-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathmain.m
185 lines (161 loc) · 5.91 KB
/
main.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Charge transfer by discrete breathers in 1D model
% written by Janis Bajars, April 2022
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
close all
clearvars
clc
set(0,'DefaultAxesFontSize',16)
set(groot,'DefaultAxesTickLabelInterpreter','latex');
set(groot,'DefaultTextInterpreter','latex');
set(groot,'DefaultLegendInterpreter','latex');
disp('Start of the computation!')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Add path
addpath('Functions')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Compute parameter values in structure <parm>
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Parameter_Values;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Define simulation variables (u,a,p,b) in structure <vars>
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Define_Variables;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Set initial conditions
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % % % Initial conditions: stationary breather + charge
% % % L = round(parm.N/2);
% % % % Lattice
% % % gamma = 0.4;
% % % vars.p(L-1) = -1*gamma;
% % % vars.p(L) = 2*gamma;
% % % vars.p(L+1) = -2*gamma;
% % % vars.p(L+2) = 1*gamma;
% % % % Charge
% % % vars.a(L) = 1;
% % % vars.b(L) = -1;
% Initial conditions: moving breather + charge
L = round(parm.N/4);
% Lattice
gamma = 0.6;
vars.p(L-1) = -1*gamma;
vars.p(L) = 2*gamma;
vars.p(L+1) = -1*gamma;
% Charge
vars.a(L) = 1;
vars.b(L) = -1;
% Make sure that charge constraint is satisfied
C2 = sum(vars.a.^2 + vars.b.^2);
vars.a = vars.a/sqrt(C2)*parm.tau_f;
vars.b = vars.b/sqrt(C2)*parm.tau_f;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Matrices for saving data in time
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
U = zeros(parm.N,parm.Nsteps+1);
U(:,1) = vars.u;
Q = zeros(parm.N,parm.Nsteps+1);
Q(:,1) = parm.x + vars.u;
P = zeros(parm.N,parm.Nsteps+1);
P(:,1) = vars.p;
A = zeros(parm.N,parm.Nsteps+1);
A(:,1) = vars.a;
B = zeros(parm.N,parm.Nsteps+1);
B(:,1) = vars.b;
H = zeros(parm.Nsteps+1,1);
H(1,1) = Comp_Hamiltonian(parm,vars);
C2 = zeros(parm.Nsteps+1,1);
C2(1,1) = Comp_Charge_Total(parm,vars);
C2_density = zeros(parm.N,parm.Nsteps+1);
C2_density(:,1) = Comp_Charge_Density(parm,vars);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Time integration
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for n=1:parm.Nsteps
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Explicit Runge-Kutta 4 method
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % % vars = Method_RK4(parm,vars,parm.h);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Semi-implicit splitting methods
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % % vars = Method_Im_PQCimQP(parm,vars,parm.h);
% % % vars = Method_Im_QPCimPQ(parm,vars,parm.h);
% % %
% % % vars = Method_Im_PQDWimDQP(parm,vars,parm.h);
% % % vars = Method_Im_QPDWimDPQ(parm,vars,parm.h);
% % %
% % % vars = Method_Im_PQDWimDQP_sc(parm,vars,parm.h);
% % % vars = Method_Im_QPDWimDPQ_sc(parm,vars,parm.h);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Explicit splitting methods
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % % vars = Method_Ex_PQABDBAQP(parm,vars,parm.h);
% % % vars = Method_Ex_PQBADABQP(parm,vars,parm.h);
% % %
vars = Method_Ex_PQDABADQP(parm,vars,parm.h);
% % % vars = Method_Ex_PQDBABDQP(parm,vars,parm.h);
% % %
% % % vars = Method_Ex_DABQPQBAD(parm,vars,parm.h);
% % % vars = Method_Ex_DBAQPQABD(parm,vars,parm.h);
% % %
% % % vars = Method_Ex_ABDQPQDBA(parm,vars,parm.h);
% % % vars = Method_Ex_BADQPQDAB(parm,vars,parm.h);
% Save data in time
U(:,n+1) = vars.u;
Q(:,n+1) = parm.x + vars.u*1.5;
P(:,n+1) = vars.p;
A(:,n+1) = vars.a;
B(:,n+1) = vars.b;
H(n+1,1) = Comp_Hamiltonian(parm,vars);
C2(n+1,1) = Comp_Charge_Total(parm,vars);
C2_density(:,n+1) = Comp_Charge_Density(parm,vars);
end
% % % % Save data: optional
% % % save('SavedData/charge_transfer_simulation.mat','parm','vars',...
% % % 'U','Q','P','A','B','H','C2','C2_density')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Plot results and errors
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure(1)
set(gcf, 'Position', [100, 550, 700, 400])
colormap(flipud(hot))
contourf(parm.t,parm.x,C2_density,'edgecolor','none')
shading flat
caxis([0 1])
c=colorbar;
set(c,'TickLabelInterpreter','latex')
hold on
plot(parm.t,Q','-k','linewidth',1)
axis on
box on
xlabel('$t$')
ylabel('$q_n^0+1.5u_n$','interpreter','latex')
axis([0 parm.Tend 0 parm.N-1])
legend('Charge probability $P_n$')
set(legend,'location','northwest')
% % % % Save figure: optional
% % % exportgraphics(gcf,'Figures/mov_solution.png','Resolution',300)
figure(2)
set(gcf, 'Position', [900, 550, 700, 400])
ErrorH = abs((H-H(1))/H(1));
plot(parm.t,ErrorH,'-r','linewidth',1.5)
axis on
box on
grid on
xlabel('$t$')
ylabel('Relative Hamiltonian error')
figure(3)
set(gcf, 'Position', [500, 50, 700, 400])
ErrorC = abs((C2-C2(1))/C2(1));
plot(parm.t,ErrorC,'-b','linewidth',1.5)
axis on
box on
grid on
xlabel('$t$')
ylabel('Relative probability error')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Remove path
rmpath('Functions')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%