Related papers: From Brownian Dynamics to Markov Chain: an Ion Cha…
We theoretically analyze the dynamics of an atomic double-well system with a single ion trapped in its center. We find that the atomic tunnelling rate between the wells depends both on the spin of the ion via the short-range spin-dependent…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
In many practically important problems which rely on particles' transport in realistic corrugated channels, one is interested to know the probability that either of the extremities, (e.g., the one containing a chemically active site, or…
Experiments measuring currents through single protein channels show unstable currents, a phenomena called the gating of a single channel. Channels switch between an 'open' state with a well defined single amplitude of current and 'closed'…
"Quantum trajectories" are solutions of stochastic differential equations also called Belavkin or Stochastic Schr\"odinger Equations. They describe random phenomena in quantum measurement theory. Two types of such equations are usually…
For one-dimensional Jump-Drift and Jump-Diffusion processes converging towards some steady state, the large deviations of a long dynamical trajectory are described from two perspectives. Firstly, the joint probability of the empirical…
This study investigates the flux ratios of ionic flows using Poisson-Nernst-Planck (PNP) models. The flux ratio measures the effect of permanent charge on the ion fluxes and can exhibit bifurcation, where a small parameter change causes a…
Using the scheme of mesoscopic nonequilibrium thermodynamics, we construct the one- and two- particle Fokker-Planck equations for a system of interacting Brownian particles. By means of these equations we derive the corresponding balance…
Brownian ratchet like stochastic theory for the electrochemical membrane system of Hodgkin-Huxley (HH) is developed. The system is characterized by a continuous variable $Q_m(t)$, representing mobile membrane charge density, and a discrete…
We derive explicit forms of Markovian transition probability densities for the velocity space, phase-space and the Smoluchowski configuration-space Brownian motion of a charged particle in a constant magnetic field. By invoking a…
The transport of particles through channels holds immense significance in physics, chemistry, and biological sciences. For instance, the motion of solutes through biological channels is facilitated by specialized proteins that create…
In this article we address the three-dimensional modeling and simulation of biological ion channels using a continuum-based approach. Our multi-physics formulation self-consistently combines, to the best of our knowledge for the first time,…
This is an early but comprehensive review of the PNP Poisson Nernst Planck theory of ion channels. Extensive reference is made to the earlier literature. The starting place for this theory of open channels is a theory of electrodiffusion…
We study stochastic particle transport between two reservoirs along a channel, where the particles are pumped against a bias by a traveling wave potential. It is shown that phase transitions of period-averaged densities or currents occur…
Particles confined to a single file, in a narrow quasi-one dimensional channel, exhibit a dynamic crossover from single file diffusion to Fickian diffusion as the channel radius increases and the particles can begin to pass each other. The…
The dynamics of Brownian motion has widespread applications extending from transport in designed micro-channels up to its prominent role for inducing transport in molecular motors and Brownian motors. Here, Brownian transport is studied in…
Rate processes are simple and analytically tractable models for many dynamical systems which switch stochastically between a discrete set of quasi stationary states but they may also approximate continuous processes by coarse grained,…
Active particles exhibit self-propulsion, leading to transport behavior that differs fundamentally from passive Brownian motion. In confined or structured domains, activity strongly influence escape probabilities and first-passage behavior.…
We consider a simple working hypothesis that all permeation properties of open ionic channels can be predicted by understanding electrodiffusion in fixed structures, without invoking conformation changes, or changes in chemical bonds. We…
To model a complex system intrinsically separated by a barrier, we use two random Hamiltonians, coupled to each other either by a tunneling matrix element or by an intermediate transition state. We study that model in the universal limit of…