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Commit ad18b356 authored by Lars Hubatsch's avatar Lars Hubatsch
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Automatic distinction between client and constituent equations.

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@Ternary_model/Ternary_model.m
+ 13
− 11
View file @ ad18b356
......@@ -7,7 +7,8 @@ classdef Ternary_model < handle
properties
pa = '~/Desktop/DropletFRAP/Latex/Figures/FigModel/';
geometry = 2; % 2 ... Radial, 1 ... Cylindrical, 0 ... Slab
ic = 'FRAP'
ic %'FRAP', 'Gauss', 'Uniform'
mode % 'Constituent': LLPS molecules move. 'Client': client moves
precision = 5;
sol
t
......@@ -30,18 +31,19 @@ classdef Ternary_model < handle
function T = Ternary_model(geometry, ic, params, t, prec)
T.geometry = geometry;
T.ic = ic;
T.t = t;
T.precision = prec;
T.t = t;
if ~isempty(params)
T.a = params(1);
T.b = params(2);
T.u0 = params(3);
T.e = params(4);
T.e_g0 = params(5);
T.u_g0 = params(6);
T.system_size = params(7);
T.x0 = params(8);
T.v = params(9);
T.a = params{1};
T.b = params{2};
T.u0 = params{3};
T.e = params{4};
T.e_g0 = params{5};
T.u_g0 = params{6};
T.system_size = params{7};
T.x0 = params{8};
T.v = params{9};
T.mode = params{10};
end
T.create_mesh();
T.phi_t = Ternary_model.phi_tot(T.x, T.a, T.b, T.e, T.u0, 0);
......
@Ternary_model/create_mesh.m
+ 28
− 25
View file @ ad18b356
......@@ -2,34 +2,37 @@ function create_mesh(T)
%CREATE_MESH creates mesh for solving Ternary_model.
% Mesh density larger for steeper gradients.
if strcmp(T.mode, 'Constituent')
% Start with left side of mesh, at r=0/x=0, with a given step size
x = [0, 0.01/T.precision/10];%/10
x = linspace(0, 0.75, 40);
x = [x, x(end)+0.01/T.precision/10];%/10
while x(end)<-T.a
x_temp = x(end)-x(end-1);
phi_nm1 = T.phi_tot(x(end), T.a, T.b, T.e, T.u0, 0);
phi_n = T.phi_tot(x(end)+x_temp, T.a, T.b, T.e, T.u0, 0);
while phi_nm1-phi_n > 0.002/T.precision
x_temp = x_temp/2;
x = [0, 0.01/T.precision/10];%/10
x = linspace(0, 0.75, 40);
x = [x, x(end)+0.01/T.precision/10];%/10
while x(end)<-T.a
x_temp = x(end)-x(end-1);
phi_nm1 = T.phi_tot(x(end), T.a, T.b, T.e, T.u0, 0);
phi_n = T.phi_tot(x(end)+x_temp, T.a, T.b, T.e, T.u0, 0);
while phi_nm1-phi_n > 0.002/T.precision
x_temp = x_temp/2;
phi_n = T.phi_tot(x(end)+x_temp, T.a, T.b, T.e, T.u0, 0);
end
x = [x, x(end)+x_temp];
end
x = [x, x(end)+x_temp];
end
x = [x, x(end)+cumsum(fliplr(diff(x)))];
x_middle = linspace(-2*T.a+x(end)-x(end-1), -10*T.a, 100*T.precision);
x_right = linspace(-10*T.a+0.1, T.system_size, 100*T.precision);
T.x = [x, x_middle, x_right];
T.x = T.x(1:find(T.x-T.system_size>=0, 1)-1);
x = [x, x(end)+cumsum(fliplr(diff(x)))];
x_middle = linspace(-2*T.a+x(end)-x(end-1), -10*T.a, 100*T.precision);
x_right = linspace(-10*T.a+0.1, T.system_size, 100*T.precision);
T.x = [x, x_middle, x_right];
T.x = T.x(1:find(T.x-T.system_size>=0, 1)-1);
% Fine mesh close to x0 if ic = 'Gauss'
[~, ind] = min(abs(T.x-T.x0));
if T.x(ind+20)-T.x(ind) > 0.1
T.x = [T.x(1:ind-21), linspace(T.x(ind-20), T.x(ind+20),...
ceil((T.x(ind+20)-T.x(ind-20))*200)),...
T.x(ind+21:end)];
% Fine mesh close to x0 if ic = 'Gauss'
[~, ind] = min(abs(T.x-T.x0));
if T.x(ind+20)-T.x(ind) > 0.1
T.x = [T.x(1:ind-21), linspace(T.x(ind-20), T.x(ind+20),...
ceil((T.x(ind+20)-T.x(ind-20))*200)),...
T.x(ind+21:end)];
end
elseif strcmp(T.mode, 'Client')
% T.x = [linspace(3, 5., 500), linspace(5.05, 6.05, 3000),...
% linspace(6.06, 7.1, 500), linspace(7.15, 20, 3000)];
T.x = linspace(0, 20, 8000);
end
% T.x = [linspace(3, 5., 500), linspace(5.05, 6.05, 3000),...
% linspace(6.06, 7.1, 500), linspace(7.15, 20, 3000)];
% T.x = linspace(0, 20, 8000);
end
@Ternary_model/plot_sim.m
+ 2
− 2
View file @ ad18b356
......@@ -11,8 +11,8 @@ if strcmp(mode, 'mov')
figure(20); hold on;
for i = 1:nth:length(T.t)
cla; xlim([-T.a-1, -T.a+3]);
xlim([0, 10]);
ylim([0, 0.4]);
xlim([-10, 10]);
ylim([0, 4]);
ax = gca;
ax.FontSize = 12;
xlabel('position'); ylabel('probability [not normalized]');
......
@Ternary_model/solve_tern_frap.m
+ 12
− 8
View file @ ad18b356
......@@ -4,26 +4,30 @@ function solve_tern_frap(T)
fh_ic = @(x) flory_ic(x, T.a, T.u0, T.e, T.ic, T.x0);
fh_bc = @(xl, ul, xr, ur, t) flory_bc(xl, ul, xr, ur, t, T.u0, T.e);
fh_pde = @(x, t, u, dudx) flory_hugg_pde(x, t, u, dudx, T.a, T.b, T.e,...
T.u0, T.e_g0, T.u_g0, T.v);
T.u0, T.e_g0, T.u_g0, T.v,...
T.mode);
T.sol = pdepe(T.geometry, fh_pde, fh_ic, fh_bc, T.x, T.t);
end
%% Function definitions for pde solver
function [c, f ,s] = flory_hugg_pde(x, t, u, dudx, a, b, e, u0,...
e_g0, u_g0, v)
e_g0, u_g0, v, mode)
% Solve with full ternary model. Analytical derivatives.
% pt ... phi_tot
% gra_a ... analytical gradient of phi_tot
pt = Ternary_model.phi_tot(x, a, b, e, u0, v*t);
gra_a = Ternary_model.gradient_analytical(x, a, b, e, v*t);
g0 = Ternary_model.gamma0(x, a+t*v, b, e_g0, u_g0, v*t);
% g0 = 0.5;
c = 1;
f = g0*(1-pt)/pt*(pt*dudx-u*gra_a);
% chi_phi = -4.530864768482371;
% f = g0*(dudx+chi_phi*u*gra_a);
s = 0;
c = 1;
if strcmp(mode, 'Constituent')
g0 = Ternary_model.gamma0(x, a+t*v, b, e_g0, u_g0, v*t);
f = g0*(1-pt)/pt*(pt*dudx-u*gra_a);
elseif strcmp(mode, 'Client')
g0 = 0.5;
chi_phi = -4.530864768482371;
f = g0*(dudx+chi_phi*u*gra_a);
end
end
function u = flory_ic(x, a, u0, e, ic, x0)
......
prob_laplace.m
+ 25
− 6
View file @ ad18b356
......@@ -44,16 +44,34 @@ x_right = linspace(0, 4, 1000);
%% Moving boundary
t = linspace(0, 10, 300);
tic
T_mov = Ternary_model(0, 'Uniform', [-10, b(7/3, 10^-6), 0.5, e(7/3),...
0, 1, 10, 7, 0.5], t, 0.02);
T_mov = Ternary_model(0, 'Uniform', {-10, b(7/3, 10^-6), 0.5, e(7/3),...
0, 1, 10, 7, 0.5, 'Client'}, t, 0.02);
T_mov.solve_tern_frap();
toc
%%
csvwrite('MovingBound.csv', [T_mov.x', T_mov.sol(1, :)', T_mov.sol(end, :)'])
%% Flux moving boundary
chi_phi = -4.530864768482371;
i = 300;
x_interp = (T_mov.x(1:end-1)+T_mov.x(2:end))/2;
u = T_mov.sol(i, :);
u_interp = (u(1:end-1)+u(2:end))/2;
gra_a = Ternary_model.gradient_analytical(x_interp, T_mov.a, T_mov.b,...
T_mov.e, T_mov.v*T_mov.t(i));
dudx = diff(u)./diff(T_mov.x);
f = dudx+chi_phi.*u_interp.*gra_a;
figure; hold on;
plot(0:10, zeros(1, 11), 'LineWidth', 2);
plot(x_interp, f, 'LineWidth', 2)
set(gca,'fontsize', 18)
make_graph_pretty(['x [' char(956) 'm]'], 'flux', '', [0, 10, -0.1, 5.2])
% breakyaxis([0.6, 4.5])
% s = '~/Nextcloud/Langevin_vs_MeanField/Data_Figs_FokkPla/Mov_Bou_Flux.csv';
% csvwrite(s, [x_interp; f])
%% FRAP jump length
t = linspace(0, 5, 300);
T_mov = Ternary_model(0, 'FRAP', [-5, b(7/3, 10^-6), 0.5, e(7/3),...
0, 1, 10, 7, 0], t, 0.2);
T_mov = Ternary_model(0, 'FRAP', {-5, b(7/3, 10^-6), 0.5, e(7/3),...
0, 1, 10, 7, 0, 'Constituent'}, t, 0.2);
T_mov.solve_tern_frap();
% csvwrite('FRAP.csv', [T_mov.x', T_mov.sol(1, :)', T_mov.sol(end, :)'])
......@@ -70,11 +88,12 @@ gra_a = Ternary_model.gradient_analytical(x_interp, T_mov.a, T_mov.b,...
g0 = Ternary_model.gamma0(x_interp, T_mov.a+T_mov.v*T_mov.t(i), T_mov.b,...
T_mov.e_g0, T_mov.u_g0, T_mov.v*T_mov.t(i));
dudx = diff(u)./diff(T_mov.x);
f = g0.*(1-pt)./pt.*(pt.*dudx-u_interp.*gra_a);
hold on; cla;
plot(x_interp, g0.*(1-pt)./pt.*(pt.*dudx-u_interp.*gra_a))
plot(x_interp, f)
pause()
end
% csvwrite('FRAP.csv', [T_mov.x', T_mov.sol(1, :)', T_mov.sol(end, :)'])
csvwrite('FRAP_Flux.csv', [x_interp; f])
%% Plot with full ternary model
T_temp = T_mov;
D_m = 1*(1-T_temp.u0-T_temp.e); % to make equal to ternary FRAP
......
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