Related papers: Modeling Cosmic-Ray Transport: A CRPropa based sto…
We model the transport of cosmic ray nuclei in the Galaxy by means of a new numerical code. Differently from previous numerical models we account for a generic spatial distribution of the diffusion coefficient. We found that in the case of…
We present the systematic formalism to derive the path-integral formulation for the hard-core particle systems far from equilibrium. Writing the master equation for a stochastic process of the system in terms of the annihilation and…
For a plasma in a stationary homogeneous turbulence, the Fokker-Planck equation is derived from the nonlinear Vlasov equation by introducing the entropy principle. The ensemble average in evaluating the kinetic diffusion tensor, whose…
Coulomb collision is a fundamental diffusion process in plasmas that can be described by the Landau-Fokker-Planck (LFP) equation or the stochastic differential equation (SDE). While energy and momentum are conserved exactly in the LFP…
Cosmic rays (CR), constrained by scattering on magnetic irregularities, are believed to propagate diffusively. But a well-known defect of diffusive approximation whereby some of the particles propagate unrealistically fast has directed…
Score-based modeling through stochastic differential equations (SDEs) has provided a new perspective on diffusion models, and demonstrated superior performance on continuous data. However, the gradient of the log-likelihood function, i.e.,…
An analysis of traveling wave solutions of partial differential equation (PDE) systems with cross-diffusion is presented. The systems under study fall in a general class of the classical Keller-Segel models to describe chemotaxis. The…
We have developed a novel computer code designed to follow the evolution of cosmic-ray modified shocks, including the full momentum dependence of the particles for a realistic diffusion coefficient model. In this form the problem is…
In this paper we focus on a discrete physical model describing granular crystals, whose equations of motion can be described by a system of differential difference equations (DDEs). After revisiting earlier continuum approximations, we…
The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability of N stochastic variables with Lochner's generalized Dirichlet distribution (R.H. Lochner, A Generalized…
We extend the unified kernel framework for transport equations and Koopman eigenfunctions, developed in previous work by the authors for deterministic systems, to stochastic differential equations (SDEs). In the deterministic setting, three…
Cosmic ray (CR) transport is usually modeled with a single diffusion coefficient, but this description captures only the growth of the variance and not the full transport process. Distinct transport mechanisms can share the same effective…
The Fokker-Planck equation describing the transport of energetic particles interacting with turbulence is difficult to solve analytically. Numerical solutions are of course possible but they are not always useful for applications. In the…
Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…
Experiments for radio detection of UHE particles such as e.g. ARA/ARIANNA or NuMoon require detailed understanding of the propagation of radio waves in the surrounding matter. The index of refraction in e.g. polar ice or lunar rock may have…
We establish the gradient flow representation of diffusion with mobility $b$ with respect to the modified Wasserstein quasi-metric $W_h$, where $h(r)=rb(r)$. The appropriate selection of the free energy functional depends on the specific…
Research in many areas of modern physics and astrophysics such as, e.g., indirect searches for dark matter (DM), particle acceleration in SNR shocks, and the spectrum and origin of extragalactic gamma-ray background, rely heavily on studies…
The classical Fokker-Planck equation (FPE) is a key tool in physics for describing systems influenced by drag forces and Gaussian noise, with applications spanning multiple fields. We consider the fractional Fokker-Planck equation (FFPE),…
Diffusion models with continuous stochastic differential equations (SDEs) have shown superior performances in image generation. It can serve as a deep generative prior to solving the inverse problem in magnetic resonance (MR)…
We develop a class of non-Gaussian translation processes that extend classical stochastic differential equations (SDEs) by prescribing arbitrary absolutely continuous marginal distributions. Our approach uses a copula-based transformation…