![](bg4.png)
In the figure 4 it is showed that the rate of
diffusion of particles decays with time until the
value zero. This behavior is associated with the
potential that is not constant on time. For large value
of time, the potential presents a high and large
barrier. The result is the confinement of the
particles.
This phenomenon is also observed by the first
passage time (τ) of the particles through the barrier,
equation (11). In the figure 5 the value of τ as a
function of the time is plotted. Initially, the time is
short featuring a fast passage of particles through the
barrier, but this value increase due to the increased
and diverges (τ → ∞) for large values of time.
Figure 5: Escape time (τ) versus t for different values of
Q, with k
1
= 0.2, λ = 1 and k
2,0
= 0.05.
From the curves in figure 5, it is possible to
observe that for large values of the Q the diffusion
through the barrier become more fast and effective.
In figure 4 we note that for a time t = 4 there is a
small diffusion of particles when Q equal to 2, but
for a low value of the diffusion coefficient (for
instance, Q = 0.1) the diffusion is null for this time.
Following the same reasoning, it is observed that for
a low value of the diffusion coefficient, the time of
first passage (figure 5) becomes long for large Q
values.
5 CONCLUSIONS
The results obtained from the solution of the Fokker-
Planck equation for the potential suggested (2)
exhibit a behavior consistent with that expected from
the electrical transmission at synapses. The flow of
charge is most intense at the beginning of the signal
and tends to vanish for large values of time. This
result combined with the construction of the
potential allows concluding that this approach can be
effective to describe the dynamics of the physical
process that occurs at synapses.
The models proposed in literature usually
consider the diffusion through a fixed barrier of
energy on time and the escape rate is calculated
using only the results of the system at the stationary
state (rate of Kramer (Risken, 1989, Hänggir,
1990)), which limits quite the applicability of these
models. Then, the potential proposed here can be
useful to build more realistic models.
ACKNOWLEDGEMENTS
The authors thank CNPq, FAPESP and
FUNDUNESP (Brazilian agencies) for partial
financial support.
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