Related papers: When surface evolution meets Fokker-Planck equatio…
For the characterization of surface height profiles we present a new stochastic approach which is based on the theory of Markov processes. With this analysis we achieve a characterization of the complexity of the surface roughness by means…
This paper introduces a nonlinear acceleration technique that accelerates the convergence of solution of transport problems with highly forward-peaked scattering. The technique is similar to a conventional high-order/low-order (HOLO)…
The Fokker-Planck equation provides complete statistical description of a particle undergoing random motion in a solvent. In the presence of Lorentz force due to an external magnetic field, the Fokker-Planck equation picks up a tensorial…
Surfaces sputtered by ion beam bombardment have been known to exhibit patterns whose behavior is modeled with stochastic partial differential equations. However, we apply a new approach by the use of the famous Lorentz equations to simulate…
In this work, we propose an adaptive learning approach based on temporal normalizing flows for solving time-dependent Fokker-Planck (TFP) equations. It is well known that solutions of such equations are probability density functions, and…
This Letter introduces an approach for precisely designing surface friction properties using a conditional generative machine learning model, specifically a diffusion denoising probabilistic model (DDPM). We created a dataset of synthetic…
Anomalous diffusion and power-law distributions are observed in various complex systems. To provide a consistent dynamical foundation for these phenomena, we present a geometric derivation of the nonlinear Fokker-Planck equation by…
In this work, we propose a method to learn multivariate probability distributions using sample path data from stochastic differential equations. Specifically, we consider temporally evolving probability distributions (e.g., those produced…
Optimal-order uniform-in-time $H^1$-norm error estimates are given for semi- and full discretizations of mean curvature flow of surfaces in arbitrarily high codimension. The proposed and studied numerical method is based on a parabolic…
We study the evolution of the probability density of an asexual, one locus population under natural selection and random evolution. This evolution is governed by a Fokker-Planck equation with degenerate coefficients on the boundaries,…
We propose and analyze a mixed finite element method for the spatial approximation of a time-fractional Fokker--Planck equation in a convex polyhedral domain, where the given driving force is a function of space. Taking into account the…
The design of particle simulation methods for collisional plasma physics has always represented a challenge due to the unbounded total collisional cross section, which prevents a natural extension of the classical Direct Simulation Monte…
The new scheme of stochastic quantization is proposed. This quantization procedure is equivalent to the deformation of an algebra of observables in the manner of deformation quantization with an imaginary deformation parameter (the Planck…
Surface Stokes and Navier-Stokes equations are used to model fluid flow on surfaces. They have attracted significant recent attention in the numerical analysis literature because approximation of their solutions poses significant challenges…
While surface-hopping has emerged as a powerful method to simulate non-adiabatic dynamics in large molecules, the ad hoc nature of the necessary velocity adjustments and decoherence corrections in the algorithm somewhat reduces its…
We present a systematic approach to regularity theory of the multi-dimensional Euler alignment systems with topological diffusion introduced in \cite{STtopo}. While these systems exhibit flocking behavior emerging from purely local…
In this paper, we propose a novel method to approximate the mean field stochastic differential equation by means of approximating the density function via Fokker-Planck equation. We construct a well-posed truncated Fokker-Planck equation…
We introduce novel finite element schemes for curve diffusion and elastic flow in arbitrary codimension. The schemes are based on a variational form of a system that includes a specifically chosen tangential motion. We derive optimal $L^2$-…
Due to its parabolic character, the diffusion equation exhibits instantaneous spatial spreading, and becomes unstable when Lorentz-boosted. According to the conventional interpretation, these features reflect a fundamental incompatibility…
In this paper, we propose an approach for solving PDEs on evolving surfaces using a combination of the trace finite element method and a fast marching method. The numerical approach is based on the Eulerian description of the surface…