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MEAN SQUARED DISPLACEMENT-1D RANDOM WALK


## Routine random walk(rw) for simulating
## one-dimensional random walk
## and calculating the mean squared displacement.
x2ave=[]; ## Initial array of the squared
## displacement at initial time(meters).
Nrw=3000; ## Number of walkers (Dimensionless).
beg=1000; ## Minimum step number ( // ).
inc=1000; ## Step number increment ( // ).
Nstepsmax=10000; ## Maximum step number ( // ).
dt=1; ## Time increment(second).
##Entering the nested loops.
for Nsteps=beg:inc:Nstepsmax; ## The loop through the number
Nsteps ## of steps each in walk.
x2=0; ## Initial squared location of all of the
## walkers at all steps.
for m=1:Nrw ## The loop through the desired
## number of walkers.
r=rand_disc_rev(Nsteps,0.5); ## Calling the rw generator
## function which will give column vector
## of each elements are either 1 or -1.
x2+=sum(r)^2; ## Total displacement squared whose
## elements stems from the vector r.
endfor
x2ave=[x2ave;x2/Nrw]; ## Accumulation of the squared displacements
endfor ## at the step Nsteps into the array x2ave(Nsteps).
## Exiting the nested loops. Continuing by constructing polynomials.
hold off
plot(dt*[beg:inc:Nstepsmax],x2ave,'b*;RawData;') ## Plot of the raw data
## of mean squared displament vs. step
## number or here the time.
[p,s]=polyfit(dt*[beg:inc:Nstepsmax]',x2ave,1); ## Calculate the coefficients
## p and the quality of measure s
## of the 'imaginary' polinomial, x2ave(Nsteps).
pval=polyval(p,dt*[beg:inc:Nstepsmax]); ## The values of the fit polynomial
## in the time interval dt*[beg,Nstepsmax].
hold on
plot(dt*[beg:inc:Nstepsmax],pval,'r-;Fit;') ## Plot of fit data of x2ave vs time.
hold off

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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…