Related papers: Computation of diffusive shock acceleration using …
In this paper we construct numerical schemes to approximate linear transport equations with slab geometry by diffusion equations. We treat both the case of pure diffusive scaling and the case where kinetic and diffusive scalings coexist.…
A numerical procedure was developed for solving equations for compressible granular multiphase flows in which the particle volume fraction can range dynamically from very dilute to very dense. The procedure uses a low-dissipation and…
This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membrane-mediated receptor dynamics on cell surfaces, we…
An adpative integration technique for time advancement of particle motion in the context of coupled computational fluid dynamics (CFD) - discrete element method (DEM) simulations is presented in this work. CFD-DEM models provide an accurate…
We model the acceleration of electrons at a shock front in a relativistic blazar jet and compute the radiation they emit in a post-shock region which contains a homogeneous magnetic field. The full space, time and momentum dependence of the…
Marcus stochastic differential equations (SDEs) often are appropriate models for stochastic dynamical systems driven by non-Gaussian Levy processes and have wide applications in engineering and physical sciences. The probability density of…
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…
Diffusion-based generative processes, formulated as differential equation solving, frequently balance computational speed with sample quality. Our theoretical investigation of ODE- and SDE-based solvers reveals complementary weaknesses: ODE…
In this work the theory of diffusive shock acceleration is extended to the case of non-classical particle transport with L\'{e}vy flights and L\'{e}vy traps, when the mean square displacement grows nonlinearly with time. In this approach…
Simulation-based techniques such as variants of stochastic Runge-Kutta are the de facto approach for inference with stochastic differential equations (SDEs) in machine learning. These methods are general-purpose and used with parametric and…
We present an explicit method for simulating stochastic differential equations (SDEs) that have variable diffusion coefficients and satisfy the detailed balance condition with respect to a known equilibrium density. In Tupper and Yang…
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…
We have calculated the evolution of cosmic ray (CR) modified astrophysical shocks for a wide range of shock Mach numbers and shock speeds through numerical simulations of diffusive shock acceleration (DSA) in 1D quasi- parallel plane…
We study stochastic acceleration models for the Fermi bubbles. Turbulence is excited just behind the shock front via Kelvin--Helmholtz, Rayleigh--Taylor, or Richtmyer--Meshkov instabilities, and plasma particles are continuously accelerated…
A multiscale analysis of 1D stochastic bistable reaction-diffusion equations with additive noise is carried out w.r.t. travelling waves within the variational approach to stochastic partial differential equations. It is shown with explicit…
We describe a computational framework for simulating suspensions of rigid particles in Newtonian Stokes flow. One central building block is a collision-resolution algorithm that overcomes the numerical constraints arising from particle…
Self-propelled particles can navigate complex environments, including viscous fluid interfaces with curved geometries. In this work, we study the emergent dynamics of a suspension of self-propelled particles confined to a stationary curved…
We investigate the diffusive shock acceleration in the presence of the non-resonant streaming instability introduced by Bell (2004). The numerical MHD simulations of the magnetic field amplification combined with the analytical treatment of…
The connection between forward backward doubly stochastic differential equations and the optimal filtering problem is established without using the Zakai's equation. The solutions of forward backward doubly stochastic differential equations…
The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we…