Related papers: Comparison of Different Methods for Nonlinear Diff…
The theory of diffusive acceleration of energetic particles at shock fronts assumes charged particles undergo spatial diffusion in a uniform magnetic field. If, however, the magnetic field is not uniform, but has a stochastic or braided…
This paper develops and analyzes an efficient numerical method for solving elliptic partial differential equations, where the diffusion coefficients are random perturbations of deterministic diffusion coefficients. The method is based upon…
We present a survey of 1D kinetic particle-in-cell simulations of quasi-parallel non-relativistic shocks to identify the environments favorable for electron acceleration. We explore an unprecedented range of shock speeds $v_{\rm sh}\approx…
The most common way to sample from a probability distribution is to use Monte-Carlo methods. For distributions on a continuous state space, one can find diffusions with the target distribution as equilibrium measure, so that the state of…
We present a linear dispersive partial differential equation which manifests a number of qualitative features of dispersive shocks, typically thought to occur only in nonlinear models. The model captures much of the short time phenomenon…
A recent reformulation [1] of the problem of Coulomb gases in the presence of a dynamical dielectric medium showed that finite temperature simulations of such systems can be accomplished on the basis of completely local Hamiltonians on a…
Acoustic shock and acceleration waves in inhomogeneous fluids are investigated using both analytical and numerical methods. In the context of start-up signaling problems, and based on linear acoustics theory, we study the propagation of…
We consider moving particles in media with nonlinear friction and drive them by an asymmetric dichotomic Markov process. Due to different energy dissipations, during the forward and backward stroke, we obtain a mean non-vanishing directed…
Nonthermal particles can be produced due to incomplete thermalization at collisionless shocks and further accelerated to very high energies via diffusive shock acceleration. In a previous study we explored the cosmic ray (CR) acceleration…
Diffusive shock acceleration (DSA) at relativistic shocks is expected to be an important acceleration mechanism in a variety of astrophysical objects including extragalactic jets in active galactic nuclei and gamma ray bursts. These sources…
Beam tracking software for accelerators typically falls into two categories: fast envelope simulations limited to linear beam optics, and slower multiparticle simulations that can model nonlinear effects. To find a middle ground between…
This paper presents an overview of physical ideas and mathematical methods for implementing non-smooth and discontinuous substitutions in dynamical systems. General purpose of such substitutions is to bring the differential equations of…
Many quantum technologies rely on high-precision dynamics, which raises the question of how these are influenced by the experimental uncertainties that are always present in real-life settings. A standard approach in the literature to…
Nonlinear non-Gaussian state-space models are ubiquitous in statistics, econometrics, information engineering and signal processing. Particle methods, also known as Sequential Monte Carlo (SMC) methods, provide reliable numerical…
We describe parallel Markov chain Monte Carlo methods that propagate a collective ensemble of paths, with local covariance information calculated from neighboring replicas. The use of collective dynamics eliminates multiplicative noise and…
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…
A comprehensive review is given of the various processes proposed for accelerating particles by shocks to high energies. These energies are limited by several bounds: the non-relativistic nature of the heliospheric collisionless shocks to…
We consider nonlinear drift-diffusion equations (both porous medium equations and fast diffusion equations) with a measure-valued external force. We establish existence of nonnegative weak solutions satisfying gradient estimates, provided…
We have examined cutoffs and pile-ups due to various processes in the spectra of particles produced by shock acceleration, and found that, even in the absence of energy losses, the shape of the spectrum of accelerated particles at energies…
We describe a numerical scheme for studying time-dependent, multifluid, magnetohydrodynamic shock waves in weakly ionized interstellar clouds and cores. Shocks are modeled as propagating perpendicular to the magnetic field and consist of a…