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DIFFUSION-RANDOM WALK

## the function that takes in the initial positions
## of random walkers and the number of steps as
## an argument and returns the final positions
## in 2D. The figure of the walkers after the comple-
## tion of the walk also plotted.
function f=diffusion(Nsteps)
f=[];
Nwalkers=9;
for i=1:Nsteps ## The loop through the number
## of steps each in walk.
p=initial_positions(Nwalkers); ## Initial squared location of all of the
## walkers at all steps.
for m=1:Nwalkers ## The loop through the desired
## number of walkers.
r=rand_disc_rev(N); ## Calling the rw generator
## function which will give column vector
f=[f;p+r] ## of each elements are either 1 or -1.
## Total displacement whose
## elements stems from the vector r.
endfor
f
endfor
plot(f(:,1),f(:,2),'r*;Dif;')
endfunction

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NEWTON-RAPSON METHOD FOR HEAT FLOW

##Constants and initializations
a=5.67E-8; ## Stefan-Boltzman constant[Watt/meter^2Kelvin^4]
e=0.8; ## Rod surface emissivity [Dimensionless]
h=20; ## Heat transfer coefficient of air flow [W/m^2-K]
Tinf=Ts=25; ## Temperature of air and the walls of the close[Celcius]
D=0.1; ## Diameter of the rod[meter]
I2R=100; ## Electric power dissipated in rod (Ohmic Heat)[W]
T=[]; ## Temperature of the rod[*C]
T(1)=25; ## Initial guess of the temperature of the rod[*C]
Q=[]; ## Heat function [W]
Qp=[]; ## First derivative of Q wrt T [W/C*].
for i=1:100
Q(i)=pi*D*(h*(T(i)-Tinf)+e*a*(T(i)^4-Ts^4))-I2R;
Qp(i)=pi*D*(h+4*e*a*T(i)^3);
T(i+1)=T(i)-Q(i)/Qp(i); ## Newton-Rapson Method
endfor
printf('The steady state temperature is %f\n',T(i+1))
save -text HeatFlowTemp.dat
## The plot
t=1:100; ##temperature
for n=1:100
H(n)=pi*D*(h*(t(n)-Tinf)+e*a*(t(n)^4-Ts^4))-I2R;
endfor
plot(t,H)
xlabel('T(Celcius)');
ylabel('Q(Watt)');
legend('Q(T)');
title('Heat flow vs Temperatu…