Analysis of I_abcd model

Intramolecular isomerization between four forms

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Goals

In this notebook I will analyze and test the I_abcd model.

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clean up workspace

reset()

Set path to save results into:

ProjectName:="I_abcd";
CurrentPath:="/Users/kovrigin/Documents/Workspace/Global Analysis/IDAP/Mathematical_models/Equilibrium_thermodynamic_models/I_abcd/";

filename:=CurrentPath.ProjectName.".mb";

Display equations (change : for ; to see the equation. Makes Mupad slow if all shown)

Eq_Raeq_I_abcd;
Eq_Rbeq_I_abcd;
Eq_Rceq_I_abcd;
Eq_Rdeq_I_abcd;
Eq_KB2_I_abcd;

Display functions

fRaeq_I_abcd;
fRbeq_I_abcd;
fRceq_I_abcd;
fRdeq_I_abcd

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2. 2D plotting

Set some realistic values for constants:

Total_R:=1;
Ka1:=5;
Ka2:=5;
Kb1:=2;
K
_max:=10;

pRaeq:=  plot::Function2d(
Function=(fRaeq_I_abcd(Total_R, K_A_1, Ka2, Kb1)),
LegendText="[Ra]",
Color = RGB::Black,
XMin=(0),
XMax=(K_max),
XName=(K_A_1),
TitlePositionX=(0)):

pRbeq:=  plot::Function2d(
Function=(fRbeq_I_abcd(Total_R, K_A_1, Ka2, Kb1)),
LegendText="[Rb]",
Color = RGB::Blue,
XMin=(0),
XMax=(K_max),
XName=(K_A_1),
TitlePositionX=(0)):

pRceq:=  plot::Function2d(
Function=(fRceq_I_abcd(Total_R, K_A_1, Ka2, Kb1)),
LegendText="[Rc]",
Color = RGB::Green,
XMin=(0),
XMax=(K_max),
XName=(K_A_1),
TitlePositionX=(0)):

pRdeq:=  plot::Function2d(
Function=(fRdeq_I_abcd(Total_R, K_A_1, Ka2, Kb1)),
LegendText="[Rd]",
Color = RGB::Red,
XMin=(0),
XMax=(K_max),
XName=(K_A_1),
TitlePositionX=(0)):

plot(pRaeq,pRbeq,pRceq,pRdeq, YAxisTitle="M",
Height=180, Width=160,TicksLabelFont=["Helvetica",12,[0,0,0],Left],
AxesTitleFont=["Helvetica",14,[0,0,0],Left],
XGridVisible=TRUE, YGridVisible=TRUE,
LegendVisible=TRUE, LegendFont=["Helvetica",14,[0,0,0],Left],
ViewingBoxYMin=0, ViewingBoxYMax=1);

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4. Summary of some results

Simple test results

 Total_R:=1;Ka1:=variableKa2:=5;Kb1:=0;K_max:=10;   Here the C and D species do not form. As KA1 rises we populate B. Total_R:=1;Ka1:=variable;Ka2:=5;Kb1:=2;K_max:=10;   Here, B is not formed in the beginning, C is 2xA and D is 5xC or 10xA.   As KA1 rises we create more B and reduce D. When KA1=10 we see the same amount of B and D so KB2=1   We derived: so  5*2/10=1 !!! Yes, the derivation of the model is correct.

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Conclusions

1. I analyzed analytical solutions for the U_R_RL system. They analytical solutions seem to work correctly.

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