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%% Boundary condition: Jump makes sense
[~, ind] = min(abs(T.x+T.a)); % Find x position of boundary
plot(max(T.sol(:, 1:ind-1), [], 2)./min(T.sol(:, ind+1:end), [], 2), 'LineWidth', 2)
make_graph_pretty('time', 'ratio outside/inside', 'unbleached component');
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figure; % Shouldn't be symmetric, different SS for phi_u and phi_b??
plot(min(T.u0+T.e-T.sol(:, 1:ind-1), [], 2)./max(T.u0-T.sol(:, ind+1:end), [], 2),...
'LineWidth', 2)
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make_graph_pretty('time', 'ratio outside/inside', 'bleached component');
%% Plot flux at boundary
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%% Figures
% Time course
figure; hold on;
xlim([0, 3]); ylim([0, 0.5]);
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ax = gca;
ax.FontSize = 16;
xlabel('x [\mum]'); ylabel('volume fraction');
plot(T.x, T.sol(1:2:200, :), 'LineWidth', 2, 'Color', [135/255 204/255 250/255]);
plot(T.x, Ternary_model.phi_tot(T.x, T.a, T.b, T.e, T.u0), 'LineWidth', 4,...
'LineStyle', '--', 'Color', [247/255, 139/255, 7/255]);
print([T.pa, 'ternary_time_course'], '-depsc');
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%% Plot and check derivatives of pt
figure; hold on;
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x = linspace(40, 60, 100000);
plot(T.x, Ternary_model.phi_tot(T.x, T.a, T.b, T.e, T.u0));
plot(T.x, Ternary_model.gradient_analytical(T.x, T.a, T.b, T.e));
plot(T.x(1:end-1)+mean(diff(T.x))/2, ...
diff(Ternary_model.phi_tot(T.x, T.a, T.b, T.e, T.u0)/mean(diff(T.x))));
plot(T.x, Ternary_model.gamma0(T.x, T.a, T.b, T.e_g0, T.o_g0));
axis([0, 3, 0, 1])
plot(Ternary_model.gamma0(T.x, T.a, T.b, T.e_g0, T.o_g0),...
Ternary_model.spacing(Ternary_model.gamma0(T.x, T.a, T.b, T.e_g0, T.o_g0),...
T.a, T.b, T.e_g0, T.o_g0));
T = Ternary_model(2, 'FRAP', [], linspace(0.0, 400, 5000));
T.solve_tern_frap();
x_seed = 60;
s = T.sol(1:end, 1:30)./max(T.sol(1:end, 1:30))/1.022;
ts = T.t(1:end)';
f_min = @(x) to_minimize(s, ts, x, 'simple_drop', s(:, end));
opt = optimset('MaxFunEvals', 2000, 'PlotFcns',@optimplotfval);
x_seed = fminsearch(f_min, x_seed, opt);
%%
[cost, v_fit, r_n, v_fit_end] = to_minimize(s, ts, x_seed, 'simple_drop', s(:, end));
%% Plot for
figure; hold on;
s_all = T.sol(1:end, 1:400)./max(max(T.sol(1:end, 1:30)))/1.022;
plot(T.x(1:340), s_all(1:10:200, 1:340), 'Color', [0.5294, 0.8, 0.98], 'LineWidth', 2.5);
plot(T.x(1:30), v_fit(1:10:200, :)', '.', 'Color', [0.83, 0.23, 0.09], 'MarkerSize', 10);
make_graph_pretty('$x [\mu m]$', 'intensity [a.u.]', '');
% print([T.pa, 'Timecourse_model_only'],'-depsc')
%% Plot boundary condition (read out)
figure; hold on;
plot(ts(1:200), s(1:200, end), 'Color', [0.1608 0.5412 0.2118])
make_graph_pretty('t [s]', 'intensity [a.u.]', '');
print([T.pa, 'Timecourse_BC'],'-depsc')
%% Fit boundary condition with exponential
f = fit(ts(1:200), s(1:200, end), 'B+C-B*exp(-x/tau)-C*exp(-x/tau2)');
plot(f)
%% Plot flux at boundary (x close to 1) Only works close to boundary!
% T = Ternary_model(2, 'FRAP', [], linspace(0.0, 400, 2000));
% T.e_g0 = 0.001;
% T.b = 0.001;
% T.solve_tern_frap();
[~, ind_in] = min(abs(T.x+T.a+0.02)); % Find x position of boundary close to 0.9
% Calculate local diffusion coefficient
g0 = Ternary_model.gamma0((T.x(ind_in)+T.x(ind_in+1))/2, T.a, T.b, T.e_g0, T.o_g0);
pt = Ternary_model.phi_tot((T.x(ind_in)+T.x(ind_in+1))/2, T.a, T.b, T.e, T.u0);
D_in = g0*(1-pt);
Diffs_in = D_in*diff(T.sol')/(T.x(ind_in+1)-T.x(ind_in));
[~, ind_out] = min(abs(T.x+T.a-0.02)); % Find x position of boundary close to 0.9
% Calculate local diffusion coefficient
g0 = Ternary_model.gamma0((T.x(ind_out)+T.x(ind_out+1))/2, T.a, T.b, T.e_g0, T.o_g0);
pt = Ternary_model.phi_tot((T.x(ind_out)+T.x(ind_out+1))/2, T.a, T.b, T.e, T.u0);
D_out = g0*(1-pt);
Diffs_out = D_out*diff(T.sol')/(T.x(ind_out+1)-T.x(ind_out));
figure; hold on;
plot(Diffs_in(ind_in, :))
plot(Diffs_out(ind_out, :));
make_graph_pretty('time', '$\vec{j}$', 'boundary flux inside/outside of drop');
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axis([0, 200, 0, 0.035])
%% Check out inner and outer length scales
e_g0 = [0.01, 0.05, 0.1, 0.2, 0.5, 3, 10, 100];
for i = 1:8
% T1{i} = Ternary_model(2, 'FRAP', [], linspace(0.0, 400, 5000));
% T1{i}.e_g0 = e_g0(i);
% T1{i}.solve_tern_frap();
T1{i}.calc_time_scales();
end
%%
figure; hold on;
for i = 1:length(T1)
[~, ind] = min(abs(T1{i}.x+T1{i}.a));
plot(T1{i}.t, sum(T1{i}.sol(:, 1:ind), 2)); axis([0, 100, 0, 80]);
end
%% Mix
o_g0 = [0.01, 0.05, 0.1, 0.2, 0.5, 3, 10, 100];
for i = 1:8
T2{i} = Ternary_model(2, 'FRAP', [], linspace(0.0, 400, 5000));
T2{i}.o_g0 = o_g0(i);
T2{i}.solve_tern_frap();
T2{i}.calc_time_scales();
end
%%
figure; hold on;
for i = 1:length(T1)
[~, ind] = min(abs(T2{i}.x+T2{i}.a));
plot(T2{i}.t, sum(T2{i}.sol(:, 1:ind), 2)); axis([0, 100, 0, 80]);
end
%%
%%
o_g0 = [0.01, 0.05, 0.1, 0.2, 0.5, 3, 10, 100];
for i = 1:8
T3{i} = Ternary_model(2, 'FRAP', [], linspace(0.0, 400, 5000));
T3{i}.e_g0 = 0.01;
T3{i}.o_g0 = o_g0(i);
T3{i}.solve_tern_frap();
T3{i}.calc_time_scales();
end
%%
figure; hold on;
for i = 1:length(T1)
[~, ind] = min(abs(T2{i}.x+T2{i}.a));
plot(T2{i}.t, sum(T2{i}.sol(:, 1:ind), 2)); axis([0, 100, 0, 80]);
end
%% Outside time scale
p = logspace(1, 3, 20);
R_in = 1;
tau_out = p.^(1/3);
plot(p, tau_out);
make_graph_pretty('partitioning coefficient $\xi$', '$\tau_{out}$', '');
%%
T_large_p = Ternary_model(2, 'FRAP', [-1, 0.025, 0.0004, 0.4, 0.16, 0.2], linspace(0.0, 400, 5000));
T_large_p.solve_tern_frap()
%%
T_small_p = Ternary_model(2, 'FRAP', [-1, 0.025, 0.05, 0.4, 0.16, 0.2], linspace(0.0, 400, 5000));
T_small_p.solve_tern_frap()