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Magnetic Field #12

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381 changes: 204 additions & 177 deletions CondCode/GetCurrents.m
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Original file line number Diff line number Diff line change
@@ -1,177 +1,204 @@
function [ Curr ] = GetCurrents(ngeo, Max, nx, ny, Acond, Bcond, plot, SimType)
global im fig fc map

if SimType == 'c'
pgeo = rand(ngeo, 2);
pgeo(:, 1) = pgeo(:, 1) * nx;
pgeo(:, 2) = pgeo(:, 2) * ny;
rgeo = rand(ngeo,1)*Max;
rcircs2 = rgeo.^2;

cMap = zeros(nx,ny);

for i = 1:nx
for j = 1:ny
cMap(i,j) = Acond;
for p = 1:ngeo
dx = (pgeo(p, 1) - i);
dy = (pgeo(p, 2) - j);
if dx * dx + dy * dy < rcircs2(p)
cMap(i, j) = Bcond;
end
end
end
end
else %if SimType == 'e'
pgeo = rand(ngeo, 3);
pgeo(:, 1) = pgeo(:, 1) * nx;
pgeo(:, 2) = pgeo(:, 2) * ny;
pgeo(:, 3) = pgeo(:, 2) * 180;
rgeo = ones(ngeo, 1) * Max;

cMap = zeros(nx, ny);

for i = 1:nx
for j = 1:ny
cMap(i, j) = Acond;
for p = 1:ngeo
point = [i, j];
el = [pgeo(p, 1), pgeo(p, 2),rgeo(p), rgeo(p) / 4, pgeo(p, 3)];
if isPointInEllipse(point, el)
cMap(i, j)= Bcond;
end
end
end
end
end


G = sparse(nx*ny);
B = zeros(1,nx*ny);

for i = 1:nx
for j = 1:ny
n = j + (i - 1) * ny;

if i == 1
G(n, :) = 0;
G(n, n) = 1;
B(n) = 1;
elseif i == nx
G(n, :) = 0;
G(n, n) = 1;
elseif j == 1
nxm = j + (i - 2) * ny;
nxp = j + (i) * ny;
nyp = j + 1 + (i - 1) * ny;

rxm = (cMap(i, j) + cMap(i - 1, j)) / 2.0;
rxp = (cMap(i, j) + cMap(i + 1, j)) / 2.0;
ryp = (cMap(i, j) + cMap(i, j + 1)) / 2.0;

G(n, n) = -(rxm+rxp+ryp);
G(n, nxm) = rxm;
G(n, nxp) = rxp;
G(n, nyp) = ryp;

elseif j == ny
nxm = j + (i - 2) * ny;
nxp = j + (i) * ny;
nym = j - 1 + (i - 1) * ny;

rxm = (cMap(i, j) + cMap(i - 1, j)) / 2.0;
rxp = (cMap(i, j) + cMap(i + 1, j)) / 2.0;
rym = (cMap(i, j) + cMap(i, j - 1)) / 2.0;

G(n, n) = -(rxm + rxp + rym);
G(n, nxm) = rxm;
G(n, nxp) = rxp;
G(n, nym) = rym;
else
nxm = j + (i-2)*ny;
nxp = j + (i)*ny;
nym = j-1 + (i-1)*ny;
nyp = j+1 + (i-1)*ny;

rxm = (cMap(i,j) + cMap(i-1,j))/2.0;
rxp = (cMap(i,j) + cMap(i+1,j))/2.0;
rym = (cMap(i,j) + cMap(i,j-1))/2.0;
ryp = (cMap(i,j) + cMap(i,j+1))/2.0;

G(n,n) = -(rxm+rxp+rym+ryp);
G(n,nxm) = rxm;
G(n,nxp) = rxp;
G(n,nym) = rym;
G(n,nyp) = ryp;
end

end
end

V = G\B';

Vmap = zeros(nx,ny);
for i = 1:nx
for j = 1:ny
n = j + (i - 1) * ny;

Vmap(i, j) = V(n);
end
end

for i = 1:nx
for j = 1:ny
if i == 1
Ex(i, j) = (Vmap(i + 1, j) - Vmap(i, j));
elseif i == nx
Ex(i, j) = (Vmap(i, j) - Vmap(i - 1, j));
else
Ex(i, j) = (Vmap(i + 1, j) - Vmap(i - 1, j)) * 0.5;
end
if j == 1
Ey(i, j) = (Vmap(i, j + 1) - Vmap(i, j));
elseif j == ny
Ey(i, j) = (Vmap(i, j) - Vmap(i, j - 1));
else
Ey(i, j) = (Vmap(i, j + 1) - Vmap(i, j - 1)) * 0.5;
end
end
end

Ex = -Ex;
Ey = -Ey;

eFlowx = cMap .* Ex;
eFlowy = cMap .* Ey;

if plot
if fc == 1
fig = figure();
end

subplot(2, 2, 1), H = surf(cMap');
set(H, 'linestyle', 'none');
view(0, 90)
subplot(2, 2, 2), H = surf(Vmap');
set(H, 'linestyle', 'none');
view(0, 90)
subplot(2, 2, 3), quiver(Ex', Ey');
axis([0 nx 0 ny]);
subplot(2, 2, 4), quiver(eFlowx', eFlowy');
axis([0 nx 0 ny]);

if fc == 1
f = getframe(fig);
[im, map] = rgb2ind(f.cdata, 256, 'nodither');
im(1, 1, 1, 2) = 0;
else
f = getframe(fig);
im(:, :, 1, fc) = rgb2ind(f.cdata, map, 'nodither');
end
end

C0 = sum(eFlowx(1, :));
Cnx = sum(eFlowx(nx, :));
Curr = (C0 + Cnx) * 0.5;

end
function [ Curr ] = GetCurrents(ngeo, Max, nx, ny, Acond, Bcond, plot, SimType)
global im fig fc map

if SimType == 'c'
pgeo = rand(ngeo, 2);
pgeo(:, 1) = pgeo(:, 1) * nx;
pgeo(:, 2) = pgeo(:, 2) * ny;
rgeo = rand(ngeo,1)*Max;
rcircs2 = rgeo.^2;

cMap = zeros(nx,ny);

for i = 1:nx
for j = 1:ny
cMap(i,j) = Acond;
for p = 1:ngeo
dx = (pgeo(p, 1) - i);
dy = (pgeo(p, 2) - j);
if dx * dx + dy * dy < rcircs2(p)
cMap(i, j) = Bcond;
end
end
end
end
else %if SimType == 'e'
pgeo = rand(ngeo, 3);
pgeo(:, 1) = pgeo(:, 1) * nx;
pgeo(:, 2) = pgeo(:, 2) * ny;
pgeo(:, 3) = pgeo(:, 2) * 180;
rgeo = ones(ngeo, 1) * Max;

cMap = zeros(nx, ny);

for i = 1:nx
for j = 1:ny
cMap(i, j) = Acond;
for p = 1:ngeo
point = [i, j];
el = [pgeo(p, 1), pgeo(p, 2),rgeo(p), rgeo(p) / 4, pgeo(p, 3)];
if isPointInEllipse(point, el)
cMap(i, j)= Bcond;
end
end
end
end
end


G = sparse(nx*ny);
B = zeros(1,nx*ny);

for i = 1:nx
for j = 1:ny
n = j + (i - 1) * ny;

if i == 1
G(n, :) = 0;
G(n, n) = 1;
B(n) = 1;
elseif i == nx
G(n, :) = 0;
G(n, n) = 1;
elseif j == 1
nxm = j + (i - 2) * ny;
nxp = j + (i) * ny;
nyp = j + 1 + (i - 1) * ny;

rxm = (cMap(i, j) + cMap(i - 1, j)) / 2.0;
rxp = (cMap(i, j) + cMap(i + 1, j)) / 2.0;
ryp = (cMap(i, j) + cMap(i, j + 1)) / 2.0;

G(n, n) = -(rxm+rxp+ryp);
G(n, nxm) = rxm;
G(n, nxp) = rxp;
G(n, nyp) = ryp;

elseif j == ny
nxm = j + (i - 2) * ny;
nxp = j + (i) * ny;
nym = j - 1 + (i - 1) * ny;

rxm = (cMap(i, j) + cMap(i - 1, j)) / 2.0;
rxp = (cMap(i, j) + cMap(i + 1, j)) / 2.0;
rym = (cMap(i, j) + cMap(i, j - 1)) / 2.0;

G(n, n) = -(rxm + rxp + rym);
G(n, nxm) = rxm;
G(n, nxp) = rxp;
G(n, nym) = rym;
else
nxm = j + (i-2)*ny;
nxp = j + (i)*ny;
nym = j-1 + (i-1)*ny;
nyp = j+1 + (i-1)*ny;

rxm = (cMap(i,j) + cMap(i-1,j))/2.0;
rxp = (cMap(i,j) + cMap(i+1,j))/2.0;
rym = (cMap(i,j) + cMap(i,j-1))/2.0;
ryp = (cMap(i,j) + cMap(i,j+1))/2.0;

G(n,n) = -(rxm+rxp+rym+ryp);
G(n,nxm) = rxm;
G(n,nxp) = rxp;
G(n,nym) = rym;
G(n,nyp) = ryp;
end

end
end

V = G\B';

Vmap = zeros(nx,ny);
for i = 1:nx
for j = 1:ny
n = j + (i - 1) * ny;

Vmap(i, j) = V(n);
end
end

for i = 1:nx
for j = 1:ny
if i == 1
Ex(i, j) = (Vmap(i + 1, j) - Vmap(i, j));
elseif i == nx
Ex(i, j) = (Vmap(i, j) - Vmap(i - 1, j));
else
Ex(i, j) = (Vmap(i + 1, j) - Vmap(i - 1, j)) * 0.5;
end
if j == 1
Ey(i, j) = (Vmap(i, j + 1) - Vmap(i, j));
elseif j == ny
Ey(i, j) = (Vmap(i, j) - Vmap(i, j - 1));
else
Ey(i, j) = (Vmap(i, j + 1) - Vmap(i, j - 1)) * 0.5;
end
end
end

Ex = -Ex;
Ey = -Ey;

eFlowx = cMap .* Ex;
eFlowy = cMap .* Ey;

Ry=zeros(nx,ny);
for i= 0:(ny/2-1)
Ry(:,1+i)=(ny/2-i);
Ry(:,ny-i)=ny/2-i;
end

eFlowR=zeros(nx,ny);
for i= 1:nx
for j= 0:(ny/2-1)
eFlowR(i,j+1)=sum(eFlowx(i,(j+1):(ny-j)));
eFlowR(i,ny-j)=sum(eFlowx(i,(j+1):(ny-j)));
end
end

u_o=1.2566370614*10^(-6);

Bmap=u_o.*eFlowR./Ry;

if plot
if fc == 1
fig = figure();
end

subplot(2, 2, 1), H = surf(cMap');
set(H, 'linestyle', 'none');
view(0, 90)
subplot(2, 2, 2), H = surf(Vmap');
set(H, 'linestyle', 'none');
view(0, 90)
subplot(2, 2, 3), quiver(Ex', Ey');
axis([0 nx 0 ny]);
subplot(2, 2, 4), quiver(eFlowx', eFlowy');
axis([0 nx 0 ny]);

figure(31)
mesh(Bmap);
title('Magnetic Feild');
xlabel('Y');
ylabel('X');
zlabel('|B|');

if fc == 1
f = getframe(fig);
[im, map] = rgb2ind(f.cdata, 256, 'nodither');
im(1, 1, 1, 2) = 0;
else
f = getframe(fig);
im(:, :, 1, fc) = rgb2ind(f.cdata, map, 'nodither');
end
end

C0 = sum(eFlowx(1, :));
Cnx = sum(eFlowx(nx, :));
Curr = (C0 + Cnx) * 0.5;



end