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ODE with Initial Conditions - Electroporation

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Nasir Holliday
Nasir Holliday 2020-2-28
评论： Nasir Holliday 2020-2-28
I have to solve the following ODE equation. I have all the variables imported into code already (including Ur). I have to solve the ODE for when Vm = 0, 0.3, 0.45,0.5,0.6 for two separate initial conditions: r=1E-8 and r=5E-10.
I then have to graph each Vm for each r (for a total of 10 plots).
All I was provided was:
options=odeset('MaxStep',1e-7);
tspan=[0 1e-3];
This is my code:
%Electroporation Project
sym vars
D=5E-14; %diffusion coefficient for pore radius
kB=1.38E-23; %boltzmann constant
T=310; %temperature
F=0.70E-9; %max electric force
rh = 0.97E-9; %velocity constant
rt = 0.31E-9; %velocity constant
B=1.4E-19; %steric repulsion energy (beta)
rs = 0.51E-9; %minimum radius of hydrophilic pores (r star)
g=1.8E-11; %edge energy (gamma)
s=-1E-4; %sigmaeff
r1=1E-8; %10 nm initial condition 1
r2 = 5E-10; %0.5nm initial condition 2
V = 0; %solving ODE for these values for both r1 and r2
%Equation dr/dt=Ur
U1=(D/kB*T)
U2=((V^2*F)*(r1+rt)/(1+rh))
U3=(4*B)*(rs/r1)^4*(1/r1)-2*pi*g+2*pi*s*r1
U=(U1*(U2+U3))
options=odeset('MaxStep',1e-7);
tspan=[0 1e-3];
[t,U] =ode45(@(t,U) U,tspan,r1, options)
figure
plot(t,U)
xlabel('t')
ylabel('U')
legend('Vmax=0, r1=10nm')
Can someone please help me.
  2 个评论
Star Strider
Star Strider 2020-2-28
Post what you have coded.
Note that the ode45 call should be (in the for loop that passes the requisite values for ‘Vm’):
[t{j},r{j}] =ode45(@(t,U) U(t,r,Vm(j),sigmaeff), tspan, r1, options);
Change that to conform to your existing code for ‘U’.

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