Demo entry 6755531

steady-state soltion

   

Submitted by anonymous on Aug 01, 2018 at 13:19
Language: Matlab. Code size: 2.6 kB.

T1 = 50 * 10^-9;		%[s], longitudial relaxation time of TEMPOL radical in water, typically 0.1-10 ns
T2 = 10 * 10^-9;		%[s], transversal relaxation time of TEMPOL radical in water
R1 = 1/T1;			%[s^-1], longitudial relaxation rate
R2 = 1/T2;			%[s^-1], transversal relaxation rate
kex = 3.7 * 10^9;	%[s^-1 * M^-1], HSE rate of TEMPOL in water at 298 K
Conc = 0.1;			%[M], concentration of the TEMPOL aqueous solution
k = kex * Conc;
w1max = 7.39 * 10^8; 	%[rad/s], calculated from the H-field simulation of Vasyl with 1 [W] microwave power
Pmax = 1000;		%[mW], the maximal microwave power
a = 253 * 10^6;     %[rad/s], HFI constant
A = Pmax/(0.08*w1max^2);	%The constant between Pmax and w1max^2,
P = 0:20:1000;		%applied MW power
Z2dZ0 = (R1.*(3*R2^3*k + R1*R2^3 + 18*R2^2*k^2 + 6*R1*R2^2*k + R2^2*sqrt(P/A).^2 + 3*R2*a^2*k + R1*R2*a^2 + 27*R2*k^3 + 9*R1*R2*k^2 + 3*R2*k*sqrt(P/A).^2 + 6*a^2*k^2 + 2*R1*a^2*k))./(R1^2*R2^3 + 6*R1^2*R2^2*k + R1^2*R2*a^2 + 9*R1^2*R2*k^2 + 2*R1^2*a^2*k + 3*R1*R2^3*k + 18*R1*R2^2*k^2 + 2*R1*R2^2*sqrt(P/A).^2 + 3*R1*R2*a^2*k + 27*R1*R2*k^3 + 9*R1*R2*k*sqrt(P/A).^2 + 6*R1*a^2*k^2 + R1*a^2*sqrt(P/A).^2 + 9*R1*k^2*sqrt(P/A).^2 + 3*R2^2*k*sqrt(P/A).^2 + 18*R2*k^2*sqrt(P/A).^2 + R2*sqrt(P/A).^4 + a^2*k*sqrt(P/A).^2 + 27*k^3*sqrt(P/A).^2 + 3*k*sqrt(P/A).^4);
plot(P, Z2dZ0);
Z1dZ0 = (R1.*(3*R2^3*k + R1*R2^3 + 18*R2^2*k^2 + 6*R1*R2^2*k + R2^2*sqrt(P/A).^2 + 3*R2*a^2*k + R1*R2*a^2 + 27*R2*k^3 + 9*R1*R2*k^2 + 3*R2*k*sqrt(P/A).^2 + 6*a^2*k^2 + 2*R1*a^2*k + a^2*sqrt(P/A).^2))./(R1^2*R2^3 + 6*R1^2*R2^2*k + R1^2*R2*a^2 + 9*R1^2*R2*k^2 + 2*R1^2*a^2*k + 3*R1*R2^3*k + 18*R1*R2^2*k^2 + 2*R1*R2^2*sqrt(P/A).^2 + 3*R1*R2*a^2*k + 27*R1*R2*k^3 + 9*R1*R2*k*sqrt(P/A).^2 + 6*R1*a^2*k^2 + R1*a^2*sqrt(P/A).^2 + 9*R1*k^2*sqrt(P/A).^2 + 3*R2^2*k*sqrt(P/A).^2 + 18*R2*k^2*sqrt(P/A).^2 + R2*sqrt(P/A).^4 + a^2*k*sqrt(P/A).^2 + 27*k^3*sqrt(P/A).^2 + 3*k*sqrt(P/A).^4);
plot(P, Z1dZ0);
Z3dZ0 = (R1.*(3*R2^3*k + R1*R2^3 + 18*R2^2*k^2 + 6*R1*R2^2*k + R2^2*sqrt(P/A).^2 + 3*R2*a^2*k + R1*R2*a^2 + 27*R2*k^3 + 9*R1*R2*k^2 + 3*R2*k*sqrt(P/A).^2 + 6*a^2*k^2 + 2*R1*a^2*k + a^2*sqrt(P/A).^2))./(R1^2*R2^3 + 6*R1^2*R2^2*k + R1^2*R2*a^2 + 9*R1^2*R2*k^2 + 2*R1^2*a^2*k + 3*R1*R2^3*k + 18*R1*R2^2*k^2 + 2*R1*R2^2*sqrt(P/A).^2 + 3*R1*R2*a^2*k + 27*R1*R2*k^3 + 9*R1*R2*k*sqrt(P/A).^2 + 6*R1*a^2*k^2 + R1*a^2*sqrt(P/A).^2 + 9*R1*k^2*sqrt(P/A).^2 + 3*R2^2*k*sqrt(P/A).^2 + 18*R2*k^2*sqrt(P/A).^2 + R2*sqrt(P/A).^4 + a^2*k*sqrt(P/A).^2 + 27*k^3*sqrt(P/A).^2 + 3*k*sqrt(P/A).^4);
plot(P, Z3dZ0);
s2 = 1 - Z2dZ0;
plot(P, s2);
s = (3-Z2dZ0-Z1dZ0-Z3dZ0)./3;
plot(P, s);

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