259 research outputs found
Channel noise effects on neural synchronization
Synchronization in neural networks is strongly tied to the implementation of
cognitive processes, but abnormal neuronal synchronization has been linked to a
number of brain disorders such as epilepsy and schizophrenia. Here we examine
the effects of channel noise on the synchronization of small Hodgkin-Huxley
neuronal networks. The principal feature of a Hodgkin-Huxley neuron is the
existence of protein channels that transition between open and closed states
with voltage dependent rate constants. The Hodgkin-Huxley model assumes
infinitely many channels, so fluctuations in the number of open channels do not
affect the voltage. However, real neurons have finitely many channels which
lead to fluctuations in the membrane voltage and modify the timing of the
spikes, which may in turn lead to large changes in the degree of
synchronization. We demonstrate that under mild conditions, neurons in the
network reach a steady state synchronization level that depends only on the
number of neurons in the network. The channel noise only affects the time it
takes to reach the steady state synchronization level.Comment: 7 Figure
Properties of the reaction front in a reaction-subdiffusion process
We study the reaction front for the process in which the reagents
move subdiffusively. We propose a fractional reaction-subdiffusion equation in
which both the motion and the reaction terms are affected by the subdiffusive
character of the process. Scaling solutions to these equations are presented
and compared with those of a direct numerical integration of the equations. We
find that for reactants whose mean square displacement varies sublinearly with
time as , the scaling behaviors of the reaction front can
be recovered from those of the corresponding diffusive problem with the
substitution Comment: Errata corrected, one reference update
Breathers and Thermal Relaxation in Fermi-Pasta-Ulam Arrays
Breather stability and longevity in thermally relaxing nonlinear arrays
depend sensitively on their interactions with other excitations. We review the
relaxation of breathers in Fermi-Pasta-Ulam arrays, with a specific focus on
the different relaxation channels and their dependence on the interparticle
interactions, dimensionality, initial condition, and system parameters
Generation of dynamic structures in nonequilibrium reactive bilayers
We present a nonequlibrium approach for the study of a flexible bilayer whose
two components induce distinct curvatures. In turn, the two components are
interconverted by an externally promoted reaction. Phase separation of the two
species in the surface results in the growth of domains characterized by
different local composition and curvature modulations. This domain growth is
limited by the effective mixing due to the interconversion reaction, leading to
a finite characteristic domain size. In addition to these effects, first
introduced in our earlier work [Phys. Rev. E {\bf 71}, 051906 (2005)], the
important new feature is the assumption that the reactive process actively
affects the local curvature of the bilayer. Specifically, we suggest that a
force energetically activated by external sources causes a modification of the
shape of the membrane at the reaction site. Our results show the appearance of
a rich and robust dynamical phenomenology that includes the generation of
traveling and/or oscillatory patterns. Linear stability analysis, amplitude
equations and numerical simulations of the model kinetic equations confirm the
occurrence of these spatiotemporal behaviors in nonequilibrium reactive
bilayers.Comment: To appear in Phys. Rev.
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