Related papers: Comparizon of dynamic diffusion with explicit diff…
This survey paper is a structured concise summary of four of our recent papers on the stochastic regularity of diffusions that are associated to regular strongly local (but not necessarily symmetric) Dirichlet forms. Here by stochastic…
Dispersive shock waves (DSWs) of the defocusing radial nonlinear Schr\"odinger (rNLS) equation in two spatial dimensions are studied. This equation arises naturally in Bose-Einstein condensates, water waves and nonlinear optics. A unified…
We consider a three dimensional system consisting of a large number of small spherical particles, distributed in a range of sizes and heights (with uniform distribution in the horizontal direction). Particles move vertically at a…
Diffusion in bidisperse Brownian hard-sphere suspensions is studied by Stokesian Dynamics (SD) computer simulations and a semi-analytical theoretical scheme for colloidal short-time dynamics, based on Beenakker and Mazur's method [Physica…
We present a numerical method to deal efficiently with large numbers of particles in incompressible fluids. The interactions between particles and fluid are taken into account by a physically motivated ansatz based on locally defined drag…
Because diffusion models have shown impressive performances in a number of tasks, such as image synthesis, there is a trend in recent works to prove (with certain assumptions) that these models have strong approximation capabilities. In…
The non-Newtonian behavior of a monodisperse concentrated dispersion of spherical particles was investigated using a direct numerical simulation method, that takes into account hydrodynamic interactions and thermal fluctuations accurately.…
For the regime-switching diffusion process with and without advection term we propose an integro-differential equation describing the densities of states continuously distributed over a segment. We demonstrate that there exists a…
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…
This paper enhances the Diffuse Interface Method (DIM) for simulating compressible multiphase flows across all Mach numbers by addressing the accuracy challenges posed at low Mach regimes. A correction to the Riemann solver is introduced,…
Diffusion models have recently gained traction as a powerful class of deep generative priors, excelling in a wide range of image restoration tasks due to their exceptional ability to model data distributions. To solve image restoration…
We find an exact analytical solution of the reduced density matrix from the Feynman-Vernon influence functional theory for a wave packet influenced by an environment containing a few discrete modes. We obtain two intrinsic energy scales…
Mathematical modeling of many physical processes such as diffusion, viscosity of fluids and combustion involves differential equations with small coefficients of higher derivatives. These may be small diffusion coefficients for modeling the…
The Boeder differential equation is solved in this work over a wide range of $\alpha$, yielding the probability density functions (PDF), that describe the average orientations of rod-like macromolecules in a flowing liquid. The quantity…
The stochastic dissipative Schrodinger equation is derived for an open quantum system consisting of a sub-system able to exchange energy with a thermal reservoir. The resultant evolution of the wave function also gives the evolution of the…
We study a second order scheme for spatial fractional differential equations with variable coefficients. Previous results mainly concentrate on equations with diffusion coefficients that are proportional to each other. In this paper, by…
Rendering highly scattering participating media using brute force path tracing is a challenge. The diffusion approximation reduces the problem to solving a simple linear partial differential equation. Flux-limited diffusion introduces…
We study Diffusion Schr\"odinger Bridge (DSB) models in the context of dynamical astrophysical systems, specifically tackling observational inverse prediction tasks within Giant Molecular Clouds (GMCs) for star formation. We introduce the…
We present a theoretical model of matter-wave diffraction through a material nanostructure. This model is based on the numerical solution of the time-dependent Schr{\"o}dinger equation, which goes beyond the standard semi-classical…
We address an original approach for the convergence analysis of a finite-volume scheme for the approximation of a stochastic diffusion-convection equation with multiplicative noise in a bounded domain of $\mathbb{R}^d$ (with $d=2$ or $3$)…