Adding peaked initial conditions to ternary FRAP. Also adding figure comparing...

Adding peaked initial conditions to ternary FRAP. Also adding figure comparing time course with steady state.

ternary_frap.m

@@ -5,7 +5,7 @@
 
 a = -50;
 b = 0.025;
-c = 1/10000;
+c = 1/100;
 u0 = 0.05;
 e = 0.4;
 
@@ -22,7 +22,7 @@ x = [linspace(49.0, g_inv(2), 30), g_inv(3:end-2), ...
 tic
 % x = [linspace(49.0, 49.8, 30), linspace(49.81, 50.2, 1000), ...
 %      linspace(50.21, 51, 30) linspace(51.01, 200, 600)];
-t = linspace(0.001, 1, 100);
+t = linspace(0.001, 4, 500);
 fh_ic = @(x) flory_ic(x, a, u0);
 fh_bc = @(xl, ul, xr, ur, t) flory_bc(xl, ul, xr, ur, t, u0);
 fh_pde = @(x, t, u, dudx) flory_hugg_pde(x, t, u, dudx, a, b, e, c, u0);
@@ -39,7 +39,16 @@ for i = 1:length(t)
     plot(x, sol(i, :), 'LineWidth', 2); pause(0.06);
 % %     print([num2str(i),'.png'],'-dpng')
 end
-
+%% Figures
+% Time course
+figure; hold on;
+xlim([49, 53]); ylim([0, 0.5]); 
+ax = gca;
+ax.FontSize = 16;
+xlabel('position'); ylabel('volume fraction'); 
+plot(x, sol(1:2:300, :), 'LineWidth', 2, 'Color', [135/255  204/255 250/255]);%[0    0.4470    0.7410]
+plot(x, phi_tot(x, a, b, e, u0), 'LineWidth', 4, 'LineStyle', '--', 'Color', [247/255, 139/255, 7/255]);
+print('/Users/hubatsch/ownCloud/Dropbox_Lars_Christoph/DropletFRAP/FRAP_paper/ternary_time_course', '-depsc');
 %% Plot and check derivatives of pt
 figure; hold on;
 x = linspace(40, 60, 100000);
@@ -64,13 +73,12 @@ s = 0;
 end
 
 function u = flory_ic(x, a, u0)
-    if x < -a
-        u = 0.0;
-    else
-        u = u0;
-    end
-%     u0 = 0.3;
-%  u0 = phi_tot(x, -50, 1);
+    % FRAP initial condition
+%     if x < -a; u = 0.0; else; u = u0; end
+    % Peak outside initial condition
+    if (x < -a+0.2) && (x > -a+0.1); u = 10; else; u = 0; end
+%     u = 0.3;
+%     u = phi_tot(x, -50, 1);
 end
 
 function [pl,ql,pr,qr] = flory_bc(xl, ul, xr, ur, t, u0)