## Posts

### Second Harmonic Generation N=1:21

gnuplot> set xrange [-180:180] gnuplot> set yrange [-180:180]

splot sin(cos(x*pi/180))*sin(cos(x*pi/180))/(cos(x*pi/180)*cos(x*pi/180))*sin(cos(y*pi/180))*sin(cos(y*pi/180))/(cos(y*pi/180)*cos(y*pi/180))+sin(cos((x+1)*pi/180))*sin(cos((x+1)*pi/180))/(cos((x+1)*pi/180)*cos((x+1)*pi/180))*sin(cos((y+1)*pi/180))*sin(cos((y+1)*pi/180))/(cos((y+1)*pi/180)*cos((y+1)*pi/180))+sin(cos((x+2)*pi/180))*sin(cos((x+2)*pi/180))/(cos((x+2)*pi/180)*cos((x+2)*pi/180))*sin(cos((y+2)*pi/180))*sin(cos((y+2)*pi/180))/(cos((y+2)*pi/180)*cos((y+2)*pi/180))+sin(cos((x+3)*pi/180))*sin(cos((x+3)*pi/180))/(cos((x+3)*pi/180)*cos((x+3)*pi/180))*sin(cos((y+3)*pi/180))*sin(cos((y+3)*pi/180))/(cos((y+3)*pi/180)*cos((y+3)*pi/180))+sin(cos((x+4)*pi/180))*sin(cos((x+4)*pi/180))/(cos((x+4)*pi/180)*cos((x+4)*pi/180))*sin(cos((y+4)*pi/180))*sin(cos((y+4)*pi/180))/(cos((y+4)*pi/180)*cos((y+4)*pi/180)) +sin(cos((x+5)*pi/180))*sin(cos((x+5)*pi/180))/(cos((x+5)*pi/180)*cos((x+5)*pi/180))*sin(cos((y+5)*pi/180))*sin(cos(…
Recent posts

### Second Harmonic Generation

gnuplot> set xrange [-180:180] gnuplot> set yrange [-180:180] gnuplot> set pm3d gnuplot> set hidden3d  gnuplot> set title 'SHG' gnuplot> splot sin(cos(x*pi/180))*sin(cos(x*pi/180))/(cos(x*pi/180)*cos(x*pi/180))*sin(cos(y*pi/180))*sin(cos(y*pi/180))/(cos(y*pi/180)*cos(y*pi/180)) title 'N=1
'

### Angle of Idler in Spontaneous Parametric Down Conversion

gnuplot> set xrange [-180:180] gnuplot> set yrange [-180:180] gnuplot>splot asin(sin(x*pi/180)*(y-400)/400)*180/pi

### FREE FALL

## A function, free fall, that takes in h (in metres), and
## returns the final velocity of the ball at the
## time step just before it touches the ground and makes
## a plot of velocity versus time.
function freefall(h)
## constants and initializations
v=0; ## initial velocity(at rest) [m/sec]
y=h; ## initial altitude of the ball from the ground [m]
t=0; ## initial time[sec ]
B1=0.05; ## Coeff of the term prop to v [kg/sec]
B2=6E-4; ## Coeff of the term prop to v^2 [kg/m]
m=0.25; ## Mass of the ball [kg]
g=9.8; ## Gravitational acceleration [m/sec^2]
dt=0.1; ## Time increment [sec]
n=1; ## Initialize the loop index[dimensionless]
## Run the loop or iterate until the vertical component is
## smaller than zero.
while (y(n)>0);
## decrease the altitude in each step
y=[y;y(n)+v(n)*dt]; ## and accumlate the results in the array
## of the vertical displacement.
## increase the time in each step
t=[t;t(n)+dt]; ## and accumlate the results in the array
## of the time for the time axis in…

### INTEGRAL (TRAPEZOIDAL RULE)

## This m-file computes the integral of a function f over the
## equally spaced points x using the trapezoidal rule.
function I = trapezoid(x,f)
h = x(2)-x(1);
N = length(f);
I = 0;
for n=2:N-1,
I = I + h*f(n);
endfor
I = I + h/2*(f(1) + f(N));
endfunction

### TOTAL ISING ENERGY

function E=Ising_Energy(lattice,i,j,rneigh)
H=2; ## applied magnetic field times permeability[joule]
E=0; ## initial configuration energy[joule]
J0=1 ## coupling constant of function J, normaly in joule.
alpha=2 ## exponential constant of function J.
L=length(lattice); ## number of particles or spins in lattice
for r=1:rneigh
NN1=mod(j+r,L); NN1+=(NN1==0)*L;
NN2=mod(j-r,L); NN2+=(NN2==0)*L;
NN3=mod(i+r,L); NN3+=(NN3==0)*L;
NN4=mod(i-r,L); NN4+=(NN4==0)*L;
J=coupling(rneigh,J0,alpha);
dE=J*(lattice(i,NN1)+lattice(i,NN2)+
lattice(NN3,j)+lattice(NN4,j))-H*(sum((rand(L)>0.5)*2-1));
E+=-1*dE
endfor
endfunction

### NONUNFORM SOUND WAVE GENERATOR

## a script for a sound wave source made up of two different masses ##seperated in the middle. Let the rigth part is lighter than the
##left one that ensures that the ligther is faster, and so has
##greater r since r=cdt/dx which is dimensionless(ratio).
dx=1e-2; ## Increment in the horizontal distance (m)
c1=300; ## speed of the left one (m/s)
c2=500; ## Speed of the rigth one (m/s)
dt=dx/max(c1,c2); ## Increment in time (s). The max c, the min dt.
r1=c1*dt/dx; ## Ratio r for the left one
r2=c2*dt/dx; ## Ration r for the right one
x=-1:dx:1; ## same as the string_fixed
l=length(x);
x0=0.5;
k=1e2;