Related papers: Simulating Pitch Angle Scattering Using An Explici…
A solution of the scattering problem is obtained for the Schr\"odinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident…
The pitch-angle diffusion coefficient quantifies the effect of pitch-angle scattering on charged particles propagating through turbulent magnetic fields and is a key ingredient in understanding the diffusion of these particles along the…
Sampling from a high-dimensional distribution is a fundamental task in statistics, engineering, and the sciences. A canonical approach is the Langevin Algorithm, i.e., the Markov chain for the discretized Langevin Diffusion. This is the…
Given a convex function $f\colon\mathbb{R}^{d}\to\mathbb{R}$, the problem of sampling from a distribution $\propto e^{-f(x)}$ is called log-concave sampling. This task has wide applications in machine learning, physics, statistics, etc. In…
In this paper, we propose stochastic structure-preserving schemes to compute the effective diffusivity for particles moving in random flows. We first introduce the motion of particles using the Lagrangian formulation, which is modeled by…
A novel, conservative discontinuous Galerkin algorithm is presented for particle kinetics on manifolds. The motion of particles on the manifold is represented using using both canonical and non-canonical Hamiltonian formulations. Our…
The adiabatic invariance of the magnetic moment during particle motion is of fundamental importance to the dynamics of magnetized plasma. The related rate of pitch angle scattering is investigated here for fast particles that thermally…
We analyse the scattering operator associated with the defocusing nonlinear Schr{\"o}dinger equation which captures the evolution of solutions over an infinite time-interval under the nonlinear flow of this equation. The asymptotic nature…
We present a revision to the well known Stormer-Verlet algorithm for simulating second order differential equations. The revision addresses the inclusion of linear friction with associated stochastic noise, and we analytically demonstrate…
We propose a new algorithm---Stochastic Proximal Langevin Algorithm (SPLA)---for sampling from a log concave distribution. Our method is a generalization of the Langevin algorithm to potentials expressed as the sum of one stochastic smooth…
Particle-wave interaction is of fundamental interest in plasma physics, especially in the study of runaway electrons in magnetic confinement fusion. Analogous to the concept of photons and phonons, wave packets in plasma can also be treated…
An open source software package for simulating thermal neutron propagation in geometry is presented. In this system, neutron propagation can be treated by either the particle transport method or the ray-tracing method. Supported by an…
The problem of mass diffusion in layered systems has relevance to applications in different scientific disciplines, e.g., chemistry, material science, soil science, and biomedical engineering. The mathematical challenge in these type of…
The Landau-Lifshitz-Gilbert (LLG) equation, regarded as a gradient flow with manifold constraint, is the fundamental model describing magnetization dynamics in ferromagnetic materials. It is well known that the normalized tangent plane…
A novel particle merging algorithm for rarefied gas dynamics simulations is proposed that can conserve arbitrary velocity and spatial moments of the particle distribution via solving a non-negative least squares problem. An extension that…
Previous work on calculating energy spectra from Compton scattering events has either neglected considering the pulsed structure of the incident laser beam, or has calculated these effects in an approximate way subject to criticism. In this…
Relativistic strongly magnetized plasmas are produced in laboratories thanks to state-of-the-art laser technology but can naturally be found around compact objects such as neutron stars and black holes. Detailed studies of the behaviour of…
We introduce stochastic models for continuous-time evolution of angles and develop their estimation. We focus on studying Langevin diffusions with stationary distributions equal to well-known distributions from directional statistics, since…
The real-time correlators of quantum field theories can be directly probed through new approaches to simulation, such as quantum computing and tensor networks. This provides a new framework for computing scattering observables in lattice…
We discuss the design of state-of-the-art numerical methods for molecular dynamics, focusing on the demands of soft matter simulation, where the purposes include sampling and dynamics calculations both in and out of equilibrium. We discuss…