How to 'map' an equation in another?

Hello everyone,

I've the following equation (fig1), where mu is a function of both T and gamma_dot. Other parameters are defined in table of the same fig.1, while T_g is 373 and is costant.

I would map results in another form (fig2), finding the right values for 'D' and 'b' for the best mapping. I would do this in order to have the contribution of T and gamma_dot decoupled in the final equation. In fig.2 'gamma' is the same as the previously defined 'gamma_dot', and the same is for 'n'.

In order to do this I created the following double for, through which I extract mu values for different gamma_dot (g variable) and T values (temp variable).

n=0.33;

g=linspace(0.1,1000);

T_vector=linspace(300,600,100);

for i=1:length(g)

for j=1:length(T_vector)

temp=T_vector(j);

if(temp>373)

mu(i,j)=(3.63e11*exp(-(27.21*(temp-373.15))/(92.85+(temp-373))))/((1+(3.63e11*exp(-(27.21*(temp-373.15))/(92.85+(temp-373)))*g(i)/29000))^(1-n));

else

mu(i,j)=(3.63e11)/((1+(3.63e11*exp(-(27.21*(temp-373))/(92.85+(temp-373)))*g(i)/29000))^(1-n));

end

end

end

Now, I don't figure how to continue in this mapping process.

I will really appreciate everyone who will help me in perform this task

Answer 1

[Star Strider]

I have no idea what you want to do.

Try this:

mu0 = @(A1,A2,T,Tg,E) (E.*exp(A1.*(T-Tg)./(A2+(T-Tg)))).*(T>Tg) + E.*(T<=Tg);
mu = @(A1,A2,T,Tg,E,gammadot,tau,n) mu0(A1,A2,T,Tg,E)./(1+(gammadot.*mu0(A1,A2,T,Tg,E)/tau).^(1-n));

tau = 2.9E4;
n = 0.33;
E = 3.63E11;
A1 = 27.21;
A2 = 92.85;
Tg = 373;

% % % T = b(1),  gammadot = b(2)
[B,fval] = fminunc(@(b)mu(A1,A2,b(1),Tg,E,b(2),tau,n), randi(500,2,1));
fprintf(1,'T        = %9.3f\ngammadot = %9.3f\n', B)

Make appropriate changes to get the result you want.