Related papers: Modeling Cosmic-Ray Transport: A CRPropa based sto…
We calculate cosmic ray transport with a collisional Boltzmann Transport Equation, including E-M forces. We apply the Crank-Nicholson Method to solve this equation. At each time step, the spatial distribution of cosmic rays is applied to…
Diffusion models have recently emerged as powerful stochastic frameworks for high-dimensional inference and generation. However, existing applications to partial differential equations (PDEs) predominantly rely on physics-informed training…
This paper studies cosmic ray (CR) transport in magneto hydrodynamic (MHD) turbulence. CR transport is strongly dependent on the properties of the magnetic turbulence. We perform test particle simulations to study the interactions of CR…
(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…
A novel method for solving the linear radiative transport equation (RTE) in a three-dimensional homogeneous medium is proposed and illustrated with numerical examples. The method can be used with an arbitrary phase function A(s,s') with the…
Context. Indirect observations of the cosmic-ray electron (CRE) distribution via synchrotron emission is crucial for deepening the understanding of the CRE transport in the interstellar medium, and in investigating the role of galactic…
Recent advances in both the MHD turbulence theory and cosmic ray observations call for revisions in the paradigm of cosmic ray transport. We use the models of magnetohydrodynamic turbulence that were tested in numerical simulation, in which…
We investigate the application of fractional calculus to model stellar dynamics, focusing on Resonant Relaxation (RR) near a supermassive black hole (SMBH). Standard theories use the local Fokker-Planck (FP) equation, restricted to Gaussian…
We present PDE-FM, a modular foundation model for physics-informed machine learning that unifies spatial, spectral, and temporal reasoning across heterogeneous partial differential equation (PDE) systems. PDE-FM combines spatial-spectral…
In this paper we employ three recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a family of so-called short-pulse equations (SPE). A recent, novel application of phase-plane…
Galactic transport models for cosmic rays involve the diffusive motion of these particles in the interstellar medium. Due to the large-scale structured galactic magnetic field this diffusion is anisotropic with respect to the local field…
The transport of energetic particles in a spatially varying magnetic field is described by the focused transport equation. In the past two versions of this equation were investigated. The more commonly used standard form described a…
In this paper we study the sensitivities of electron dose calculations with respect to the stopping power and the transport coefficients. We focus on the application to radiotherapy simulations. We use a Fokker-Planck approximation to the…
This work proposes and analyzes a generalized acceleration technique for decreasing the computational complexity of using stochastic collocation (SC) methods to solve partial differential equations (PDEs) with random input data. The SC…
Moment estimation for stochastic differential equations (SDEs) is fundamental to the formal reasoning and verification of stochastic dynamical systems, yet remains challenging and is rarely available in closed form. In this paper, we study…
A correct description of cosmic-ray (CR) diffusion in turbulent plasma is essential for many astrophysical and heliospheric problems. This paper aims to present physical diffusion behavior of CRs in actual turbulent magnetic fields, model…
Mathematical models based on probability density functions (PDF) have been extensively used in hydrology and subsurface flow problems, to describe the uncertainty in porous media properties (e.g., permeability modelled as random field).…
The task of sampling from a probability density can be approached as transporting a tractable density function to the target, known as dynamical measure transport. In this work, we tackle it through a principled unified framework using…
Deterministically solving charged particle transport problems at a sufficient spatial and angular resolution is often prohibitively expensive, especially due to their highly forward peaked scattering. We propose a model order reduction…
We derive a consistent set of moments equations for CR-magnetohydrodynamics, assuming a gyrotropic distribution function (DF). Unlike previous efforts we derive a closure, akin to the M1 closure in radiation hydrodynamics (RHD), that is…