Our cases: our mathematical models
Here you find the information you need for your exercise about CARDIO, AORTA, FARMA and SUN HEATER. There are a lot of models you can use in combination with simulation systems as javaTHESIS, MacTHESIS and other THESIS systems. The aim of our practical course is: building a complete learning environment based on model-driven simulation; based on a model.
Not all the models are complete. The instructor gives then the other information you need.
The model of the electrical activity in a nerve (AXON)
t = t + dt;
BN=0.125*Math.exp(VA/80.0);
BM=4.0*Math.exp(VA/18.0);
BH=1.0/((Math.exp(VA+30.0)/10.0)+1.0);
AN=0.01*(VA+10.0)/(Math.exp((VA+10.0)/10.0)-1.0);
AM=0.1*(VA+25.0)/(Math.exp((VA+25.0)/10.0)-1.0);
AH=0.07*Math.exp(VA/20.0);
DN=AN*(1.0-N)-BN*N;
DM=AM*(1.0-M)-BM*M;
DH=AH*(1.0-HA)-BH*HA;
N=N+DN*dt;
M=M+DM*dt;
HA=HA+DH*dt;
GK=36.0*N*N*N*N;
GNA=120.0*M*M*M*HA;
IK=GK*(VA-12.0);
INA=GNA*(VA+115.0);
IL=0.3*(VA+10.6);
T2=T1+SD1;
T4=T3+SD2;
if ((t>=T1) && (t<=T2)) {IT=INA+IK+IL+SA1; PR =SA1;}
else if ((t>=T3) && (t<=T4)) {IT=INA+IK+IL+SA2; PR=SA2;}
else {IT=INA+IK+IL; PR=0.0;};
dVdt= -IT;
VA= VA + dVdt*dt;
MV= - VA - 90;
Take as starting values and parameters
Tmax = 10.0; //[mSec]; other suggestion is Tmax = 25.0 [mSec]
dt = 0.02; //[mSec]
N=0.317;
M=0.052;
HA=0.596;
GL=0.3;
GK=0.3667;
GNA=0.0106;
IK=-4.4;
IL=3.2;
INA=1.2;
IT=0.0;
T1=2.0;//suggestion //[mSec]
T2=T1+1.0;//suggestion //[mSec]
T3=4.0;//suggestion //[mSec]
T4=T3+1.0;//suggestion //[mSec]
SD1=1.0;//suggestion //[mSec]
SD2=0.5;//suggestion //[mSec]
SA1=100.0;//suggestion flow or current [mA]
SA2=90.0;//suggestion flow or current [mA]
VA=0.0; //alteration voltage AC [mV]
MV=-90.0; //potential voltage DC [mV]
Smaller or larger values can destroy the behavior of this model. That is for your own risc.
The most valuable variables and their ranges are:
- MV, the action potential in the nerve (-90) [mV] (absolute),
with range between -50.0 (Ymin) and 200.0 (Ymax) (suggestion)
- VA, the action potential in the nerve (0) [mV] (relative)
with range between 0.0 (Ymin) and 250.0 (Ymax) (suggestion)
- PR, the input (the trigger) (0) [mV]
with range between 0.0 (Ymin) and 300.0 (Ymax) (suggestion)
The most valuable paramers for intervention and their ranges are:
- T1, starting time first pulse
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- T2, end time first pulse (xx),
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- T3, starting time second pulse
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- T4, end time second pulse
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- SD1, length of the first pulse
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- SD2, length of the second pulse
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- SA1, amplitude of the first pulse
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- SA2, amplitude of the second pulse
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
The predators - prey model (BIOLOGY)
t = t+dt
dNBdt = GB * NB - SB * NB * NR - (NB * NB)/K
dNRdt = GR * NR * NB - SR * NR
NB = NB + dNBdt * dt
NR = NR + dNRdt * dt
Take as starting values and parameters
NB = 195.0, the number of prooidieren (buit) (prey) (hazen) [number/km2] (or 135)
NR = 69.0, the number of roofdieren (predators) (vossen) [number/km2] (or 51)
SR = 7.0, sterftefactor roofdieren (7)
SB = 0.4, sterftefactor prooidieren (or 0.3)
GR = 0.06, geboorte factor roofdieren
GB = 15.0, geboorte factor prooidieren (15)
K = 50.0, sterkte van het milieu (or 5, 10, 20, 40, 50)
dt = 0.03, the stapgrootte [year]
Tmin = 0.0 [year]
Tmax = 9.0 [year] (or 4.0 year)
Smaller or larger values can destroy the behavior of this model. That is for your own risc.
The most valuable variables and their ranges are:
- NR, the number of roofdieren/predators [number/km2],
with range between 0 (Ymin) and 300 (Ymax) (suggestion)
- NB, the number of prooidieren/prey (buit) [number/km2]
with range between 0 (Ymin) and 300 (Ymax) (suggestion)
The most valuable paramers for intervention and their ranges are:
- SR, sterftefactor roofdieren,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- SB, sterftefactor prooidieren (buit),
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- GR, geboorte factor roofdieren,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- GB, geboorte factor prooidieren ,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- K, sterkte van het milieu,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
The model of the RC circuit (filter) (RC NETWERK)
ui1 = A*Math.sin(2*3.14*f*t);
if (ui1 > 0.0) {ui2 = A;} else {ui2 = -A;}
if (t > staptijd) {ui3 = A;} else {ui3 = 0.0;}
ui = switch1*ui1+switch2*ui2+switch3*ui3;
i1 = (ui - u1)/R1;
du1dt = i1/C1;
u1 = u1 + du1dt*dt;
i2 = u2/R2;
duhdt = i2/C2;
uh = uh + duhdt*dt;
u2 = ui - uh;
Take as starting values, constants and/or parameters:
tmax = 5.0;
dt = 0.02;
duhdt = 0.0;
du1dt = 0.0;
ui1 = 0.0;
ui2 = 0.0;
ui3 = 0.0;
ui = 0.0;
uh = 0.0;
switch1 = 1.0;
switch2 = 0.0;
switch3 = 0.0;
staptijd = 2.0;
A = 10.0;
f = 1.0;
u1 = 0.0;
u2 = 0.0;
i1 = 0.0;
i2 = 0.0;
R1 = 0.1;
R2 = 0.1;
C1 = 0.3;
C2 = 0.3;
Smaller or larger values can destroy the behavior of this model. That is for your own risc.
The most valuable variables and their ranges are:
- u1, the output of the first filter (het 'laagdoorlaat filter'),
with range between -15 (Ymin) and 15 (Ymax) (or -60 and +40)
- u2, the output of the second filter (het 'hoogdoorlaat filter'),
with range between -15 (Ymin) and 15 (Ymax) (or -20 and +80)
- ui, the input signal,
with range between -30 (Ymin) and 30 (Ymax) (suggestion)
The most valuable paramers for intervention and their ranges are:
- R1, the resistance of the first filter,
with range between 0 (Pmin) and xxxx (Pmax) (suggestion)
- C1, the capicity in the first filter,
with range between 0 (Pmin) and xxxx (Pmax) (suggestion)
- R2, the resistance of the second filter,
with range between 0 (Pmin) and xxxx (Pmax) (suggestion)
- C2, the capicity in the second filter,
with range between 0 (Pmin) and xxxx (Pmax) (suggestion)
- switch1 (0 or 1), on or off, for the first input wave,
with range between 0 (Pmin) and 1 (Pmax) (suggestion)
- switch2 (0 or 1), on or off, for the second input wave,
with range between 0 (Pmin) and 1 (Pmax) (suggestion)
- switch3 (0 or 1), on or off, for the 3th input wave,
with range between 0 (Pmin) and 1 (Pmax) (suggestion)
- A, the amplitude of the input signal ui (10.0),
with range between 0 (Pmin) and 15 (Pmax) (suggestion)
- f, the frequency of the input signal ui (1.0),
with range between 0 (Pmin) and 10 (Pmax) (suggestion)
- staptijd, the xxx of the input signal u3 (2.0),
with range between 0 (Pmin) and 10 (Pmax) (suggestion)
The ecology model (of numbers of prey, predators and food) (LEMMINGEN)
t = t+dt
DMDT = ((MP - MIP) / PTMAX) * DT;
CP = CP + DMDT;
IF CP > MP THEN CP = MIP;
IF CP < CPKR THEN R = RMI ELSE R = RMA;
VB = VB0 + (CP - MIP) * (1 - VB0) / (MP - MIP) * (1 - COS(T * CRCL)) / 2;
VDSL = VB * KB;
DPDT = R * PRO * (VDSL - PRO - S * RO) / VDSL * DT;
DRDT = G * RO * (KR - RO + DR * PRO) / (KR+DR*PRO) * DT;
IF RO > 0.0 THEN RO = RO + DRDT
ELSE RO = 0.0;
IF PRO > 0.0 THEN PRO = PRO + DPDT
ELSE PRO = 0.0;
Take as starting values and parameters
MIP = 0.17;
MP = 0.55;
PTMAX = 4.0;
KB = 170.0;
VB0= 30.0 / KB;
RMI= 5.0;
RMA= 120;
CPKR = 0.48;
G = 16.0;
DR = 0.05;
S = 20.0 * DR;
CP = MIP;
VB = VB0;
R = RMI;
PRO= 50.0;
RO = 0.0;
KR = 2.0;
VDSL = VB0 * KB;
tmin= 0.0;
tmax= 16.0;
Smaller or larger values can destroy the behavior of this model. That is for your own risc.
The model of the aorta (and the blood pressure) (AORTA)
t = t+dt
PLV = PLVmax * sin (2 * 3.14 * F * t)
if (PLV < 0.0) then PLV = 0.0
QAO = 33.0 * (PLV - PAO)
if ((PLV - PAO) < 0) then QAO = 0.0
VAO = VAO + (QAO - QP) * dt
QP = PAO / RP
PAO = VAO / CAO
Take as starting values, constants and/or parameters:
VAO = 80.0 (ml)
PAO = 80.0 (mmHg)
F = 1.0
QAO = 80.0 (ml/sec)
QP = 70.0 (ml/sec)
PLV = 0.0 (mmHg)
RP = 1.25
CAO = 1.1
PLVmax = 120.0
dt = 0.02 (sec)
Tmin = 0 (sec)
Tmax = 4.0 (sec)
Smaller or larger values can destroy the behavior of this model. That is for your own risc.
The most valuable variables and their ranges are:
- Pao , the xx of xx/xx [xx/xx] (xx),
with range between 0.0 (Ymin) and 120.0 (Ymax) (suggestion)
- Plv , the xx of xx/xx (xx) [xx/xx] (135)
with range between 0.0 (Ymin) and 120.0 (Ymax) (suggestion)
The most valuable paramers for intervention and their ranges are:
- Cao, xx xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- Rp, xx xx (xx),
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx factor xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx factor xx ,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx van het xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
The model of the sun heater with boiler (SUN HEATER) (BOILER)
t = t + dt;
if (((t>6.0) && (t<18.0)) || ((t>30.0) && (t<42.0)) || ((t>54.0) && (t<66.0)))
{ Fz = zs*Math.sin((((t-6)*6.28)/24.0));
Fv = ref*(T11-T0);} else {Fz= 0.0; Fv = 0.0;}
dT11dt=(Cwat*Fp*(T1-T11)+Fz-Fv)/(Ccol*100.0);
T11= T11+dT11dt*dt;
if (Fp >= Fs)
{
dT10dt=(Fs *(T9-T10) + (gel*(T9-T10))/Cwat)/Vseg;
dT9dt=(Fs *(T8-T9) + (gel*(T10-2*T9+T8))/Cwat)/Vseg;
dT8dt=(Fs *(T7-T8) + (gel*(T9-2*T8+T7))/Cwat)/Vseg;
dT7dt=(Fs *(T6-T7) + (gel*(T8-2*T7+T6))/Cwat)/Vseg;
dT6dt=(Fs *(T5-T6) + (gel*(T7-2*T6+T5))/Cwat)/Vseg;
dT5dt=(Fp *(T11-T5) + (gel*(T6-2*T5+T4))/Cwat)/Vseg;
dT4dt=((Fp-Fs)*(T5-T4) + (gel*(T5-2*T4+T3))/Cwat)/Vseg;
dT3dt=((Fp-Fs)*(T4-T3) + (gel*(T4-2*T3+T2))/Cwat)/Vseg;
dT2dt=((Fp-Fs)*(T3-T2) + (gel*(T3-2*T2+T1))/Cwat)/Vseg;
dT1dt=(Fp*(T2-T1)+Fs*(T0-T2) + (gel*(T2-T1))/Cwat)/Vseg;
}
else
{
dT1dt=(Fs*(T0-T1) + (gel*(T2-T1))/Cwat)/Vseg;
dT2dt=((Fs-Fp)*(T1-T2) + (gel*(T3-2*T2+T1))/Cwat)/Vseg;
dT3dt=((Fs-Fp)*(T2-T3) + (gel*(T4-2*T3+T2))/Cwat)/Vseg;
dT4dt=((Fs-Fp)*(T3-T4) + (gel*(T5-2*T4+T3))/Cwat)/Vseg;
dT5dt=((Fs-Fp)*(T4-T5) + (gel*(T6-2*T5+T4))/Cwat)/Vseg;
dT6dt=((Fs-Fp)*(T5-T6) + (gel*(T7-2*T6+T5))/Cwat)/Vseg;
dT7dt=((Fs-Fp)*(T6-T7) + (gel*(T8-2*T7+T6))/Cwat)/Vseg;
dT8dt=((Fs-Fp)*(T7-T8) + (gel*(T9-2*T8+T7))/Cwat)/Vseg;
dT9dt=((Fs-Fp)*(T8-T9) + (gel*(T10-2*T9+T8))/Cwat)/Vseg;
dT10dt=(Fp*(T11-T9)+Fs*(T9-T10)+(gel*(T9-T10))/Cwat)/Vseg;
}
T1 = T1 + dT1dt*dt;
T2 = T2 + dT2dt*dt;
T3 = T3 + dT3dt*dt;
T4 = T4 + dT4dt*dt;
T5 = T5 + dT5dt*dt;
T6 = T6 + dT6dt*dt;
T7 = T7 + dT7dt*dt;
T8 = T8 + dT8dt*dt;
T9 = T9 + dT9dt*dt;
T10 = T10 + dT10dt*dt;
Take as starting values and parameters
Tmax = 72.0, default: 48.0 (2 days)
dt = 0.025, default: 0.02 [days]
T1 = 10.0; //the temperature in segment 1
T2 = 10.0; //the temperature in segment 2
T3 = 10.0; //the temperature in segment 3
T4 = 10.0; //the temperature in segment 4
T5 = 10.0; //the temperature in segment 5
T6 = 10.0; //the temperature in segment 6
T7 = 10.0; //the temperature in segment 7
T8 = 10.0; //the temperature in segment 8
T9 = 10.0; //the temperature in segment 9
T10 = 10.0; //the temperature in segment 10
T11 = 10.0; //(default: 10 oC); the collector temperature;
T0 = 10.0; //(default: 10 oC); the outside temperature;
Ccol = 100000.0; //(default: 100.000 J/K); the heat capacity of the collector;
Cwat = 4200000.0; //(default: 4.200.000 J/K,m3); the heat capacity of the water;
Labda = 0.61; //(default: 0.61 J/s.m.K); the conduction coefficient of the water;
Vseg = 0.1; //(default: 0.1 m2); //the volume of the storage vessel;
D = 0.8; // (default: 0.8 m); //diameter of the storage vessel;
Fp = 0.2; //(default: 0.2 m2/hour); the flux from the storage vessel
Fs = 0.0; //(default: 0.0 m2/hour); the hot water tap
zs = 18000000.0; //(default = 18.000.000);
ref = 126000.0; //(default = 126.000); //the reflexion coefficient
gel = 2000000.0; //(default: 2.000.000), the heat conduction coefficient
Smaller or larger values can destroy the behavior of this model. That is for your own risc.
The most valuable variables and their ranges are:
- T1, the xx of xx/xx [xx/xx] (suggestion),
with range between 0 (Ymin) and 100 (Ymax) (suggestion)
- T5, the xx of xx/xx (xx) [xx/xx] (suggestion)
with range between 0 (Ymin) and 100 (Ymax) (suggestion)
- T10, the xx of xx/xx (xx) [xx/xx] (suggestion)
with range between 0 (Ymin) and 100 (Ymax) (suggestion)
- Fz/1000.0, the warmth of the sun [xx/xx] (suggestion)
with range between 0 (Ymin) and 20000.0 (Ymax) (=20000000/1000)
The most valuable paramers for intervention and their ranges are:
- Fp, Pump 1 [m2/h] (0.2),
with range between 0 (Pmin) and 1.0 (Pmax) (suggestion)
- Fs, Drain-pump [m2/h] (0.0),
with range between 0.0 (Pmin) and 1.0 (Pmax) (suggestion)
- T0, Outside temp. [C] (10),
with range between -10 (Pmin) and 45.0 (Pmax) (suggestion)
- Ccol, Coll. capacity [J/K] (100000.0),
with range between 50000.0 (Pmin) and 150000.0 (Pmax) (suggestion)
- Vseg, Vassel volume [m3] (0.1),
with range between 0.03 (Pmin) and 1.0 (Pmax) (suggestion)
- ref, the reflexion coefficient (default = 126.000)
with range between xxx (Pmin) and 800000.0 (Pmax) (suggestion)
The elastic, jumping, indent ball (height en speed)
t = t + dt;
dxdt = v;
if x<= R then dvdt = - g - (W * v + K * (x - R))/M else dvdt = - g;
x = x + dxdt * dt;
v = v + dvdt * dt;
Take as starting values, constants and/or parameters:
x = 0.9, the starthoogte
v = 0.0, the startsnelheid
t = 0.0, the tijd
g = 9.8, the versnelling of the zwaartekracht
K = 1000, the veerconstante
W = 10, the wrijving met the grond
M = 1.0, the massa
R = 0.1, the straal of the bal
dt = 0.004, the stapgrootte (tijdseenheden)
Tmin = 5.0 (tijdseenheden)
Tmax = 0 (tijdseenheden)
Smaller or larger values can destroy the behavior of this model. That is for your own risc.
The most valuable variables and their ranges are:
- xx , the xx of xx/xx [xx/xx] (xxx),
with range between -xxx.0 (Ymin) and xx.0 (Ymax) (suggestion)
- xxx , the xx of xx/xx (xx) [xx/xx] (xx)
with range between -xxx.0 (Ymin) and xx.0 (Ymax) (suggestion)
The most valuable paramers for intervention and their ranges are:
- xx, xx xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx xx (xx),
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx factor xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx factor xx ,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx van het xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
The cascade model
Onderstaande model - met opvang-bakken (links en rechts) - is ons 'dummy-model'. Het is een model wat we al jaren gebruiken als 'opvulling' in onze THESIS-systemen; en nu dan ook in het JavaTHESIS systeem.
t = t+dt
dN1dt = - K1 * N1 - K3 * N1
dN2dt = + K2 * N1
dN3dt = + K3 * N1
N1 = N1 + dN1dt * dt
N2 = N2 + dN2dt * dt
N3 = N3 + dN3dt * dt
Error =1.0 - (N1 + N2 + N3)
Take as starting values, constants and/or parameters:
K1 = 1.0, the 'doorlating' of kraan 1 (per waterhoogte)
K2 = 0.5, the 'doorlating' of kraan 2 (per waterhoogte)
N1 = 1.0, (de startwaarde van) het waternivo in bak1
N2 = 0, (de startwaarde van) the waternivo in bak2
N3 = 0, (de startwaarde van) het waternivo in bak3
Error = 0, (de startwaarde van) the rekenfout (met the methode of Euler)
dt = 0.03, the stapgrootte (tijdseenheden)
Tmax = 10.0 (tijdseenheden)
Tmin = 0.0 (tijdseenheden)
Smaller or larger values can destroy the behavior of this model. That is for your own risc. De tijd kun je nemen in seconde of minuten of zelfs uren. Reken de eenheden goed na of overleg met Rik Min. Er zijn (natuurlijk) meerdere varianten of dit model. In JavaTHESIS versie 3.9x wordt deze variant dit jaar (1999) als dummy-model gebruikt.
Er zijn twee funamenteel verschillende varianten of dit cascade model:
- de parallelle variant: de bovenste bak bedient een andere bak (of meer andere bakken)
- de sequentiele variant: de bovenste bak bedient een andere bak en die tweede bak bedient een derde bak, etc; dus drie bakken bakken 'na elkaar'. Deze variant is equivalent aan zeer veel chemische reacties (die ook vaak na elkaar plaatsvinden). Ook in de enzymkinetiek, de farmacokinetiek, etc. komen dit soort keten van reacties voor.
Natuurlijk zijn er ook allerlei combinaties mogelijk. Met dit soort (hybride) varianten kun je heel goed uitleggen en demonstreren hoe verschillend ingestelde cascade-systemen ten opzichte van elkaar reageren.
The most valuable variables and their ranges are:
- N1 , the xx of xx/xx [xx/xx] (xx),
with range between -xx.0 (Ymin) and 120.0 (Ymax) (suggestion)
- N2 , the xx of xx/xx (xx) [xx/xx] (xxx)
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
The most valuable paramers for intervention and their ranges are:
- K1, xx xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- K2, xx xx (xx),
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx factor xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx factor xx ,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx van het xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
The cascade model (with water heights in cascade):
t = t + dt
dN1dt = - K1 * N1 - K2 * N1
dN2dt = .....
dN3dt = ......
N1 = N1 + dN1dt * dt
N2 = N2 + dN2dt * dt
N3 = N3 + dN3dt * dt
Take as starting values, constants and/or parameters:
K1 = 1.0, the 'doorlating' of kraan 1 [bijv. liter/sec/liter]
K2 = ..., the 'doorlating' of kraan 2 [idem]
N1 = 1.0, (de startwaarde van) het waternivo in bak1 [bijv. liter]
N2 = 0.0, (de startwaarde van) het waternivo in bak2 [idem]
N3 = 0.0, (de startwaarde van) het waternivo in bak3 [idem]
dt = 0.03, the stapgrootte (in tijdseenheden)
Tmax = ... (in tijdseenheden) [bijv. seconde]
Tmin = 0.0 (in tijdseenheden)
Dit soort modellen komen ook voor in de chemie, de enzymkinetiek, de farmacokinetiek, etc. (zie hiervolgend.)
The most valuable variables and their ranges are:
- N1 , the xx of xx/xx [xx/xx] (xx),
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
- N2 , the xx of xx/xx (xx) [xx/xx] (xx)
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
The most valuable paramers for intervention and their ranges are:
- K1, xx xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx xx (xx),
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx factor xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx factor xx ,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx van het xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
The model of a first order enzym-reaction:
t = t + dt
dSdt = - ... * ... - ... * ...
dEdt = .....
dESdt = .....
dPdt = ......
S = S + dSdt * dt
E = E + dEdt * dt
ES = ES + dESdt * dt
P = P + dPdt * dt
Take as starting values, constants and/or parameters:
k1 = ..., de '....' [bijv. .....]
k2 = ..., de .....
k3 = ..., de .....
S = 1.0, (de startwaarde van) ..... [bijv. ....]
E = 1.0, (de startwaarde van) .... [idem]
P = 0.0, (de startwaarde van) .... [idem]
dt = 0.03, de stapgrootte (in tijdseenheden)
Tmax = ... (in tijdseenheden) [bijv. seconde]
Tmin = 0.0 (in tijdseenheden)
The most valuable variables and their ranges are:
- xx , the xx of xx/xx [xx/xx] (xx),
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
- xx , the xx of xx/xx (xx) [xx/xx] (xx)
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
The most valuable paramers for intervention and their ranges are:
- xx, xx xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx xx (xx),
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx factor xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx factor xx ,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx van het xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
The model of a (first order) enzym-reaction:
t = t + dt
dPdt= + k0*ES;
P=P+dPdt*dt;
dSdt= - k1*E*S + k2*ES;
S=S+dSdt*dt;
dEdt= - k1*E*S + k2*ES + k0*ES;
E=E+dEdt*dt;
dESdt= + k1*E*S - k2*ES - k0*ES;
ES=ES+dESdt*dt;
Take as starting values, constants and/or parameters:
P=0.0, {umoles/ml}
S=1000.0, {umoles/ml}
E=200.0, {umoles/ml}
ES=0.0;
k0=0.5, {1/sec}
k1=0.0008, {1/umoles.sec}
k2=0.000125, {1/sec}
dt = 0.03, de stapgrootte (in tijdseenheden)
Tmax = ... (in tijdseenheden) [bijv. seconde]
Tmin = 0.0 (in tijdseenheden)
The most valuable variables and their ranges are:
- xx , the xx of xx/xx [xx/xx] (xx),
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
- xx , the xx of xx/xx (xx) [xx/xx] (xx)
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
The most valuable paramers for intervention and their ranges are:
- xx, xx xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx xx (xx),
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx factor xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx factor xx ,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx van het xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
The two-compartment model (farmacokinetics) (FARMA I):
t = t + dt
dC1dt = - ... * ... - ... * ...
dC2dt = - ... * ... - ... * ...
C1 = C1 + dC1dt * dt
C2 = C2 + dC2dt * dt
Take as starting values, constants and/or parameters:
k1 = ..., de '....' [bijv. .....]
k2 = ..., de .....
k3 = ..., de .....
C1 = 0.0, (de startwaarde van) ..... [bijv. ....]
C2 = 0.0, (de startwaarde van) ..... [bijv. ....]
dt = 0.03, de stapgrootte (in tijdseenheden)
Tmax = ... (in tijdseenheden) [bijv. ...]
Tmin = 0.0 (in tijdseenheden)
The most valuable variables and their ranges are:
- xx , the xx of xx/xx [xx/xx] (xx),
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
- xx , the xx of xx/xx (xx) [xx/xx] (xx)
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
The most valuable paramers for intervention and their ranges are:
- xx, xx xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx xx (xx),
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx factor xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx factor xx ,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx van het xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
The two-compartment model (farmacokinetics) (FARMA II):
t = t + dt;
if ((t > 1.0) & (t < 1.0 + Duur)) {IJ = Dosis/(Duur*Vol1)};
if (t <= 1.0) {IJ = 0.0};
if (t >= 1.0 + Duur) {IJ = 0.0};
Concnew1 = Concold1 + IJ;
Concnew1 = Concnew1 + ((k21 * Concold2) - ((k10 + k12) * Concold1)) * dt;
Concold1 = Concnew1;
Concnew2 = Concold2;
Concnew2 = Concnew2 + ((k12 * Concold1) - (k21 * Concold2)) * dt;
Concold2 = Concnew2;
Take as starting values, constants and/or parameters:
Concnew1 = 0.0;
Concold1 = 0.0;
Concnew2 = 0.0;
Concold2 = 0.0;
Weight = 110.0;
Dosis = 4.0;
Vol1 = 0.524;
Vol2 = 0.379;
k10 = 1.132;
k12 = 7.56;
k21 = 10.45;
Tdw = 0.0;
Grdos = 20.0;
Duur=0.01;
IV=0.0;
IJ=0.0;
IM=0.0;
T4 = 0.20;
T05 =2.0;
dt = ..., de stapgrootte (in tijdseenheden)
Tmax = ... (in tijdseenheden) [bijv. ...]
Tmin = 0.0 (in tijdseenheden)
The most valuable variables and their ranges are:
- xx , the xx of xx/xx [xx/xx] (xx),
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
- xx , the xx of xx/xx (xx) [xx/xx] (xx)
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
The most valuable paramers for intervention and their ranges are:
- xx, xx xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx xx (xx),
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx factor xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx factor xx ,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx van het xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
The cannonball model (distance and height)
t = t + dt;
vx = vx - vx * R * dt
vy = vy - vy * R * dt - ay * dt
x = x + vx * dt
y = y + vy * dt
Take as starting values, constants and/or parameters:
x = 0, de startwaarde v.d. afstand (t.o.v het vertrekpunt)
y = 0, de startwaarde v.d. hoogte
vx = 35, de (start-)snelheid (v) in x-richting
vy = 50, de (start-)snelheid (v) in y-richting
ay = 9.8, de versnelling of de zwaartekracht (g)
R = 0.3, de luchtweerstand
dt = 0.1, de stapgrootte (tijdseenheden)
Tmin = 0.0 (tijdseenheden)
Tmax = 3.0 (tijdseenheden)
Smaller or larger values can destroy the behavior of this model. That is for your own risc.
The transistor model (AC versus DC)
t = t + dt;
UB = Ucc*R2/(R1+R2);
URE = URE + ((UB - 0.7) - URE)*0.03;
IR2 = UB/R2;
IR1 = (Ucc - UB)/R1;
IE0 = URE/RE;
IC0 = IE0;
IB0 = 0.0;
UC = Ucc - IC0*RC;
UCE = UC - URE;
ui = 100*A * Math.sin(2* 3.1418 * f * t);
if (ui > A) {ui = A;}
if (ui < -A) {ui = -A;}
ui1 = ui1 + (ui - ui1)*0.2;
i1 = ui/R1;
i2 = ui/R2;
ib = i1-i2;
ic = -beta*ib;
uo = -40*IC0*RC*ui1;
Uuit = UC + uo;
Uin = UB + 15.0*ui;
Error = Ucc - (IC0*RC + UCE + URE);
Controle = R1*IR1+R2*IR2;
Take as starting values, constants and/or parameters:
A = 0.01;
f = 1.0; [1/msec]
RC = 4.0;
R1 = 174.0;
R2 = 56.0;
RE = 1.99;
Ucc = 12.0; [Volt]
beta = 200.0;
IB0 = 0.0; (verwaarloosbaar klein)
IE0 = 1.116; [mA]
IC0 = 1.116; [mA]
q = 1.6E-19;
K = 1.38E-23;
S = 40.0*IC0;
ui = 0.0; [Volt]
uo = 0.0; [Volt]
U0 = 7.533; [Volt]
ui1 = 0.0; [Volt]
IR2 = 0.052; [mA]
IR1 = 0.052; [mA]
URE = 2.221; [Volt]
UCE = 5.312; [Volt]
Tmin = 0.0;
t = 0.0; [msec]
dt = 0.01; [msec]
Tmax = 8.0; [msec]
Smaller or larger values can destroy the behavior of this model. That is for your own risc.
The most valuable variables and their ranges are:
- ui, the xx of xx/xx [xx/xx] (xx),
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
- uo, the xx of xx/xx (xx) [xx/xx] (xx)
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
The most valuable paramers for intervention and their ranges are:
- RC [k Ohm] (4.0),
with range between 3.0(Pmin) and 13.0 (Pmax) (suggestion)
- RE [k Ohm] (1.99),
with range between 1.5 (Pmin) and 12.0 (Pmax) (suggestion)
- R1 [k Ohm] (174.0),
with range between 120.0(Pmin) and 220.0 (Pmax) (suggestion)
- R2 [k Ohm] (56.0),
with range between 30.0(Pmin) and 80.0 (Pmax) (suggestion)
- C1 [pF] (0.199),
with range between 0.0(Pmin) and 1.0(Pmax) (suggestion)
- C2 [pF] (0.40),
with range between 0.0(Pmin) and 1.0 (Pmax) (suggestion)
- Ce [pF] (0.174),
with range between 0.0(Pmin) and 1.0 (Pmax) (suggestion)
- A [V] (0.01),
with range between 0.0(Pmin) and 0.2 (Pmax) (suggestion)
A model of a fish pond ecosystem / food chain
By Svirezhev, Krysanova & Voinov.
t = t + dt;
DFDT = QGF - QFZ - QFB - QFS - QFD - QFE);
DZDT = QFZ + QDZ - QZB - QZC - QZD - QZE;
DBDT = QFB + QZB + QDB - QBC - QBD - QBE;
DCDT = QAC + QBC + QZC - QCD - QCE;
DSDT = QFS + QDS - QSD - QSE;
DPDT = PU + QDP - QPF - QPD;
DNDT = NU + QDN - QNF;
DODT = OU + QFO + RE*(REA - O) -QOF -QOZ -QOB -QOC -QOS -QOD;
DADT = AU + AU - QAC - QAD;
DDDT = QFD +QZD +QBD +QCD +QSD + QAD -QPD -QDN -QDZ -QDB -QDS -SED*D;
F = F + DFDT*dt;
Z = Z + DZDT*dt;
B = B + DBDT*dt;
C = C + DCDT*dt;
S = S + DSDT*dt;
P = P + DPDT*dt;
N = N + DNDT*dt;
O = O + DODT*dt;
A = A + DADT*dt;
D = D + DDDT*dt;
Take as starting values, constants and/or parameters:
C = 0.0; Carp
S = 0.0; Silvercarp
H = 0.0; Bighead
F = 20.0; Phytoplankton (Algen)
Z = 0.0; Zoo-plankton (Watervlooien)
P = 0.003; Dissolved biogenic (mineral) element; Phosphorus
N = 0.15; Dissolved biogenic (inorganic) element; Nitrogen
D = 7.2; Detritus plus bacteria
O = ...; Oxygen
A = ...;
B = ...; Bodemdieren
PU = ...; Fosfaat (als parameter)
NU = ...; Nitraat (als parameter)
AU = ...; Visvoer (als parameter)
OU = ...; Zuurstof (als parameter)
TEMP = ...; temperature
Tmin = ...; de starttijd 'Tmin'
dt = ...; de toename of de simulatietijd 'dt'[...]
Tmax = ...; de maximale eindrekentijd 'Tmax' [...]
Smaller or larger values can destroy the behavior of this model. That is for your own risc.
The most valuable variables and their ranges are:
- Zilverkarper, the xx of xx/xx [xx/xx] (xx),
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
- Karpers , the xx of xx/xx (xx) [xx/xx] (xx)
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
The most valuable paramers for intervention and their ranges are:
- xx, xx xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx xx (xx),
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx factor xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx factor xx ,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx van het xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
A model of growing (a ecosystem) (SUCROS)
By the Universiteit of Wageningen.
t = t + dt;
Dry weight of plant organs, growth rate and partitioning:
WLV = WLV + (GLV-DLV)*dt;
WST = WST + GST*dt;
WSO = WSO + GSO*dt;
WRT = WRT + GRT*dt;
Weight of leaf blades, stems, (true stems and leaf steath)
Storage organs and roots resp., in kg/ha
Weight of leaves and roots at emergence:
GTW=(GPHOT-MAINT)*CVF;
Growth rate of all organs combined, in kg/ha/day:
GRT=GTW*(1.-FSH);
GSH=GTW*FSH;
GLV=GTW*FLV;
GST=GTW*FST;
GSO=GTW*FSO;
Growth rates of roots and shoots (leaves, stems, storage organs) in Kg/Ha/Day:
RDR= FUNC( DVS, 0., 0., 1., 0., 1.01, 0.03, 2., 0.03.......);
DLV = WLV*RDR;
Death rate of leaves, in kg/ha/day:
WLVD = WLVD + DLV*dt;
Dead material (leaves) at the field in kg/ha:
FSH = FUNC( DVS, 0., 0.5, 0.3, 0.5, 0.45, 0.775, 0.7, 0.825, 1., 1., 2., 1.........);
Fraction of growth occuring in shoots as function of development stage;
FLV = FUNC(DVS, 0., 1., 0.45, 1., 0.85, 0., 2., 0.........);
FST = FUNC(DVS, 0., 0., 0.45, 0., 0.85, 1., 1., 1., 1.01, 0., 2., 0.........);
FSO = 1.-FLV-FST;
Carbon balance processes:
LAI = WLV*SLFA;
Leaf area index in hh/hh and specific leaf area in ha leaf/kg leaf weight:
GPHOT=DTGA*30./44.;
DTGH = FOV*DGAD+(1.-FOV)*DGAC;
Growth photosynthesis in kg (ch2o and co2 resp.) per ha per day, calculated from leaf characteristics (hmhx, eff), lai and actual daily radiation (avrad), and corrected for daylegnth (dl and dle):
DGAC=INSW(LAI-5.,PHCL,PHCH);
DGAO=INSW(LAI-5.,PHOL,PHOH);
PHCH=0.95*(PHCH1+PHCH2)+20.5;
PHCH1=SSLAE*AMAX*DLE*X/(1.+X);
X=ALOG(1.+0.45*DRC/(DLE*3600.)*EFFE/(SSLAE*AMAX));
PHCH2=(5.-SSLAE*)AMAX*DLE*Y/(1.+Y);
Y=ALOG(1.+0.55*DRC/(DLE*360.0)*EFFE/((5.-SSLAE)*AMAX));
SSLAE=SIN((90.+DEC-LAT)*PI/180.);
PHCL=AMIN1(PHC3,PHC4)*(1.-EXP(-(AMAX1(PHC3,PHC4)/AMIN1(PHC3,PHC4))));
PHC3=PHCH*(1.-EXP(-0.8*LAI));
PHC4=DL*LAI*AMAX;
PHOH=0.9935*PHOH1+1.1;
PHOH1=5.*AMAX*DLE*Z/(1.+Z);
Z=DRO/(DLE*3600.)*EFFE/(5.*AMAX);
PHOL=AMIN1(PHO3,PHC4)*(1.-EXP(-(AMAX1(PHO3,PHC4)/AMIN1(PHO3,PHC4))));
PHO3=PHOH*(1.-EXP(-0.8*LAI));
EFFE=(1.-REFLC)*EFF;
Initial light use efficiency and light saturated co2 assimilation rate of individual leaves. units: kg co2/ha/hr/(j/m2/s) and kg co2/ha leafhr;
FOV = (DRC-AVRAD)-(0.8*DRC);
Average fraction of perion overcast during a day. Calculation of daily radiation of a clear and an overcast sky (drc and dro, p.a.r., in j/m2) and of daylength (in hr) as a function of latitude (lat, in degree), declination (dec, in degree) and date:
DRC=0.5*1300.*RDN*EXO(-0.1/(RDN/(DL*3600.)));
DRO=0.2*DRC;
RDN=300.*(SINLD*DL+24./PI*COSLD*SQRT(1.-(SINLD/COSLD)**2));
SINLD=SIN(DEC*PI/180.)*SIN(LAT*PI/180.);
COSLD=COS(DEC*PI/180.)*COS(LAT*PI/180.);
DEC=-23.4*COS(2.*PI*DAY+10.)/365.);
DL=12.*(PI+2.*ASIN(SINLD/COSLD))/PI;
DLE=12.*(PI+2.*ASIN((-SIN(8.*PI/180.)+SINLD)/COSLD))/PI;
DLP=12.*(PI+2.*ASIN((-SIN(-4.*PI/180.)+SINLD)/COSLD))/PI;
Maintenance respiration:
MAINT =AMIN1(GPHOT,MAINTS*TEFF);
MAINTS=WLV*0.03+WST*0.015+WSO*0.01+WRT*0.01;
TEFF=Q10**(0.1*TMPA-2.5);
Growth efficiency:
CVF= (FLV*0.72+FST*0.69+FSO*CVFSO)*FSH+(1.-FSH)*0.72;
Development of the vegetation:
xxx = INSW(DVS-1.,DVRV,DVRR);
DVS = DVS + xxx*dt;
if DVS = 2.0 then .....stoppen...;
yyy=FUNC(DLP,10.,0.223,11.,0.425,12.,0.575,13.,0.685,14.,0.767,15.,0.828,16.,0.872,17.,0.906............);
DVRV= 0.0252 * yyy * FUNC(TMBA,10.,.63, 15.,.83, 20.,.92, 25.,.96, 30.,.98,35.,.99......);
DVRR= 0.0477 * FUNC(TMBA,10.,.08, 15.,.38, 20.,.575, 25.,.71, 30.,.8, 35.,.865....);
NWRT =-WRT;
WLVT = WLV+WLVD;
WVEG = WLVT+WST;
TADRW = WVEG+WSO;
Take as starting values, constants and/or parameters:
WLVI=25.0;
WRTI=25.0;
EFF= 0.5;
AMAX = 30;
REFLC=.08;
SLFA = 0.0020;
PI = 3.1416;
LAT = -15.0;
Q10 = 2.0;
CVFSO=0.73;
WLV = WLVI;
WST = 0.0;
WSO = 0.0; dry weight of plant organs, growth rate and partitioning
WRT = WRTI; dry weight of plant organs, growth rate and partitioning
WLVD =0.0; death rate of leaves, in kg/ha/day
DVS = 0.0;
WLV;
GLV; growth rate of ... combined, in kg/ha/day
DLV;
WST;
GST; growth rate of ... combined, in kg/ha/day
WSO;
GSO; growth rate of ... combined, in kg/ha/day
WRT;
GRT; growth rate ... combined, in kg/ha/day
GSH; growth rate of .... combined, in kg/ha/day
GTW;
FINTIM = 1000.0; (Tmax);
DELT = 1.0; (dt);
PRDEL = 2.0; (dtg ??);
OUTDEL= 2.0; (dtgX ??);
Tmax = 365; de maximale simulatietijd [dag];
Tmin = 0.0; de starttijd [...];
t = 0.0; de simulatietijd [...];
dt = ...; de toename of de simulatietijd [...]
Smaller or larger values can destroy the behavior of this model. That is for your own risc.
The most valuable variables and their ranges are:
- xx , the xx of xx/xx [xx/xx] (xx),
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
- xx , the xx of xx/xx (xx) [xx/xx] (xx)
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
The most valuable paramers for intervention and their ranges are:
- xx, xx xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx xx (xx),
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx factor xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx factor xx ,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx van het xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
The cardiovasculaire model of the human body (CARDIO)
By Coleman, Guyton and Min
More information:
(Click here)
Take as starting values, constants and/or parameters:
Smaller or larger values can destroy the behavior of this model. That is for your own risc.
The most valuable variables and their ranges are:
- AP, the main arterial pressure of xx/xx [xx/xx] (xx),
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
- CO, the cardiac output of xx/xx (xx) [xx/xx] (xx)
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
The most valuable paramers for intervention and their ranges are:
- xx, xx xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx xx (xx),
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx factor xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx factor xx ,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx van het xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
The economy model (of Van Miltenburg) (ECONOMY)
More information:
(Click here)
Take as starting values, constants and/or parameters:
m1 = xxx
m2 = xxx
m3 = xxx
m4 = xxx
m5 = xxx
Smaller or larger values can destroy the behavior of this model. That is for your own risc.
The most valuable variables and their ranges are:
- y1, the xx of xx/xx [xx/xx] [year],
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
- y2, the xx of xx/xx (xx) [xx/xx] (xx)
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
- y3, the xx of xx/xx [xx/xx] (xx),
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
- y4, the xx of xx/xx (xx) [xx/xx] (xx)
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
- y5, the xx of xx/xx [xx/xx] (xx),
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
- score, the score per jaar [xx/xx] (xx),
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
- tscore, the total score over 4 year(xx) [xx/xx] (xx)
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
The most valuable paramers for intervention and their ranges are:
- m1, xx xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- m2, xx xx (xx),
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- m3, xx factor xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- m4, xx factor xx ,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- m5, xx van het xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
A model of the body fluids and salt regulations (in the human body) (FLUIDS)
More information:
(Click here)
Take as starting values, constants and/or parameters:
Smaller or larger values can destroy the behavior of this model. That is for your own risc.
The most valuable variables and their ranges are:
- xx , the xx of xx/xx [xx/xx] (xx),
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
- xx , the xx of xx/xx (xx) [xx/xx] (xx)
with range between -xx.0 (Ymin) and xx.0 (Ymax) (suggestion)
The most valuable paramers for intervention and their ranges are:
- xx, xx xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx xx (xx),
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx factor xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx factor xx ,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
- xx, xx van het xx,
with range between xxx (Pmin) and xxxx (Pmax) (suggestion)
Enschede, 1995-2002;