3,010 research outputs found
A nonlinear equation for ionic diffusion in a strong binary electrolyte
The problem of the one dimensional electro-diffusion of ions in a strong
binary electrolyte is considered. In such a system the solute dissociates
completely into two species of ions with unlike charges. The mathematical
description consists of a diffusion equation for each species augmented by
transport due to a self consistent electrostatic field determined by the
Poisson equation. This mathematical framework also describes other important
problems in physics such as electron and hole diffusion across semi-conductor
junctions and the diffusion of ions in plasmas. If concentrations do not vary
appreciably over distances of the order of the Debye length, the Poisson
equation can be replaced by the condition of local charge neutrality first
introduced by Planck. It can then be shown that both species diffuse at the
same rate with a common diffusivity that is intermediate between that of the
slow and fast species (ambipolar diffusion). Here we derive a more general
theory by exploiting the ratio of Debye length to a characteristic length scale
as a small asymptotic parameter. It is shown that the concentration of either
species may be described by a nonlinear integro-differential equation which
replaces the classical linear equation for ambipolar diffusion but reduces to
it in the appropriate limit. Through numerical integration of the full set of
equations it is shown that this nonlinear equation provides a better
approximation to the exact solution than the linear equation it replaces.Comment: 4 pages, 1 figur
Entropic transport - A test bed for the Fick-Jacobs approximation
Biased diffusive transport of Brownian particles through irregularly shaped,
narrow confining quasi-one-dimensional structures is investigated. The
complexity of the higher dimensional diffusive dynamics is reduced by means of
the so-called Fick-Jacobs approximation, yielding an effective one-dimensional
stochastic dynamics. Accordingly, the elimination of transverse, equilibrated
degrees of freedom stemming from geometrical confinements and/or bottlenecks
cause entropic potential barriers which the particles have to overcome when
moving forward noisily. The applicability and the validity of the reduced
kinetic description is tested by comparing the approximation with Brownian
dynamics simulations in full configuration space. This non-equilibrium
transport in such quasi-one-dimensional irregular structures implies for
moderate-to-strong bias a characteristic violation of the Sutherland-Einstein
fluctuation-dissipation relation.Comment: 15 pages, 6 figures ; Phil. Trans. R. Soc. A (2009), in pres
Propagators weakly associated to a family of Hamiltonians and the adiabatic theorem for the Landau Hamiltonian with a time-dependent Aharonov-Bohm flux
We study the dynamics of a quantum particle moving in a plane under the
influence of a constant magnetic field and driven by a slowly time-dependent
singular flux tube through a puncture. The known adiabatic results do not cover
these models as the Hamiltonian has time dependent domain. We give a meaning to
the propagator and prove an adiabatic theorem. To this end we introduce and
develop the new notion of a propagator weakly associated to a time-dependent
Hamiltonian.Comment: Title and Abstract changed, will appear in Journal of Mathematical
Physic
New derivation for the equations of motion for particles in electromagnetism
We present equations of motion for charged particles using balanced
equations, and without introducing explicitly divergent quantities. This
derivation contains as particular cases some well known equations of motion, as
the Lorentz-Dirac equations. An study of our main equations in terms of order
of the interaction with the external field conduces us to the Landau-Lifshitz
equations. We find that the analysis in second order show a special behavior.
We give an explicit presentation up to third order of our main equations, and
expressions for the calculation of general orders.Comment: 11 pages, 2 figures. Minor changes. Closer to published versio
Unidirectional hopping transport of interacting particles on a finite chain
Particle transport through an open, discrete 1-D channel against a mechanical
or chemical bias is analyzed within a master equation approach. The channel,
externally driven by time dependent site energies, allows multiple occupation
due to the coupling to reservoirs. Performance criteria and optimization of
active transport in a two-site channel are discussed as a function of reservoir
chemical potentials, the load potential, interparticle interaction strength,
driving mode and driving period. Our results, derived from exact rate
equations, are used in addition to test a previously developed time-dependent
density functional theory, suggesting a wider applicability of that method in
investigations of many particle systems far from equilibrium.Comment: 33 pages, 8 figure
Steady state existence of passive vector fields under the Kraichnan model
The steady state existence problem for Kraichnan advected passive vector
models is considered for isotropic and anisotropic initial values in arbitrary
dimension. The model includes the magnetohydrodynamic (MHD) equations, linear
pressure model (LPM) and linearized Navier-Stokes (LNS) equations. In addition
to reproducing the previously known results for the MHD and linear pressure
model, we obtain the values of the Kraichnan model roughness parameter
for which the LNS steady state exists.Comment: Improved text & figures, added references & other correction
Focusing in Multiwell Potentials: Applications to Ion Channels
We investigate out of equilibrium stationary distributions induced by a
stochastic dichotomous noise on double and multi-well models for ion channels.
Ion-channel dynamics is analyzed both through over-damped Langevin equations
and master equations. As a consequence of the external stochastic noise, we
prove a non trivial focusing effect, namely the probability distribution is
concentrated only on one state of the multi-well model. We also show that this
focusing effect, which occurs at physiological conditions, cannot be predicted
by a simple master equation approach.Comment: 8 pages, 7 figure
Monte Carlo simulation for statistical mechanics model of ion channel cooperativity in cell membranes
Voltage-gated ion channels are key molecules for the generation and
propagation of electrical signals in excitable cell membranes. The
voltage-dependent switching of these channels between conducting and
nonconducting states is a major factor in controlling the transmembrane
voltage. In this study, a statistical mechanics model of these molecules has
been discussed on the basis of a two-dimensional spin model. A new Hamiltonian
and a new Monte Carlo simulation algorithm are introduced to simulate such a
model. It was shown that the results well match the experimental data obtained
from batrachotoxin-modified sodium channels in the squid giant axon using the
cut-open axon technique.Comment: Paper has been revise
Entropic Stochastic Resonance
We present a novel scheme for the appearance of Stochastic Resonance when the
dynamics of a Brownian particle takes place in a confined medium. The presence
of uneven boundaries, giving rise to an entropic contribution to the potential,
may upon application of a periodic driving force result in an increase of the
spectral amplification at an optimum value of the ambient noise level. This
Entropic Stochastic Resonance (ESR), characteristic of small-scale systems, may
constitute a useful mechanism for the manipulation and control of
single-molecules and nano-devices.Comment: 4 pages, 3 figure
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