- Author:
- aram148 <a.rampadarath@auckland.ac.nz>
- Date:
- 2021-11-04 16:02:42+13:00
- Desc:
- Updated USMC-Bursztyn model
- Permanent Source URI:
- http://models.cellml.org/workspace/6b0/rawfile/4c1ab73f48d7150c2094cf8017425482a1594ccf/USMC/DM+Mijaailovich_huxley_copy/mis1.m
function [F]=mis1(r)
%N number of time points
%trange specifies the interval of time steps
%T time grid
%X0 space grid
%T=linspace(trange(1),trange(2),N);
%X=linspace(xrange(2),xrange(1),M);
%dt=timestep
%Initial conditions
R=[r(1);r(2);r(3);r(4);r(5);r(6);r(7)];
% L=lengthvar(t,f);
%L=0.1;
k1=0.35;
k6=0.35;
k2=0.1;
k3=0.44;
k4=0.11;
k5=0.1;
k7=0.005;
g1=2.*k7;
g2=20.*g1;
g3=3.*g1;
fp1=2.*k3;
gp1=2.*k4;
gp2=4.*(fp1+gp1);
gp3=3.*gp1;
r(1)=R(1);
r(2)=R(2);
r(3)=R(3);
r(4)=R(4);
r(5)=R(5);
r(6)=R(6);
r(7)=R(7);
%Mean for cdf
p1=r(2)/r(1);
p2=r(5)/r(4);
%Standard deviation for cdf
q1=(sqrt((r(3)/r(1))-((r(2)/r(1)).^(2))));
q2=(sqrt((r(6)/r(4))-((r(5)/r(4)).^(2))));
%r,phi and I values for 1st PDE M1_lambda
r0=-p1/q1;
r1=(1-p1)/q1;
rinf=(Inf-p1)/q1;
%phi0=erf(-p1./q1);
phi0=cdf('Normal',r0,p1,q1);
phi1=cdf('Normal',r1,p1,q1);
% phi1=erf((1-p1)./q1);
phinf=cdf('Normal',rinf,p1,q1);
%phinf=erf((Inf-p1)./q1);
I0=-(exp(-((-p1./q1).^(2))/2))/(sqrt(2*pi));
I1=-(exp(-((((1-p1)./q1)).^(2))/2))/(sqrt(2*pi));
I2=-(exp(-(((Inf-p1)./q1)).^(2))/2)/(sqrt(2*pi));
%r,phi and I values for 2nd PDE M2_lambda
r20=-p2/q2;
r21=(1-p2)/q2;
r2inf=(Inf-p2)/q2;
%phi20=erf(r20);
%phi21=erf(r21);
%phi2inf=erf(r2inf);
phi20=cdf('Normal',r20,p2,q2);
phi21=cdf('Normal',r21,p2,q2);
phi2inf=cdf('Normal',r2inf,p2,q2);
%
I20=-(exp(-((-p2./q2).^(2))/2))/(sqrt(2*pi));
I21=-(exp(-((((1-p2)./q2)).^(2))/2))/(sqrt(2*pi));
I2in=-(exp(-(((Inf-p2)./q2)).^(2))/2)/(sqrt(2*pi));
%Functions for the rhs of the first PDE M1_lambda
J0=phi0;
J01=phi1;
J0inf=phinf;
J10=((p1.*phi0)+(q1.*I0));
J11=(p1.*phi1)+(q1.*I1);
J12=(p1.*phinf)+(q1.*I2);
J20=((p1.^(2)).*phi0)+((2*p1.*q1).*I0)+((q1.^(2)).*(phi0+(r0*I0)));
J21=((p1.^(2)).*phi1)+((2*p1.*q1).*I1)+((q1.^(2)).*(phi1+(r1*I1)));
J22=((p1.^(2)))+((2*p1.*q1).*I2)+((q1.^(2)));
J30=(p1.^(3).*phi0)+((3.*p1.^(2).*q1).*I0)+((3.*p1.*q1.^(2)).*((phi0)+(r0*I0)))+((q1.^(3).*(2+r0.^(2)).*I0));
J31=(p1.^(3).*phi1)+((3.*p1.^(2).*q1).*I1)+((3.*p1.*q1.^(2)).*(phi1+(r1*I1)))+(q1.^(3).*(2+(r1.^(2))).*I1);
J32=(p1.^(3))+((3.*p1.^(2).*q1).*I2)+((3.*p1.*q1.^(2)));
%Functions defined for the RHS of the second PDE M2_lambda
K0=phi20;
K01=phi21;
K0inf=phi2inf;
K10=((p2.*phi20)+(q2.*I20));
K11=(p2.*phi21)+(q2.*I21);
K12=(p2.*phinf)+(q2.*I2in);
K20=((p2.^(2)).*phi20)+((2*p2.*q2).*I20)+((q2.^(2)).*(phi20+(r20*I20)));
K21=((p2.^(2)).*phi21)+((2*p2.*q2).*I21)+((q2.^(2)).*(phi21+(r21*I21)));
K22=((p2.^(2)))+((2*p2.*q2).*I2in)+((q2.^(2)));
K30=(p2.^(3).*phi20)+((3.*p2.^(2).*q2).*I20)+((3.*p2.*q2.^(2)).*((phi20)+(r20*I20)))+((q2.^(3).*(2+r20.^(2)).*I20));
K31=(p2.^(3).*phi21)+((3.*p2.^(2).*q2).*I21)+((3.*p2.*q2.^(2)).*(phi21+(r21*I21)))+(q2.^(3).*(2+(r21.^(2))).*I21);
K32=(p2.^(3))+((3.*p2.^(2).*q2).*I2in)+((3.*p2.*q2.^(2)));
%Components for the matrix F that will represent each moment,
%M1_lambda and M2_lambda
%Gaussian defined for namp and nam
% namp=(r(1)/((sqrt(2*p1))*q1)).*exp(-((X-p1).^(2))/(2*(q1.^(2))));
% nam=(r(4)/((sqrt(2*p2))*q2)).*exp(-((X-p2).^(2))/(2*(q2.^(2))));
% pd1 = makedist('Uniform');
% pdf1 = pdf(pd1,x);
% nmp=pdf1;
A0=((fp1*(1-r(7)))/2)-(fp1*(J11-J10)*r(1));%-2*(fp1*(K11-K10)*r(4));
A1=((fp1*(1-r(7)))/3)-(fp1*(J21-J20)*r(1));%-2*(fp1*(K21-K20)*r(4));
A2=((fp1*(1-r(7)))/4)-(fp1*(J31-J30)*r(1));%-2*(fp1*(K31-K30)*r(4));
% quadgk(@(t) arrayfun(@(s)el_en1(s, C0),t), 0, 1)
B0=(gp2*J0)+gp1*(J11-J10)+(gp1+gp3)*(p1-J11);
B1=(gp2*J10)+gp1*(J21-J20)+(gp1+gp3)*((p1.^(2)+q1.^(2))-J21);
B2=(gp2*J20)+gp1*(J31-J30)+(gp1+gp3)*((p1.^(3)+3*p1*q1.^(2))-J31);
C0=k1;
C1=k1*p2;
C2=k1*(p2.^(2)+q2.^(2));
D0=k2;
D1=k2*p1;
D2=k2*(p1.^(2)+q1.^(2));
E0=(g2*K0)+g1*(K11-K10)+(g1+g3)*(p2-K11);
E1=(g2*K10)+g1*(K21-K20)+(g1+g3)*((p2.^(2)+q2.^(2))-K21);
E2=(g2*K20)+g1*(K31-K30)+(g1+g3)*(p2.^(3)+(3*p2*q2.^(2))-K31);
% Putting together the matrix F for the RHS of the system of
% equations
% F=[A0-B0*r(1)+C0*r(4)-k2*r(1);A1-B1*r(1)+C1*r(4)-k2.*r(2);A2-B2*r(1)+C2*r(4)-k5*r(3);D0*r(1)-E0*r(4)-k6*r(4);D1*r(1)-E1*r(4)-k6*r(5);D2*r(1)-E2*r(4)-k6*r(6);-k1*r(7)+(1-r(7))*k2];
F=[A0-B0*r(1)+C0*r(4)-k2*r(1);A1-B1*r(1)+C1*r(4)-k2.*r(2);A2-B2*r(1)+C2*r(4)-k2*r(3);D0*r(1)-E0*r(4)-k1*r(4);D1*r(1)-E1*r(4)-k1*r(5);D2*r(1)-E2*r(4)-k1*r(6);-k1*r(7)+(1-r(7))*k2];
% Force(i)=trapz(X,X.*(m11+m21)');
