Biomedical Engineering Reference
In-Depth Information
The reactive fluxes, the polarity vector, and the ATP consumption rate, are given
next.
D
D
d
A
1
2
.
ph
N
I
r
0
k
2
I
Dt
C
pp
p
k
C
C
hp
/
CN
1
p
hI
;
1
2
D
2
Dt
2
P
r
D
1
r
v
p
N
1
Tr.
r
v
/
p
;
N
Tr.
r
r
r
v
/
C
0
k
2
Tr.
r
D
pp
Wr
C
k
v
p
v
/;
(38)
where ;
N
;
0
;
1
;
N
1
are model parameters and
D
2
v
v
/Tr
d
I
r
d
C
d
v
/
d
A
r
C
3
Tr.
r
C
4
Tr.
r
C
5
Tr
d
r
W
d
I
;
v
C
6
r
v
(39)
where
i
are the model parameters analogous to the eight-constant Oldroyd model.
Combining the reactive and dissipative parts, the total stress, polarity vector, and
the ATP consumption rate are finally given by
1
C
D
Dt
C
pp
C
A
C
N
I
C
0
k
2
I
2
D
D
p
k
1
2
.
ph
C
hp
Q
1
.
p
h
/
I
/;
1
2
D
2
Dt
2
P
1
2
D
2
Dt
2
h
1
C
1
p
D
1
D
Dt
.
1
r
v
p
CQ
1
Tr.
r
v
/
p
/;
C
N
Tr.
r
r
.b/
r
D
ƒ
C
1
p
h
C
p
C
pp
Wr
v
v
/
C
0
k
2
Tr.
r
k
p
v
/:
(40)
By restricting
p
to be a unit vector and using a free energy for polar liquid crystals
Z
K
1
2
.
r
2
d
x
;
K
3
2
k
h
j
2
k
p
/
2
2
F
D
C
p
r
p
k
C
k
r
p
p
k
(41)
Kruse et al. studied point defects in two dimensions [
64
]. This model was later
extended to a multicomponent active fluid model by Joanny et al. [
55
].
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