Related papers: Diffusion over a saddle with a Langevin equation
Discontinuous transitions into absorbing states require an effective mechanism that prevents the stabilization of low density states. They can be found in different systems, such as lattice models or stochastic differential equations (e.g.…
We study the temperature control problem for Langevin diffusions in the context of non-convex optimization. The classical optimal control of such a problem is of the bang-bang type, which is overly sensitive to errors. A remedy is to allow…
This paper is devoted to the development of a theoretical and computational framework to efficiently sample the statistically significant thermally activated reaction pathways, in multi-dimensional systems obeying Langevin dynamics. We show…
The well known scaling of the Edwards-Wilkinson equation is essentially determined by dimensional analysis. Once a drift term is added, more sophisticated reasoning is required, which initially suggests that the drift term dominates over…
We consider stochastic systems involving general -- non-Gaussian and asymmetric -- stable processes. The random quantities, either a stochastic force or a waiting time in a random walk process, explicitly depend on the position. A…
We propose a solution for linear inverse problems based on higher-order Langevin diffusion. More precisely, we propose pre-conditioned second-order and third-order Langevin dynamics that provably sample from the posterior distribution of…
This study handles spatial three-dimensional solution of the nonlinear diffusion equation without particular initial conditions. The functional behavior of the equation and the concentration have been studied in new ways. An auxiliary…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
Pervasive across diverse domains, stochastic systems exhibit fluctuations in processes ranging from molecular dynamics to climate phenomena. The Langevin equation has served as a common mathematical model for studying such systems, enabling…
We consider the diffusion of markers in a layered medium, with the lateral diffusion coefficient being the function of hight. We show that the probability density of the lateral displacements follows one-dimensional Batchelor's equation…
In this research paper, we present an exact matrix form analytical solution of the multi-dimensional generalized Langevin equation with quadratic potentials. Our investigation provides detailed expressions for the two-dimensional…
The phase diffusion in a self-sustained oscillator, which produces oscillator's spectral linewidth, is inherently governed by a nonlinear Langevin equation. Over past 40 years, the equation has been treated with linear approximation,…
The long-time diffusion of two-dimensional dusty plasmas on a one-dimensional periodic substrate with varied widths is investigated using Langevin dynamical simulations. When the substrate is narrow and the dust particles form a single row,…
We study the Langevin dynamics of a dipole diffusing in a random electrical field E derived from a quenched Gaussian potential. We show that in a suitable adiabatic limit (where the dynamics of the dipole moment is much faster than the…
We formulate a martingale problem that describes a diffusion process in a multidimensional Euclidean space with a membrane located on a given smooth surface and having the properties of skewing and delaying. The theorem on the existence of…
The problem of estimating small transition probabilities for overdamped Langevin dynamics is considered. A simplification of Girsanov's formula is obtained in which the relationship between the infinitesimal generator of the underlying…
In this paper, we propose a new adaptation of the D-iteration algorithm to numerically solve the differential equations. This problem can be reinterpreted in 2D or 3D (or higher dimensions) as a limit of a diffusion process where the…
The linear intensity profile of multiply scattered light in a slab geometry extrapolates to zero at a certain distance beyond the boundary. The diffusion equation with this "extrapolated boundary condition" has been used in the literature…
We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially-dependent diffusion coefficient of the form $D(x)\sim |x|^c$, at constant temperature. The particle's probability distribution function…
The behavior of the self diffusion constant of Langevin particles interacting via a pairwise interaction is considered. The diffusion constant is calculated approximately within a perturbation theory in the potential strength about the bare…