New offset and stretch parameters for gamma0() and spacing().

ternary_frap.m

@@ -8,22 +8,26 @@ b = 0.025;
 c = 1/100;
 u0 = 0.05;
 e = 0.4;
-
+e_g0 = 0.16;
+o_g0 = 0.2;
+%%
+g0 = gamma0(x, a, b, e_g0, o_g0);
 %% Make useful mesh (by inverting the tanh profile and using this as spacing)
 x = linspace(-a-1, -a+1, 3000);
-g = gamma0(x, a, 1*b, e);
+g = gamma0(x, a, 1*b, e_g0, o_g0);
 g_unique = unique(g);
 x = linspace(g_unique(1), g_unique(end-1), 300);
-g_inv = spacing(x, a, 2*b, e);
+g_inv = spacing(x, a, 2*b, e_g0, o_g0);
 g_inv = g_inv(2:end-1);
 x = [linspace(-a-1, g_inv(2), 30), g_inv(3:end-2), ...
     linspace(g_inv(end-1), -a+1, 30), linspace(-a+1.1, 300, 300)];
 %% Solve pde
 tic
-t = linspace(0.001, 4, 500);
+t = linspace(0.001, 0.5, 250);
 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);
+fh_pde = @(x, t, u, dudx) flory_hugg_pde(x, t, u, dudx, a, b, e, c, u0,...
+                                         e_g0, o_g0);
 sol = pdepe(2, fh_pde, fh_ic, fh_bc, x, t);
 toc
 %% Plotting
@@ -34,7 +38,7 @@ for i = 1:length(t)
     ax.FontSize = 16;
     xlabel('position'); ylabel('volume fraction');
     plot(x, phi_tot(x, a, b, e, u0), 'LineWidth', 2, 'LineStyle', '--'); 
-    plot(x, sol(i, :), 'LineWidth', 2); pause(0.06);
+    plot(x, sol(i, :), 'LineWidth', 2); pause();
 % %     print([num2str(i),'.png'],'-dpng')
 end
 %% Figures
@@ -47,7 +51,7 @@ xlabel('position'); ylabel('volume fraction');
 plot(x, sol(1:2:300, :), 'LineWidth', 2, 'Color', [135/255  204/255 250/255]);
 plot(x, phi_tot(x, a, b, e, u0), 'LineWidth', 4, 'LineStyle', '--', 'Color',...
     [247/255, 139/255, 7/255]);
-print([pa, 'ternary_time_course'], '-depsc');
+% print([pa, 'ternary_time_course'], '-depsc');
 %% Plot and check derivatives of pt
 figure; hold on;
 x = linspace(40, 60, 100000);
@@ -58,14 +62,15 @@ plot(x(1:end-1)+mean(diff(x))/2, ...
 plot(x, gamma0(x, a, b, e));
 figure; plot(gamma0(x, a, b, e), spacing(gamma0(x, a, b, e), a, b, e));
 %% Function definitions for pde solver
-function [c, f ,s] = flory_hugg_pde(x, t, u, dudx, a, b, e, c_p, u0)  
+function [c, f ,s] = flory_hugg_pde(x, t, u, dudx, a, b, e, c_p, u0,...
+                                    e_g0, o_g0)  
 % Solve with full ternary model. Analytical derivatives.
 % pt ... phi_tot
 % gra_a ... analytical gradient of phi_tot
 
 pt = phi_tot(x, a, b, e, u0);
 gra_a = gradient_analytical(x, a, b, e);
-g0 = gamma0(x, a, b, e);
+g0 = gamma0(x, a, b, e_g0, o_g0);
 c = c_p;
 f = g0*(1-pt)/pt*(pt*dudx-u*gra_a);
 s = 0;
@@ -91,12 +96,12 @@ function [pl,ql,pr,qr] = flory_bc(xl, ul, xr, ur, t, u0)
     qr = 0;
 end
 
-function g0 = gamma0(x, a, b, e)
-    g0 = 1*e*(tanh((x+a)/b)+1)/2+0.001;
+function g0 = gamma0(x, a, b, e_g0, o_g0)
+    g0 = e_g0*(tanh((x+a)/b)+1)/2+o_g0;
 end
 
-function sp = spacing(x, a, b, e)
-    sp = b*atanh(2/(1*e)*(x-0.001)-1)-a;
+function sp = spacing(x, a, b, e_g0, o_g0)
+    sp = b*atanh(2/(e_g0)*(x-o_g0)-1)-a;
 end
 
 function p = phi_tot(x, a, b, e, u0)