHUH XVHG LQ WKH SUHVHQW VWXG\ ZHUH RSHQ FKHVW 0HO LQV HW DO f KDYH VKRZQ WKDW LQWHUVWLWLDO SUHVVXUH LV UHODWHG WR SOHXUDO SUHVVXUH VXJJHVWLQJ WKDW LQ DQ RSHQ FKHVW DQLPDO WKH LQWHUVWLWLDO SUHVVXUH PLJKW QRW EH DV QHJDWLYH DV LQ D FORVHG FKHVW DQLPDO ,Q DGGLWLRQ WKH OXQJV RI VRPH RI WKH DQLPDOV LQ WKH SUHVHQW VWXG\ ZHUH ILOOHG ZLWK OLTXLG UDWKHU WKDQ DLU $JDLQ 0HOOLQV KDV LQGLFDWHG WKDW WKH LQWHUVWLWLDO SUHVVXUH LQ D IOXLGILOOHG OXQJ LV QRW DV QHJDWLYH DV LQ DQ DLUILOOHG OXQJ
PAGE 143

/RSH]0XQL] HW DO f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n WXUH ZDV SDUDO\]HG E\ GLUHFW LQMHFWLRQ RI QLJ RI SDSDYHULQH K\GURn FKORULGH 7KH LQMHFWLRQ ZDV PDGH LQWR WKH SXOPRQDU\ DUWHU\ RI WKH IOXLGaIL OHG OHIW OXQJ RI WZR IHWXVHV LQ ZKLFK WKH ULJKW OXQJ ZDV EHLQJ YHQWLODWHG ZLWK DLU 7KH LQMHFWLRQ UHVXOWHG LQ D GHFUHDVH LQ 3 IURP WR PP+J LQ RQH DQLPDO DQG IURP WR PP+J LQ WKH RWKHU 7KH LQMHFWLRQ ZDV DOVR PDGH LQWR WKH IOXLGILOOHG OHIW OXQJ RI WZR IHWXVHV ZKLOH ERWK OXQJV ZHUH LQ WKH XQYHQWLODWHG VWDWH 3V GHFUHDVHG IURP WR PP+J LQ RQH DQLPDO DQG IURP WR PP+J LQ WKH RWKHU 7KHVH IHZ H[SHULPHQWV LQGLFDWH WKDW VPRRWK PXVFOH GRHV FRQWULEXWH WR 3V ,Q QRQH RI WKHVH IRXU DQLPDOV ZDV D 3V HYHU PHDVXUHG WKDW DSSURDFKHG PP+J 7KLV LV LQWHUHVWLQJ VLQFH 1LFKRO HW DO f IRXQG WKDW WKH FULWLFDO FORVLQJ SUHVVXUH LQ WKH KLQGOLPE RI WKH IURJ FRXOG QRW EH UHGXFHG WR PP+J HYHQ E\ SHUIXVLRQ ZLWK 5LQJHUnV VROXWLRQ DQG

PAGE 144

r SRLVRQLQJ ZLWK VRGLXP F\DQLGH 1RW XQWLO D ZHWWLQJ DJHQW ZDV LQWURn GXFHG LQWR WKH SHUIXVLQJ IOXLG GLG KH REWDLQ FULWLFDO FORVLQJ SUHVVXUHV RI PP+J 7KHVH UHVXOWV VXJJHVWHG WKDW WKHUH ZHUH VXUIDFH WHQVLRQ IRUFHV WHQGLQJ WR FROODSVH YHVVHOV EHWZHHQ WKH YHVVHO ZDOO DQG WKH SHUIXVLRQ IOXLG ZKLFK GLG QRW FRPSOHWHO\ ZHW WKH ZDOO ,W LV SRVVLEOH WKDW WKHUH PD\ EH VXFK IRUFHV H[LVWLQJ LQ WKH SXOPRQDU\ YDVFXODWXUH ZKLFK DOVR FRQWULEXWH WR 3 $V VKRZQ LQ ILJXUH 3 LV KLJK LQ WKH XQYHQWLODWHG IHWDO OXQJ PP+Jf EXW GHFUHDVHG WR PP+J ZKHQ WKH OXQJV ZHUH YHQWLODWHG ZLWK DLU +RZHYHU LQ QHZERUQ DQLPDOV PRUH WKDQ rr KRXUV ROG 3 DYHUDJHG PP+J ILJXUH f ZKLOH WKHVH OXQJV ZHUH EHLQJ YHQWLODWHG ZLWK DLU ,Q ERWK JURXSV WKH OXQJV ZHUH YHQWLODWHG ZLWK DLU EXW LQ WKH QHZO\ YHQWLODWHG OXQJV RI WKH IHWXV 3 ZDV KLJKHU WKDQ LQ QHZERUQ JRDWV 5S ZDV DOVR KLJKHU LQ WKH IHWDO OXQJV QHZO\ YHQWLODWHG ZLWK DLU PP+Jr.JPLQPOf WKDQ LQ WKH QHZERUQ OXQJV YHQWLODWHG ZLWK DLU 2r} PP+J f .J rPL QPOf 5HPRYDO RI IOXLG IURP QHZO\ YHQWLODWHG OXQJV PD\ DFFRXQW IRU WKH GLIIHUHQFH LQ 3V DQG 5S $KHUQH DQG 'DZNLQV f DQG +XPSKUH\V HW DO f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

PAGE 145

:KHQ XQYHQWLODWHG IHWDO OXQJV ZHUH YHQWLODWHG ZLWK IHWDO JDV ILJXUH f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f YHVVHOV DFWLQJ DV 6WDUOLQJ UHVLVWRUV DUH WKRVH H[SRVHG WR DOYHRODU SUHVVXUH SUHVXPDEO\ FDSLOODULHV DV ZHOO DV VPDOO DUWHULROHV DQG YHQXOHV ,Q WKH H[SHULPHQWV SUHVHQWHG KHUH PHDVXUHPHQWV ZHUH PDGH ZKHQ DOYHRODU SUHVVXUH ZDV PP+J 7KHUHIRUH YHVVHOV ZKLFK DFW DV 6WDUOLQJ UHVLVWRUV DUH QRW QHFHVVDULO\ WKH VDPH DV ZKHQ DOYHRODU SUHVVXUH LV JUHDWHU WKDQ PP+J 7KHUH LV LQGLUHFW HYLGHQFHKRZHYHU ZKLFK VXJJHVWV WKDW WKH 6WDUOLQJ UHVLVWRUV PD\ EH ORFDWHG LQ YHVVHOV GLVWDO WR FDSLOODULHV LQ ERWK WKH IXLGaIL OHG DQG YHQWLODWHG OXQJ ,Q IHWDO DQLPDOV WKH OXQJV SURGXFH IOXLG ZKLFK FRPHV RXW WKH WUDFKHD )OXLG LQ IHWDO OXQJV LV SURGXFHG PDLQO\ E\ ILOWUDWLRQ DW WKH FDSLOODU\ OHYHO WKXV QHFHVn VLWDWLQJ D KLJK FDSLOODU\ K\GURVWDWLF SUHVVXUH f $ FDSLOODU\

PAGE 146

SUHVVXUH KLJK HQRXJK IRU ILOWUDWLRQ ZRXOG EH SRVVLEOH LI WKH 6WDUOLQJ UHVLVWRUV ZHUH GLVWDO WR FDSLOODULHV )LOWUDWLRQ ZRXOG EH GLIILFXOW WR H[SODLQ LI WKH 6WDUOLQJ UHVLVWRUV ZHUH SUR[LPDO WR FDSLOODULHV 7KH SUHOLPLQDU\ H[SHULPHQWV ZLWK SDSDYHULQH PHQWLRQHG DERYH VXJJHVW WKDW VPRRWK PXVFOH FRQWULEXWHV WR 3 6PRRWK PXVFOH LV DOVR LPSOLFDWHG E\ ILJXUHV A DQG LQ ZKLFK ERWK LQFUHDVHG 3T DQG EUDG\NLQLQ FDXVHG 3 WR GHFUHDVH LQ WKH XQYHQWLODWHG OXQJ ,W LV GRXEWIXO LI VPRRWK PXVFOH H[LVWV LQ FDSLOODULHV RU HYHQ LQ WKH VPDOOHU YHQXOHV f VR WKDW WKH 6WDUOLQJ UHVLVWRUV ZRXOG KDYH WR EH LQ YHVVHOV DW OHDVW DW WKH OHYHO RI ODUJH YHQXOHV LI WKH\ DUH GLVWDO WR FDSLOODULHV ,Q YHQWLODWHG OXQJV %URG\ HW DO f GHWHUPLQHG WKH GLVWULEXWLRQ RI SXOPRQDU\ YDVFXODU UHVLVWDQFH LQ DGXOW GRJV E\ LQMHFWLQJ D ORZ YLVFRVLW\ IOXLG LQWR WKH SXOPRQDU\ DUWHU\ DQG REVHUYLQJ WKH HIIHFW RQ SXOPRQDU\ DUWHU\ SUHVVXUH 7KH\ UHSRUWHG QRUPDOO\ r}b RI WKH WRWDO UHVLVWDQFH ZDV ORFDWHG LQ WKH SXOPRQDU\ DUWHULHV Ab LQ WKH FDSLOODULHV DQG b LQ SXOPRQDU\ YHLQV ,Q RWKHU ZRUGV b RI WKH WRWDO UHVLVWDQFH ZDV IRXQG LQ YHVVHOV GRZQ WR WKH HQG RI WKH FDSLOODULHV ,Q ILJXUH LQ WKH IHWXVHV YHQWLODWHG ZLWK DLU EDUV ODEHOOHG 9$f 5S DFFRXQWHG IRU $b RI WKH WRWDO UHVLVWDQFH DQG 5J DFFRXQWHG IRU b ,Q ILJXUH LQ WKH QHZERUQ DQLPDOV YHQWLODWHG ZLWK DLU 5S FRQVWLWXWHG a@Kb RI WKH WRWDO UHVLVWDQFH DQG 5J FRQVWLWXWHG b ,I WKH GLVWULEXWLRQ RI UHVLVWDQFH LV WKH VDPH LQ WKHVH WZR JURXSV RI DQLPDOV DV LQ DGXOW GRJV WKLV ZRXOG VXJJHVW WKDW 5S LQFOXGHG UHVLVWDQFH RIIHUHG E\ DUWHULHV DQG FDSLOODULHV LQGLFDWLQJ WKDW WKH 6WDUOLQJ UHVLVWRUV DUH DW OHDVW DW WKH HQG RI WKH FDSLODULHV )LJXUHV DQG LQGLFDWH WKH UHODWLRQ EHWZHHQ 5S DQG SXOPRQDU\ DUWHULDO 3T LQ ERWK WKH YHQWLODWHG DQG XQYHQWLODWHG OXQJ 7KH UHODWLRQ

PAGE 147

LQ ERWK W\SHV RI OXQJV LV EDVLFDOO\ WKH VDPH LQ WKDW 5S GHFUHDVHV PDUNHGO\ XS WR D 3 RI DERXW E2 PP+J 5DLVLQJ 3 KLJKHU GRHV QRW GHFUHDVH 5S IXUWKHU 7KH VDPH SDWWHUQ LV GHPRQVWUDWHG LQ WKH UHODWLRQ EHWZHHQ 5J DQG SXOPRQDU\ YHQRXV 3 LQ ILJXUHV DQG 5J GHFUHDVHV DV 3 LQFUHDVHV XS WR A PP+J $W KLJKHU YDOXHV IRU 3R! 5G UHPDLQV WKH VDPH 5XGROSK DQG b 2f 5S DQG 5J URVH VLJQLILFDQWO\ DV GLG 3 DOVR 3UREDEO\ WKHVH HIIHFWV FDQ EH H[SODLQHG EHVW E\ WKH FRQVWULFWLRQ RI YDVFXODU VPRRWK PXVFOH LQ UHVSRQVH WR WKH K\SR[LD 7KH HIIHFWV RI R[\JHQ RU WKH ODFN RI LW RQ WKH SXOPRQDU\ FLUFXODWLRQ PD\ DOVR EH GXH LQ SDUW WR UHIOH[ QHUYRXV FRQWURO LQLWLDWHG E\ FKHPR UHFHSWRUV +RZHYHU WKHUH LV DOVR HYLGHQFH WR LQGLFDWH WKDW WKH ZDWHU FRQWHQW RI WKH OXQJ LQFUHDVHV LQ UHVSRQVH WR K\SR[LD f ,I

PAGE 148

ZDWHU ,V ORVW IURP SXOPRQDU\ YHVVHOV LQWR WKH SHULYDVFXODU VSDFHV WKH LQFUHDVH LQ LQWHUVWLWLDO SUHVVXUH FDXVHG E\ WKH ZDWHU PLJKW DOVR FRQn WULEXWH WR WKH ULVH LQ 5S 5S DQG 3 LQ UHVSRQVH WR K\SR[LD )LJXUHV DQG LQGLFDWH WKDW EUDG\NLQLQ FDXVHV D UHGXFWLRQ LQ 5S LQ ERWK WKH XQYHQWLODWHG DQG YHQWLODWHG OXQJ +RZHYHU LQ QHLWKHU VWDWH ZDV 5S GHFUHDVHG E\ EUDG\NLQLQ 7KHVH UHVXOWV DUH LQ DJUHHPHQW ZLWK WKRVH DOUHDG\ UHSRUWHG LQ ZKLFK EUDG\NLQLQ SURGXFHG D GHFUHDVH LQ SXOPRQDU\ YDVFXODU UHVLVWDQFH $2 E f +RZHYHU WKH\ DUH QRW LQ DJUHHPHQW ZLWK WKH UHVXOWV RI +\PDQ Af ZKR VXJJHVWHG WKDW EUDG\NLQLQ FDXVHG DQ DFWLYH YHQRFRQVWULFWLRQ ZKLFK ZDV PDVNHG E\ D SDVVLYH DUWHULDO GLODWDWLRQ LQ UHVSRQVH WR DQ LQFUHDVH LQ FDUGLDF RXWn SXW FDXVHG E\ WKH EUDG\NLQLQ ,Q WKH UHVXOWV SUHVHQWHG LQ ILJXUHV DQG EUDG\NLQLQ ZDV VKRZQ QRW WR LQFUHDVH VLJQLILFDQWO\ 5S ZKLFK SUREDEO\ FRQWDLQV WKH SXOPRQDU\ YHLQV $OVR WKH GHFUHDVH LQ 5S GHPRQVWUDWHG E\ WKHVH GDWD FRXOG QRW EH D SDVVLYH RQH LQ UHVSRQVH WR DQ LQFUHDVH LQ IORZ VLQFH 5S ZDV FDOFXODWHG DW WKH VDPH IORZ UDWHV EHIRUH GXULQJ DQG DIWHU WKH LQIXVLRQ RI EUDG\NLQLQ 7KH GDWD SUHVHQWHG LQ ILJXUHV DQG RIIHU QR GLUHFW VXSSRUW IRU WKH SURSRVDO RI VRPH r} f WKDW EUDG\NLQLQ LV WKH PHGLDWRU RI WKH FLUFXODWRU\ FKDQJHV WKDW RFFXU XSRQ YHQWLODWLRQ RI IHWDO OXQJV +RZHYHU WKH GDWD SUHVHQWHG LQ WKHVH H[SHULPHQWV ZRXOG EH FRPSDWLEOH ZLWK VXFK D SURSRVDO )LJXUH GRHV VKRZ WKDW EUDG\NLQLQ UHGXFHV UHVLVWDQFH LQ IHWDO OXQJV 5XGROSK DQG
PAGE 149

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f VKRZV WKDW WKH PHFKDQLFDO HYHQWV DFFRPSDQ\n LQJ YHQWLODWLRQ SOD\ D SDUW LQ UHGXFLQJ SXOPRQDU\ UHVLVWDQFH ,W ZDV DOVR LQWHUHVWLQJ WR VWXG\ EUDG\NLQLQ LQ YLHZ RI LWV SRVn VLEOH XVH LQ WKH WUHDWPHQW RI UHVSLUDWRU\ GLVWUHVV V\QGURPH LQ QHZERUQV &KX HW DO Af DQG 6WUDQJ f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f

PAGE 150

6800$5< $1' &21&/86,216 $ PRGHO ZDV SURSRVHG WR FDOFXODWH UHVLVWDQFH LQ WZR VHJPHQWV RI WKH SXOPRQDU\ FLUFXODWLRQ EDVHG RQ WKH FRQFHSW WKDW WKH SXOPRQDU\ YDVFXODU EHG FRQWDLQV 6WDUOLQJ UHVLVWRUV 7KLV PRGHO ZDV XVHG DOVR WR H[SODLQ WKH UHODWLRQ EHWZHHQ SXOPRQDU\ DUWHU\ SUHVVXUH DQG SXOPRQDU\ YHQRXV SUHVVXUH DQG EHWZHHQ SXOPRQDU\ DUWHU\ SUHVVXUH DQG IORZ H[KLELWHG E\ WKH SXOPRQDU\ FLUFXODWLRQ &KDQJHV LQ UHVLVWDQFH SUR[LPDO 5Sf DQG GLVWDO 5Gf WR WKH 6WDUOLQJ UHVLVWRUV DQG VXUURXQGLQJ SUHVVXUH 3Vf LQ UHVSRQVH WR YHQWLODWLRQ FKDQJHV LQ EORRG JDVHV DQG EUDG\NLQLQ LQ PDWXUH IHWDO JRDWV DQG K\SR[LD LQ QHZERUQ JRDWV ZHUH UHSRUWHG f D 9HQWLODWLRQ RI ERWK OXQJV ZLWK D JDV WKDW GLG QRW FKDQJH EORRG JDVHV IHWDO JDVf UHVXOWHG LQ D GHFUHDVH LQ 5S DQG 3V 9HQWLODWLRQ ZLWK DLU FDXVHV 5S 5J DQG 3V WR GHFUHDVH HYHQ IXUWKHU E 9HQWLODWLRQ RI WKH ULJKW OXQJ RQO\ ZLWK IHWDO JDV SURGXFHG QR FKDQJH LQ 5S 5S RU 3V LQ WKH OHIW OXQJ EXW DOO WKUHH YDOXHV GHFUHDVHG XSRQ YHQWLODWLRQ RI WKH ULJKW OXQJ ZLWK DLU F 5S 5T DQG 3V LQFUHDVHG LQ UHVSRQVH WR K\SR[LD b cQ 1f LQ QHZERUQ JRDWV G %UDG\NLQLQ LQIXVLRQ FDXVHG 5S DQG 3V WR GHFUHDVH LQ XQYHQWLODWHG IHWXVHV EXW UHVXOWHG LQ D GHFUHDVH LQ RQO\ 5S LQ IHWXVHV YHQWLODWHG ZLWK DLU $ 7KH VLWH RI WKH 6WDUOLQJ UHVLVWRUV LQ WKH SXOPRQDU\ EHG ZDV GLVFXVVHG DQG SURSRVHG WR EH GLVWDO WR FDSLOODULHV LQ ERWK XQYHQWLODWHG DQG YHQWL O$2 ODWHG DQLPDOV

PAGE 151

$33(1',; 3URJUDPV IRU +HZOHWW3DFNDUG XVHG Q WKLV LQYHVWLJDWLRQ FDOFXODWRU I

PAGE 152

7LULR 3[L-JML6LLLB-BB(\HLXVB(!LQB4QDB-EHAQLRH@f 3&L42 BB QVVRORY 6RUVTH 6WHS .H\ ; \ ] I H G F E D fR L R B FOHDU LQW 5S 4 MO VWRS n URO U c G Oi E URO 5' UG c UG /D UG cf ; cF URO B <4 f S H Q D c I;< F c= URO L U V E c ; OLL D /E F /LG

PAGE 153

r} 7LW 3URJUDP FRQWf 6WHS .H\ 'LVSOD\ r 6WRUDQR ; \ ; L H G F E D YV ; 7 H URO ,W c ? $ /L c ; URO c )07 c /D FOHDU; OE O& ,G H R JRWRf // F c URO + /?O E c ; URO  M /r _E ; e H 6FO URO L

PAGE 154

+LOH 3UrJ UDP BFRQWf ,0} 6WHS .H\ 'LVSOD\ 6WR UHQH ; \ ] I FO F E D D L f V UU  ; ,, & URO L U r )07 c L > FOHDU; c cD H /2 JRWRf F cG c  c > / c c c Oe /E F / FO

PAGE 155

7LWOH 3URJUDP SDUW 3c YHUVXV 3' LQ IRXU 3DJH WXEH PRGHO IORZ LQ DOO WXEHV &r -/ B .H\ 'LVRLDY 6 IRUFHMH EWHS ; \ ] I H F F E &O RLJ OHDU; 36 S6 36" 3VM cL c A VWRS c RO I c c /, 0f c D > r' LG r' /N URO I F MG n4 /L ; c URO c c 0f > E ,6 F ,, c L I;< c D Lr URO LE G F LG H ,

PAGE 156

A 7LILR 3URUDP SDUW FRQWf 3*WM2 2 .H\ 'LVSOD\ 6WRUDJH R L *S ; \ ] H F F E D 7R f c7 I + 9 L 4 r 4 4 URO 5 5 c ; /D URO >E G • I L I;!< ?-a N A ,9 LL 5 /9 ; c D c URO c /e ,E /F ; /N URO

PAGE 157

7LWOH 3URJUDP SDUW FRQWf 3DJH .H\ 'LVSOD\ 6WRL nfJR RLHS ; \ ] -O H FO & E D )07 D /i MRWR2 c F c URO + 4 /6, nT D ; 4 D URO G Lk L ; RO )07 O D `RWRf n c Oe G LE c I;< LG F

PAGE 158

ILOOV 3URUDQL SDUW FRQWf 3DJV 6W VS .H\ 'LVSOD\ 6WR UFDR ; \ ] U U FO F E D > nL H + I ,6  4 O 4 O= t URO 5 /IL 5 /E ; & UROO M FO 8* I /" I O L I;!< O / ; D Oe URO -O & R B LO R

PAGE 159

7LW 3URJUDP SDUW FRQWf 3DJR 6WHS .H\ a 'LL7GY 6WRUDJH ; \ ] $ H FO F E T & f ; URO U OL L O )07 ?O @f D OL 7a 2 c U e OL f R 8 U E LF / f URO OL f R OL ; L D c& f URO O L ] ,I f [ e f URO + OL f )07 X c D ,& A ,I JRWRf L /W OL VWrS _& L L Â’

PAGE 160

7LWOH 3URJUDP SDUW 'LVSOD\ 6IRUDQR RnL&S .H\ ; \ ; L H G F E D R > E 36L} 36 36 LiL 3R SR URO H LI;< $ > ; ,UQM H O >4 I LE _& 4 FL 2 4 URO + 5 5 $ ; O URO I D c I;!< F ,G

PAGE 161

7LILR SURJUDP SDUW FRQWf 3DJR r .H\ 'LVRODY 6IRL n*IM2 RLFS ; \ I G F E D O2 ,, ; c D URO ,W G L > > ; URO 7 )07 /IO E D & JRWRf G c E O URO I G ; G D URO Oe E ; F URO ,G )07

PAGE 162

7LWO2 3URUDP SDUW FRQWf BB 3HLQR HS .H\ 'LVSOD\ ; \ ] I 4 ,, D URO ?$ /n URO + > /H ,E cI;< c ; c I /L 4 ,E 4 /F 4 LG URO + Z!

PAGE 163

I MI_4 B3URJ UDP SDUW B FRQWf 3DJH .H\ 'LVSOD\ 6WRUFIOR WHS ; \ I H G F E c 5 c, 5 ; URO N I = I / c I;!< /D G >E /r -G ; n/4 D /B UROO W c ; URO SL c )07 c D JRWRf N F F E

PAGE 164

r} 7LILR 3URJUDP SDUW FRQWf 3DJH .H\ 'LVSOD\ 6W HUDULR 6S ; \ R U G F E D c URO W L L c ; / D ,URO ,W > /, / > ; _FL URO )07 /F LG D c JRWRf O } c c VWRS 9 c ‘D /L 3 LG

PAGE 165

7M+H 3URJUDP SDUW 3DJH B 6WHS .H\ 'LVSOD\ 6IRUDQR ; \ ] b& H _G F E &O ROR E 36$ S6 L6LO SVL 3R 3T Q URO 4 c 4 c 4 URO ,W c 5 ,, 5 c ; $ D I >E URO & -LL n ,4 c ; D / URO /L ` LL ; c URO c )07 /L W E D OF URO -G

PAGE 166

7LILR B URJUDP SDUW FRQWf 6WHS .H\ 'LVSOD\ 6 IRUDQR n ; \ ] L H F F E D ^R cL Lr D c E c URO c > ,, 0f i E c JRWRf c, /E cF LG // / > ^ c c / LL ce /OL-

PAGE 167

7LILH} 3URJUDP SDUW 3c YHUVXV 34 LQ IRXU 3IL+L2 f U L LU P , nr1LU ‘ ‘ f}f§f}m 7 U U XU f§ fn} fO Q! }m}rn rfrf WXEH PRGHO IORZ LQ SDUWLDO QXPEHU RI WXEHV 6WHS c .H\ FOHDU; c ,, /D fE I I D URO I F OHL ‘ /L /KL /L /i n c /e 4 4 4 URO I 5S 5S ; [ URO ,I
PAGE 168

OLWLR 3URJUDPBBBBBBJDMW FRQW‘f m aH n 3HJR R r .H\ '7V,JY f 6 WRUHTH 6WHS ; \ ] U L G F E D R 5 n 5 ; F /L O6 G O -/ H L V I & K >œ S f§ G I c I;!< O/ O O > Fr ,6 ; D c URO ,W 2 Oe O ; F UR@ ,G )07

PAGE 169

7L _T 3URJUDP SDUW FRQWf 6WHS .H\ n'LVSOD\ 6IRUFHR ; \ MU L H G F E D @3B K D c JRWRf c E f E ; I > cD I ,E H F c I;!< B G / > ; $ LM D ! URO c c c c ; LD URO ,E )07 OF LG D B-

PAGE 170

7LILR 3URJUDP SDUW FRQWf 3&fIMf2

PAGE 171

7cWL I!URUDP SDUW FRQWf 3 3DJH 6WHS .H\ 'OVSU£\ 6WRUDJH ; \ I F F E -/ f L [ G R ; L D L L URO &O E F ; FO URO R )07 L L L D JRWRf UV $ HQG FL E G

PAGE 172

7LILR 3URJUDP SDUW 6WHS .H\ 'LVSOD\ 6 WRUHUR ; f \ ] I H G F E D fc4 E 3V] SV 36 SVL 3R 3R K URO  G c c I;< c f c E 4 , 4 c 4 URO f _& 5 f§ K OL/ 5 LF ; c&O E n c _O G c c H \? ,rn / I _= c K a c I ,D LI;!< E >F F LG

PAGE 173

7LILR B 3URJUDP SDUW FRQWf .H\ 'LVSOD\ 6IRL UFDR RUHS ; \ ] U L H G F E &O rL ; D URO /a c ; R X URO c )07 /J OE D S URO ,W F U M2
PAGE 174

7LWOH 3URJUDP SDUW FRQWf nHS 7R O &/ EM 6O FL L r &EB e G .H\ a 'LVSOD\ 6WRUDJH ; \ ] I H G F f &O I r fI H c I;!< ; D URO ; URO )07 JRWRf E ; H

PAGE 175

7nL* 3URJUDP SDUW FRQWf 3&+-* B 6WHS .H\ 'LVSOD\ 6 WR UHQH ; \  H F F E D O4 L G c I;!< c c c c c ; c D c URO L &O cE /" ,G ; URO )07 c f c JRWRf c c E c c ; c G c ,D LL" OF ; G D L

PAGE 176

O WOR 3URJUDP SDUW FRQWf 6WHS .H\ r 'LVQID\ 6WRUHTR ; \ ] I L G F E D V E URO ,W c > ; URO + )07 , > JRWRf /T E /E HQG >F $ R // c cB c  /i  c /e E LF P

PAGE 177

LI 3URJUDP $ 3c YHUVXV 4 LQ RQH WXEH PRGHO 3FLIM Z

PAGE 178

7LWOH 3URJUDP K FRQWf 6WHS .H\ 'LVSOD\ 6WRUDJH ; \ ] I H G F E D LM2 E OL M [M f§ f§L cURM > c H O ; ? D 2 W2 URO L H OD ; >E URO O& )07 /G >2 JRWRf c, c D URO G c, F c URO I Oe LE URO ce fI -LL H

PAGE 179

7LWk 3URJUDP FRQWf 3DJH 6WHS .H\ 'LVSOD\ ; / ] DR ; c D c URO + c H ; URO )07 c JRWRf c >R > F -G c c ?= } 9 m I c J c cD E & LG I 6WRUDJH G & 4

PAGE 180

7cW-H 3URUDP 3c YHUVXV 4 LQ IRXU WXEH PRGHO 6WHS .H\ 'LVSOD\ a 6WRUDJH ; \ ] I H G F E &L 7 I 3L URO > c URO Yf I O 36MB T /nn 3VL c r O! 5M & 5_ B-G M \O L n&2 1!  36 O 5 U I D LL r E < F E Q

PAGE 181

f 7LLn,2 3URJUDP FRQWf .H\ 'LVSOD\ n 6RUFLTR 6WRS ; \ ] U Q 9 G F E D c2 i-B c S6 c B UB c 5-B c E c= c • rLI c 5LI /D 6 F c >
PAGE 182

7LILR 3URJUDP FRQWf 6WHS .H\ 'LVSOD\ 6WRL n*&_* ; \ ] U ? H G & E D r MR ; f c c ;< cR )07 O c JRWRf  c 36 S6 >2M cI;< ?K MH F cHO H -2 ; D c UROO c H c ; c URO 7 c ;W< ,, )07 UR 7 c JRWR Fc c!B & 36 /N 3r

PAGE 183

7LWOH 3UrUDP FRQWf f'LVSOD\ 6IRL n&L&f2 RUHS L?H\ ; \ ]  G F E D LRL L I;< H Le ; O E c URO O= H O ; O URO LQ ;< E )07 S L ,G JRWRf S ?n] 36 S6 c I;< OJ _= nV H ; F Oe URO /E H ] ; LG URO

PAGE 184

r} 3URJUDP FRQWf 6WHS .H\ 'LVSOD\ 6 IRUFHMR ; \ ] R 9 H HO F E D c2 ,7 [\ )07 c c JRWR4 /i H ; G URO + Oe H LE ; F URO c F ;< /2 )07 c /" JRWRf c c > c c c / /E F OH W

PAGE 185

$33(1',; $X[LOLDU\ GDWD

PAGE 186

7$%/( 'DWD IURP )HWXVHV LQ WKH 8QYHQW L DWHG 6WDWH )f 'XULQJ 9HQWL ODWLRQ RI %RWK /XQJV ZL WK )HWDO *DV 9)*f DQG YL WK $ L U 9$f $QLPDO &RQGLWLRQ 5S U' SV 3XOPRQDU\ $UWHU\ S 3& 3+ ) 9)* ) 9$ ) 9)* ) 9)* 2 9$ ) 9)* 9$ ) 9)* 9$ 9$ ) 9)* 9$ ) 9)* 9$ ) 9)* ) 9$ 9)* 9$ ) 9)* 9$ ) 9)* 9$ ) 9)* 9$

PAGE 187

7$%/( 'DWD IURP $QLPDO IURP 7DEOH &RQGLWLRQ 3$3 393 4 "6 5S U' 8QYHQWLODWHG $YH 9HQWLODWHG ZLWK )HWDO *DV $YH 9HQWLODWHG ZLWK $L U $YH $QLPDO :HLJKW .L RJ UDPV

PAGE 188

7$%/( 'DWD IURP 9HQWLODWHG $QLPDOV %HIRUH %f 'XULQJ 'f DQG $IWHU $f ,QIXVLRQ RI %UDG\NLQLQ $QLPDO &RQGLWLRQ % $ % $ % $ $ % $ % $ % $ % $ 5S 5G 36 $2 3XOP $UWHU\ 3 S& S+ 2 3XOP 9HLQ S SFR S+

PAGE 189

7$%/( 'DWD )URP $QLPDO IURP 7DEOH &RQGLWLRQ 3$3 393 4 3F 5S r' %HIRUH %UDG\NLQLQ  $YH 'XULQJ $ %UDG\NLQLQ f $YH $IWHU %UDG\NLQLQ 2 2 ‘ $YH $QLPDO :HLJKW .LORJ UDPV

PAGE 190

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n ROHV DQG YHVVHOV RI WKH LVRODWHG SHUIXVHG OXQJV $FWD 3K\VLRO 6FDQG 'H%XUJK 'DO\ DQG 0 'H%XUJK 'DO\ 7KH HIIHFW RI VWLPXODWLRQ RI WKH FDURWLG ERG\ FKHPRUHFHSWRUV RQ WKH SXOPRQDU\ YDVFXODU EHG LQ WKH GRJ WKH YDVRVHQVRU\ SHUIXVHG OLYLQJ DQLPDO SUHSDUDWLRQ 3K\VLRO 'H%XUJK 'DO\ DQG 0 'H%XUJK 'DO\ 7KH HIIHFWV RI VWLPXODWLRQ RI WKH FDURWLG ERG\ FKHPRUHFHSWRUV RQ SXOPRQDU\ YDVFXODU UHVLVWDQFH LQ WKH GRJ 3K\VLRO 'DZHV 6 )RHWDO DQG 1HRQDWDO 3K\VLRORJ\ &KLFDJR
PAGE 191

'DZHV 6 DQG & 0RWW 7KH YDVFXODU WRQH RI WKH IRHWDO OXQJ 3K\VLRO AA &DVVLQ 6 6 'DZHV DQG % % 5RVV 3XOPRQDU\ EORRG IORZ DQG YDVFXODU UHVLVWDQFH LQ LPPDWXUH IHWDO ODPEV 3K\VLRO &DVVLQ 6 6 'DZHV & +RWW % % 5RVV DQG / % 6WUDQJ 7KH YDVFXODU UHVLVWDQFH RI WKH IHWDO DQG QHZO\ YHQWLODWHG OXQJ RI WKH ODPE 3K\VLRO /DXHU 5 0 $ (YDQV + $RNL DQG & ) .LWWOH )DFWRUV FRQn WUROOLQJ SXOPRQDU\ YDVFXODU UHVLVWDQFH LQ IHWDO ODPEV 3HGLDW &RRN & 3 $ 'ULQNHU + 1 -DFREVRQ + /HYLVRQ DQG / % 6WUDQJ &RQWURO RI SXOPRQDU\ EORRG IORZ LQ WKH IRHWDO DQG QHZO\ ERUQ ODPE 3K\VLRO &DPSEHOO $ 0 ) &RFNEXUQ 6 'DZHV DQG ( 0LOOLJDQ 3XOPRQDU\ EORRG IORZ DQG FURVV FLUFXODWLRQ EHWZHHQ WZLQ IRHWDO ODPEV 3K\VLRO 3 %URG\ 6 ( 6WHPPLHU DQG $ % 'X%RLV /RQJLWXGLQDO GLVWULn EXWLRQ RI YDVFXODU UHVLVWDQFH LQ WKH SXOPRQDU\ DUWHULHV YHLQV DQG FDSLOODULHV &OLQ ,QY a %HUJRIVN\ ( + ) +DDV DQG 5 3RUFHOOL 'HWHUPLQDWLRQ RI WKH VHQVLWLYH YDVFXODU VLWHV IURP ZKLFK K\SR[LD DQG K\SHUFDSQLD HOLFLW ULVHV LQ SXOPRQDU\ DUWHULDO SUHVVXUH )HGHUDWLRQ 3URF *LOEHUW 5 3 / % +LQVKDZ + .XLGD DQG 0 % 9LVVFKHU (IIHFWV RI KLVWDPLQH K\GUR[\WU\SWDPLQH DQG HSLQHSKULQH RQ SXOPRQDU\ KHPRG\QDPLFV ZLWK SDUWLFXODU UHIHUHQFH WR DUWHULDO DQG YHQRXV VHJn PHQW UHVLVWDQFH $P 3K\VLRO )HHO\ : 7 /HH DQG 9 5 0LOQRU $FWLYH DQG SDVVLYH FRPn SRQHQWV RI SXOPRQDU\ YDVFXODU UHVSRQVH WR YDVRDFWLYH GUXJV LQ WKH GRJ $P 3K\VLRO 6L ORYH ( 7 ,QRXH DQG 5 ) *URYHU &RPSDULVRQ RI K\SR[LD S+ DQG V\PSDWKRPLPHWLF GUXJV RQ ERYLQH SXOPRQDU\ YDVFXODWXUH $SSO 3K\VLRO 6LORYH ( DQG 5 ) *URYHU (IIHFWV RI DOSKD DGUHQHUJLF EORFNDGH DQG WLVVXH FDWHFKRODPLQH GHSOHWLRQ RQ WKH SXOPRQDU\ YDVn FXODU UHVSRQVH WR K\SR[LD &OLQ ,QY AA %DUHU 5 DQG 5 0F&XUULH 3XOPRQDU\ YDVRPRWRU UHVSRQVHV LQ WKH FDW WKH HIIHFWV DQG LQWHUUHODWLRQVKLSV RI GUXJV K\SR[LD DQG K\SHUFDSQLD 4XDUW ([S 3K\VLRO

PAGE 192

+\PDQ $ 7KH GLUHFW HIIHFW RI QRUHSLQHSKULQH DQG DQJLRWHQVLQ RQ WKH SXOPRQDU\ YHLQV RI LQWDFW GRJV 3KDUPDFRO ([S 7KHU %DUHU 5 5HDFWLYLW\ RI YHVVHOV RI FROODSVHG DQG YHQWLODWHG OXQJV WR GUXJV DQG K\SR[LD &LUFXODWLRQ 5HV %DUHU 5 7KH HIIHFW RI FDWHFKRODPLQH EORFNLQJ DQG GHSOHWLQJ DJHQWV RQ WKH FKDQJHV LQ WKH SXOPRQDU\ FLUFXODWLRQ FDXVHG E\ K\SR[LD DQG K\SHUFDSQLD 3K\VLRO 33 +DXJH $ 3 /XQGH DQG % $ :DDOHU (IIHFWV RI SURVWDJODQGLQ (@ DQG DGUHQDOLQH RQ WKH SXOPRQDU\ YDVFXODU UHVLVWDQFH 395f LQ LVRODWHG UDEELW OXQJV /LIH 6FLHQFH 7KLOHQLXV % 0 &DQGLOR DQG / %HXJ (IIHFW RI DGUHn QHUJLF EORFNDGH RQ K\SR[LD LQGXFHG SXOPRQDU\ YDVRFRQVWULFWLRQ LQ DZDNH GRJV $P 3K\VLRO r 6KHSDUG ) 0 : %ODQNHQVKLS DQG 0 6WDKOPDQ &DUGLRYDVFXODU UHVSRQVH RI WKH QHRQDWDO ODPE WR DFHW\OFKROLQH $P 3K\VLRO r +\PDQ $ / 7KH GLUHFW HIIHFWV RI YDVRDFWLYH DJHQWV RQ SXOPRQDU\ YHLQV 6WXGLHV RI UHVSRQVHV WR DFHW\OFKROLQH VHURWRQLQ KLVWDPLQH DQG LVRSURWHUHQRO LQ LQWDFW GRJV 3KDUPDFRO ([S 7KHU r} &KX $ &OHPHQWV ( &RWWRQ 0 + .ODXV DQG $ < 6ZHHW 7KH SXOPRQDU\ K\SRSHUIXVLRQ V\QGURPH 3HGLDWULFV A %MXUH ( +HODQGHU 6( /LQGHO % 6RGHUKROP DQG + :HVWOLQJ (IIHFW RI DFHW\OFKROLQH DQG KLVWDPLQH RQ WKH SXOPRQDU\ FLUFXODWLRQ LQ QRUPDO PHQ DQG ZRPHQ 6FDQG 5HVS 'LV 6DW\DQDUD\DQD 5 % + 0ROOHU DQG ( (GZDUGV 3ULPDU\ SXOn PRQDU\ K\SHUWHQVLRQ LQ D FKLOG 5HVSRQVH WR SKDUPDFRORJLF DJHQWV &LUFXODWLRQ f f } +DJXH $ 5ROH RI KLVWDPLQH LQ K\SR[LF SXOPRQDU\ K\SHUWHQVLRQ LQ WKH UDW %ORFNDGH RU SRWHQWLDWLRQ RI HQGRJHQRXV DPLQHV NLQLQV DQG $73 &LUFXODWLRQ 5HV +DJXH $ DQG 1 & 6WDXE 3UHYHQWLRQ RI K\SR[LF YDVRFRQVWULFWLRQ LQ FDW OXQJ E\ KLVWDPLQH UHOHDVLQJ DJHQW $SSO 3K\VLRO +DJXH $ &RQGLWLRQV JRYHUQLQJ WKH SUHVVRU UHVSRQVH WR YHQWLODWLRQ K\SR[LD LQ LVRODWHG SHUIXVHG UDW OXQJV $FWD 3K\VLRO 6FDQG &DPSEHOO $ 0 6 'DZHV $ 3 )LVKPDQ DQG $ +\PDQ %UDG\NLQLQ DQG SXOPRQDU\ EORRG IORZ LQ WKH IRHWDO OXQJ 3K\VLRO 3

PAGE 193

O -RVNL 5 9 6WDQHN 6 6LQJKDO DQG 1 6HJHO 7KH DFWLRQ RI EUDG\NLQLQ RQ WKH SXOPRQDU\ FLUFXODWLRQ RI QRUPDO PHQ &OLQ 6FLHQFH +\PDQ $ / 7KH HIIHFWV RI EUDG\NLQLQ RQ WKH SXOPRQDU\ YHLQV 3KDUPDFRO ([S 7KHU +H\PDQQ + $ $ 0 5XGROSK $ 6 1HLV DQG / 0HOPRQ %UDG\n NLQLQ SURGXFWLRQ DVVRFLDWHG ZLWK R[\JHQDWLRQ RI WKH IHWDO ODPE &LUFXODWLRQ 5HV A %DQLVWHU DQG 5 : 7RUUDQFH 7KH HIIHFWV RI WKH WUDFKHDO SUHVn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a 3HUPXWW 6 DQG 5 / 5LOH\ +HPRG\QDPLFV RI FROODSVLEOH YHVVHOV ZLWK WRQH WKH YDVFXODU ZDWHUIDOO $SSO 3K\VLRO :HVW % & 7 3 'ROOHU\ DQG $ 1DLPDUN 'LVWULEXWLRQ RI EORRG IORZ LQ LVRODWHG OXQJV UHODWLRQ WR YDVFXODU DQG DOYHRODU SUHVVXUH $SSO 3K\VLRO f :HVW % ,QIOXHQFH RI K\GURVWDWLF SUHVVXUH RQ WKH SXOPRQDU\ FLUFXODWLRQ -DS +HDUW 6KHHKDQ 5 0 $ VOXLFH PRGHO RI WKH FLUFXODWLRQ LQ WKH OXQJ ZLWK VKXQWV &RPS %LRPHG 5HV f f

PAGE 194

&DPSEHOO $ 0 6 'DZHV $ 3 )LVKPDQ DQG $ +\PDQ 3XOPRQDU\ YDVRFRQVWULFWLRQ GXULQJ DVSK\[LD LQ LPPDWXUH IRHWDO ODPEV 3K\VLRO OO33 :DDOHU % $ 7KH HIIHFW RI EUDG\NLQLQ LQ DQ LVRODWHG SHUIXVHG GRJ OXQJ SUHSDUDWLRQ 3K\VLRO 'H3DVTXDOH 1 3 6DQFKH] ( %XUFK DQG $ & 4XLUR] (IIHFWV RI EUDG\NLQLQ RQ WKH SXOPRQDU\ YDVFXODU EHG RI WKH LQWDFW GRJ $P +HDUW 'H)UHLWDV ) 0 ( = )DUDFR DQG ) 'H$]HYHGR *HQHUDO FLUn FXODWRU\ DOWHUDWLRQV LQGXFHG E\ LQWUDYHQRXV LQIXVLRQ RI V\QWKHWLF EUDG\NLQLQ LQ PDQ &LUFXODWLRQ %LVKRS 0 3 +DUULV DQG 1 6HJHO 7KH HIIHFW RI EUDG\NLQLQ RQ WKH SXOPRQDU\ DQG V\VWHPLF FLUFXODWLRQ LQ PDQ 3K\VLRO 3 5XGROSK $ 0 DQG 3 $ 0 $XOG 3K\VLFDO IDFWRUV DIIHFWLQJ QRUn PDO DQG VHURWRQLQ FRQVWULFWHG SXOPRQDU\ YHVVHOV $P 3K\VLRO %RUVW + + 0F*UHJRU / :KL WWHQEHUJHU DQG ( %HUJOXQG ,QIOXHQFH RI SXOPRQDU\ DUWHULDO DQG OHIW DWULDO SUHVVXUHV RQ SXOn PRQDU\ YDVFXODU UHVLVWDQFH &LUFXODWLRQ 5HV $f! 1LFKRO ) *LUOLQJ : -HUUDUG ( % &OD[WRQ DQG $ & %XUWRQ )XQGDPHQWDO LQVWDELOLW\ RI WKH VPDOO EORRG YHVVHOV DQG FULWLFDO FORVLQJ SUHVVXUHV LQ YDVFXODU EHGV $P 3K\VLRO %XUWRQ $ & 2Q WKH SK\VLFDO HTXLOLEULXP RI VPDOO EORRG YHVVHOV $P 3K\VLRO %XUWRQ $ & 7KH UHODWLRQ EHWZHHQ SUHVVXUH DQG IORZ LQ WKH SXOPRn QDU\ EHG ,Q 3XOPRQDU\ &LUFXODWLRQ HGLWHG E\ : 5 $GDPV DQG 9HLWK 1HZ
PAGE 195

$KHUQH : DQG 0 5 'DZNLQV 7KH UHPRYDO RI IOXLG IURP WKH SXOPRQDU\ DLUZD\V DIWHU ELUWK LQ WKH UDEELW DQG WKH HIIHFW RI WKLV RQ SUHPDWXULW\ DQG SUHQDWDO K\SR[LD %LRO 1HRQDW +XPSKUH\V 3 : & 6 1RUPDQG ( 5 5H\QROGV DQG / % 6WUDQJ 3XOPRQDU\ O\PSK IORZ DQG WKH XSWDNH RI OLTXLG IURP WKH OXQJV RI WKH ODPE DW WKH VWDUW RI EUHDWKLQJ 3K\VLRO f 5RVV % % &RPSDULVRQ RI IHWDO SXOPRQDU\ IOXLG ZLWK IHWDO SODVPD DQG DPQLRWLF IOXLG 1DWXUH $GDPV ) + 7 )XMLZDUD DQG 5RZVKDQ 7KH QDWXUH DQG RULJLQ RI WKH IOXLG LQ WKH IHWDO ODPE OXQJ 3HGLDW r :HLEHO ( 5 DQG 0 *RPH] 7KH DUFKLWHFWXUH RI WKH KXPDQ OXQJ 6FLHQFH f 5XGROSK $ 0 DQG 6
PAGE 196

9,7$ 7KH DXWKRU ZDV ERUQ LQ -DFNVRQYLOOH )ORULGD -DQXDU\ ?6NE +H DWWHQGHG 5REHUW ( /HH +LJK 6FKRRO -DFNVRQYLOOH )ORULGD DQG ZDV JUDGXDWHG IURP WKHUH LQ -XQH ,Q -XQH r KH UHFHLYHG WKH $VVRFLDWH RI $UWV 'HJUHH IURP )ORULGD &ROOHJH 7HPSOH 7HUUDFH )ORULGD DQG LQ -XQH KH UHFHLYHG WKH %DFKHORU RI 6FLHQFH 'HJUHH IURP WKH 8QLYHUVLW\ RI )ORULGD 7KH DXWKRU WKHQ HQWHUHG JUDGXDWH VFKRRO DW WKH 8QLYHUVLW\ RI )ORULGD &ROOHJH RI 0HGLFLQH +H ZDV VXSSRUWHG IRU WKH ILUVW WKUHH \HDUV E\ DQ 1'($ 7LWOH ,9 )HOORZVKLS DQG WKH WZR \HDUV IROORZLQJ WKDW E\ D JUDGXDWH DVVL VWDQWVKLS 7KH DXWKRU LV PDUULHG WR WKH IRUPHU 6DQGUD $O\QQH %\UG

PAGE 197

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

PAGE 198

7KLV GLVVHUWDWLRQ ZDV VXEPLWWHG WR WKH 'HDQ RI WKH &ROOHJH RI 0HGLFLQH DQG WR WKH *UDGXDWH &RXQFLO DQG ZDV DFFHSWHG DV SDUWLDO IXOILOOPHQW RI WKH UHTXLUHPHQWV IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ -XQH 'HDQ *UDGXDWH 6FKRRO

PAGE 199

>DM+ VI R PL


[ajH
(sf 4 (o
mi