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hubatsch
Frap Theory
Commits
2022d0cf
Commit
2022d0cf
authored
4 years ago
by
Lars Hubatsch
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Revert "Changing plots order."
This reverts commit
9e00834c
.
parent
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prob_laplace.m
+26
-71
26 additions, 71 deletions
prob_laplace.m
with
26 additions
and
71 deletions
prob_laplace.m
+
26
−
71
View file @
2022d0cf
...
...
@@ -2,59 +2,17 @@
% Define parameters for tanh, according to Weber, Zwicker, Julicher, Lee.
b
=
@
(
chi
,
nu
)
nu
^
(
1
/
3
)
*
sqrt
(
chi
/(
chi
-
2
));
e
=
@
(
chi
)
sqrt
(
3
/
8
*
(
chi
-
2
));
t
=
[
0
,
0.
0
1
,
0.05
,
50
];
t
=
[
0
,
0.1
,
1
,
9.9
];
%% Try out different precisions
% prec = [0.5, 0.5, 1, 2, 3.5, 5];
fac
=
[
1
,
5
,
10
];
%, 10, 100];
for
i
=
1
:
length
(
fac
)
prec
=
[
0.25
,
0.5
,
1
,
2
,
3.5
,
5
];
parfor
i
=
1
:
length
(
prec
)
tic
b
=
2e-4
;
u0
=
0.5
;
P
=
1
;
D_i
=
2
;
D_o
=
20
;
a
=
-
1
;
[
b
,
u0
,
e
,
e_g
,
u_g
]
=
calc_tanh_params
(
fac
(
i
)
*
P
,
D_i
,
fac
(
i
)
*
D_o
,
a
,
b
,
u0
);
T_prec
(
i
)
=
Ternary_model
(
2
,
'FRAP'
,
{
-
1
,
b
,
u0
,
...
e
,
e_g
,
u_g
,
300
,
7
,
0
,
'Constituent'
},
...
t
,
2000
);
% T_prec(i) = Ternary_model(2, 'FRAP', {-1, b(7.7/3, 10^-5), u0, ...
% e(7.7/3), e_g, u_g, 300, 7, 0, 'Constituent'},...
% t, 0.2);
T_prec
(
i
)
=
Ternary_model
(
0
,
'Gauss'
,
[
-
6
,
b
(
7.7
/
3
,
10
^-
6
),
0.5
,
...
e
(
7.7
/
3
),
0
,
1
,
300
,
7
],
t
,
prec
(
i
));
T_prec
(
i
)
.
solve_tern_frap
()
toc
end
%% Test partitioning == 1 compared to natural no mobility case.
% Tg1: g0 = 1 everywhere.
Tpt1
=
Ternary_model
(
0
,
'FRAP'
,
{
-
1
,
b
(
7
/
3
,
10
^-
18
),
0.5
,
e
(
7
/
3
),
...
0
,
1
,
300
,
7
,
0
,
'Constituent'
},
...
t
,
1
);
Tpt1
.
solve_tern_frap
();
%%
% Rescale mobility, such that phi_tot=1 everywhere achieves same flux
Gi
=
(
1
-
Tpt1
.
phi_t
(
1
))/(
1
-
Tpt1
.
phi_t
(
1
));
Go
=
Tpt1
.
phi_t
(
1
)/
Tpt1
.
phi_t
(
end
)
*
(
1
-
Tpt1
.
phi_t
(
end
));
%%
Tga1
=
Ternary_model
(
0
,
'FRAP'
,
{
-
1
,
b
(
7
/
3
,
10
^-
18
),
Tpt1
.
phi_t
(
1
),
0
,
...
(
Go
-
Gi
),
Gi
,
300
,
7
,
0
,
'Constituent'
},
...
t
,
1
);
Tga1
.
solve_tern_frap
();
%%
Tpt1
.
plot_sim
(
'plot'
,
1
,
'g'
)
%%
Tga1
.
plot_sim
(
'plot'
,
1
,
'k'
)
%%
figure
(
3
);
hold
on
;
% fact = [0.9965, 0.94, 1.01, 1.98];fact(i)*
c
=
{
'g'
,
'm'
,
'k'
,
'r'
};
for
i
=
1
:
3
%length(T_prec)
% T_prec(i).plot_sim('plot', 1, c{i})
% Is this the right normalization? %/T_prec(i).phi_t(1)
plot
(
T_prec
(
i
)
.
x
,
T_prec
(
i
)
.
sol
'
/
T_prec
(
i
)
.
phi_t
(
1
),
c
{
i
});
axis
([
0
,
20
,
-
inf
,
1
]);
end
axis
([
0
,
2
,
0
,
1
])
%% Same precisions, different starting positions
x0
=
[
-
0.05
,
-
0.03
,
-
0.01
,
0.01
,
0.03
,
0.05
];
parfor
i
=
1
:
length
(
x0
)
...
...
@@ -71,8 +29,8 @@ end
%% Frank's/Stefano via Laplace transform vs Fokker Planck
t
=
linspace
(
0
,
10
,
1000
);
tic
T_mov
=
Ternary_model
(
0
,
'Gauss'
,
{
-
6
,
b
(
7
/
3
,
10
^-
15
),
0.5
,
e
(
7
/
3
),
...
19
,
1
,
300
,
7
,
0
,
'Constituent'
}
,
t
,
0.2
);
T_mov
=
Ternary_model
(
0
,
'Gauss'
,
[
-
6
,
b
(
7
/
3
,
10
^-
15
),
0.5
,
e
(
7
/
3
),
...
0
,
1
,
300
,
7
,
0
]
,
t
,
0.2
);
T_mov
.
solve_tern_frap
()
toc
%%
...
...
@@ -83,28 +41,6 @@ p_in = @(D_p, D_m, ga, x0, x, t) 1./(sqrt(pi*t)*(sqrt(D_m)+...
ga
*
sqrt
(
D_p
)))
*
exp
(
-
(
x
-
x0
*
sqrt
(
D_m
/
D_p
))
.^
2
/(
4
*
D_m
*
t
));
x_left
=
linspace
(
-
4
,
0
,
1000
);
x_right
=
linspace
(
0
,
4
,
1000
);
%% 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
D_p
=
20
*
(
1
-
T_temp
.
u0
+
T_temp
.
e
);
ga
=
(
T_temp
.
u0
-
T_temp
.
e
)/(
T_temp
.
u0
+
T_temp
.
e
);
for
i
=
1
:
100
%length(T_mov.t)
cla
;
figure
(
1
);
hold
on
;
xlim
([
-
2
,
2
]);
ylim
([
0
,
1
]);
plot
(
T_temp
.
x
+
T_temp
.
a
,
T_temp
.
sol
(
i
,
:),
'r.'
);
%, 'LineWidth', 2);
plot
(
x_left
,
p_in
(
D_p
,
D_m
,
ga
,
T_temp
.
x0
+
T_temp
.
a
,
x_left
,
...
t
(
i
)
+
0.01
/
1000
),
'k-.'
,
'LineWidth'
,
2
);
plot
(
x_right
,
p_out
(
D_p
,
D_m
,
ga
,
T_mov
.
x0
+
T_temp
.
a
,
x_right
,
...
t
(
i
)
+
0.01
/
1000
),
'k-.'
,
'LineWidth'
,
2
);
plot
(
x_left
,
p_in
(
10
*
D_p
,
D_m
,
ga
/
1
,
T_temp
.
x0
+
T_temp
.
a
,
x_left
,
...
t
(
i
)
+
0.01
/
1000
),
'b-.'
,
'LineWidth'
,
2
);
make_graph_pretty
([
'x ['
char
(
956
)
'm]'
],
'c [a.u.]'
,
''
,
...
[
T_temp
.
a
,
10
,
0
,
inf
])
% print([num2str(i),'.png'],'-dpng')
shg
;
pause
();
end
%% Moving boundary
t
=
linspace
(
0
,
10
,
9000
);
tic
...
...
@@ -171,6 +107,25 @@ s_dot(i) = sum(diff(T_mov.x).*f.^2./(g0.*(1-pt).*u_interp));
end
csvwrite
([
s
,
'FRAP_Flux.csv'
],
[
x_interp
;
f
])
csvwrite
([
s
,
'FRAP_entropy.csv'
],
[
T_mov
.
t
;
s_dot
]);
%% 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
D_p
=
1
*
(
1
-
T_temp
.
u0
+
T_temp
.
e
);
ga
=
(
T_temp
.
u0
-
T_temp
.
e
)/
(
T_temp
.
u0
+
T_temp
.
e
);
for
i
=
1
:
100
%length(T_mov.t)
cla
;
figure
(
1
);
hold
on
;
xlim
([
-
2
,
2
]);
ylim
([
0
,
1
]);
plot
(
T_temp
.
x
+
T_temp
.
a
,
T_temp
.
sol
(
i
,
:),
'r.'
);
%, 'LineWidth', 2);
plot
(
x_left
,
p_in
(
D_p
,
D_m
,
ga
,
T_temp
.
x0
+
T_temp
.
a
,
x_left
,
...
t
(
i
)
+
0.01
/
1000
),
'k-.'
,
'LineWidth'
,
2
);
plot
(
x_right
,
p_out
(
D_p
,
D_m
,
ga
,
T_mov
.
x0
+
T_temp
.
a
,
x_right
,
...
t
(
i
)
+
0.01
/
1000
),
'k-.'
,
'LineWidth'
,
2
)
make_graph_pretty
([
'x ['
char
(
956
)
'm]'
],
'c [a.u.]'
,
''
)
% print([num2str(i),'.png'],'-dpng')
shg
;
pause
();
end
%% Check integral of solution, should be mass conserving and sum to 1.
% integrate to 50, to avoid right boundary
[
~
,
ind
]
=
min
(
abs
(
T_prec
(
4
)
.
x
-
50
));
...
...
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