Related papers: From Brownian Dynamics to Markov Chain: an Ion Cha…
We consider a finite state discrete time process X. Without loss of generality the finite state space can be identified with the set of unit vectors {e1, e2, . . . , eN} with ei = (0, . . . , 0, 1, 0, . . . , 0)0 2 RN. For a Markov chain…
We propose a particle system of diffusion processes coupled through a chain-like network structure described by an infinite-dimensional, nonlinear stochastic differential equation of McKean-Vlasov type. It has both (i) a local chain…
We describe a method to simulate the dynamics of charged colloidal particles suspended in a liquid containing dissociated ions and salt ions. Regimes of prime current interest are those of large volume fraction of colloids, highly charged…
Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…
For continuous-time Markov jump processes on irreducible networks with time-independent rate constants, we employ a transition-based formalism to express the long-time precision of a single integrated current over an observable channel in…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
Molecular dynamics are extremely complex, yet understanding the slow components of their dynamics is essential to understanding their macroscopic properties. To achieve this, one models the molecular dynamics as a stochastic process and…
A self-consistent mode coupling theory (MCT) with microscopic inputs of equilibrium pair correlation functions is developed to analyze electrolyte dynamics. We apply the theory to calculate concentration dependence of (i) time dependent ion…
Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by…
We analyze the escape of Brownian particles over potential barriers using the Fokker-Planck equation in a similar way to that of Chandrasekhar (Rev. Modern Phys., 1943), deriving a formula for the particle deposition velocity to a surface…
A variety of enhanced statistical and numerical methods are now routinely used to extract comprehensible and relevant thermodynamic information from the vast amount of complex, high-dimensional data obtained from intensive molecular…
Donsker Theorem is perhaps the most famous invariance principle result for Markov processes. It states that when properly normalized, a random walk behaves asymptotically like a Brownian motion. This approach can be extended to general…
We analyze the dynamics of a tracer particle embedded in a bath of hard spheres confined in a channel of varying section. By means of Brownian dynamics simulations we apply a constant force on the tracer particle and discuss the dependence…
The dynamics of dissipative many-body quantum systems sometimes admit an emergent classical description in terms of a Markov chain even though the corresponding state space contains highly entangled states. In particular, a bad-cavity laser…
We study singularities in the large deviation function of the time-averaged current of diffusive systems connected to two reservoirs. A set of conditions for the occurrence of phase transitions, both first and second order, are obtained by…
The diffusion of a system of ferromagnetic dipoles confined in a quasi-one-dimensional parabolic trap is studied using Brownian dynamics simulations. We show that the dynamics of the system is tunable by an in-plane external homogeneous…
We study diffusion-controlled processes in nonequilibrium steady states, where standard rate theory assumptions break down. Using transition path theory, we generalize the relations between reactive probability fluxes and measures of the…
The phase offset between surface charge modulation and geometric undulations in a corrugated nanochannel provides a tunable mechanism for rectified, diode-like ion transport under purely pressure-driven conditions: reversing the applied…
This work proposes a method for the two-dimensional simulation of Brownian particles in a fluid with restrictions. The method is based on simple numerical rules between two matrices. One of the matrix represent the identification of all…
The transport of independent active Brownian particles within a two-dimensional narrow channel, modeled as an open-wedge, is studied both numerically and theoretically. We show that the active force tends to localize the particles near the…