File:Partial transmittance.gif

% Partial transmittance and reflectance of a wave
% Code is messed up, don't have time to clean it now
function main()
 
   % KSmrq's colors
   red    = [0.867 0.06 0.14];
   blue   = [0, 129, 205]/256;
   green  = [0, 200,  70]/256;
   yellow = [254, 194,   0]/256;
   white = 0.99*[1, 1, 1];
   black = [0, 0, 0];
 
   % length of the string and the grid
   L = 5;
   N = 151;
   X=linspace(0, L, N);
 
   h = X(2)-X(1); % space grid size
   c = 0.5; % speed of the wave
   tau = 0.25*h/c; % time grid size
 
   % form a medium with a discontinuous wave speed
   C = 0*X+c;
 
   D=L/2;
   c_right = 0.5*c; % speed to the right of the disc
   for i=1:N
      if X(i) > D
         C(i) = c_right;
      end
   end
   % Now C = c for x < D, and C=c_right for x > D
 
   K = 5; % steepness of the bump
   S = 0; % shift the wave
   f=inline('exp(-K*(x-S).^2)', 'x', 'S', 'K'); % a gaussian as an initial wave
   df=inline('-2*K*(x-S).*exp(-K*(x-S).^2)', 'x', 'S', 'K'); % derivative of f
 
   % wave at time 0 and tau
   U0 = 0*f(X, S, K);
   U1 = U0 - 2*tau*c*df(X, S, K);
 
   U = 0*U0; % current U
 
   % plot between Start and End
   Start=130; End=500;
 
   % hack to capture the first period of the wave
   min_k = 2*N; k_old = min_k; turn_on = 0; 
 
   frame_no = 0;
   for j=1:End
 
      %  fixed end points
      U(1)=0; U(N)=0;
 
      % finite difference discretization in time
      for i=2:(N-1)
         U(i) = (C(i)*tau/h)^2*(U1(i+1)-2*U1(i)+U1(i-1)) + 2*U1(i) - U0(i);
      end
 
      % update info, for the next iteration
      U0 = U1; U1 = U;
 
      spacing=7;
 
     % plot the wave
      if rem(j, spacing) == 1 & j > Start
 
         figure(1); clf; hold on;
         axis equal; axis off; 
         lw = 3; % linewidth
 
         % size of the window
         ys = 1.2;
 
         low = -0.5*ys;
         high = ys;
         plot([D, D], [low, high], 'color', black, 'linewidth', 0.7*lw)
%         fill([X(1), D, D, X(1)], [low, low, high, high], [0.9, 1, 1], 'edgealpha', 0);
%         fill([D X(N), X(N), D],  [low, low, high, high], [1, 1, 1], 'edgealpha', 0);
 
         plot(X, U, 'color', red, 'linewidth', lw);
 
         % plot the ends of the string
         small_rad = 0.06;
 
         axis([-small_rad, 0.82*L, -ys, ys]);
 
         % small markers to keep the bounding box fixed when saving to eps
         plot(-small_rad, ys, '*', 'color', white);
         plot(L+small_rad, -ys, '*', 'color', white);
 
         pause(0.1)
         frame_no = frame_no + 1;
         %frame=sprintf('Frame%d.eps', 1000+frame_no); saveas(gcf, frame, 'psc2');
         frame=sprintf('Frame%d.png', 1000+frame_no);% saveas(gcf, frame);
         disp(frame)
         print (frame, '-dpng', '-r300');
 
      end
   end
 
 
% The gif image was creating with the command
% convert -antialias -loop 10000  -delay 8 -compress LZW -scale 20% Frame10*png Partial_transmittance.gif
% and was later cropped in Gimp