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Inspired by one--dimensional light--particle systems, the dynamics of a non-Hamiltonian system with long--range forces is investigated. While the molecular dynamics does not reach an equilibrium state, it may be approximated in the…
Vlasov equations model the dynamics of plasma in the collisionless regime. A standard approach for numerically solving the Vlasov equation is to operator split the spatial and velocity derivative terms, allowing simpler time-stepping…
The phase-field crystal equation, a parabolic, sixth-order and nonlinear partial differential equation, has generated considerable interest as a possible solution to problems arising in molecular dynamics. This is because the phase-field…
Due to their capability to reduce turbulent transport in magnetized plasmas, understanding the dynamics of zonal flows is an important problem in the fusion programme. Since the pioneering work by Rosenbluth and Hinton in axisymmetric…
We find for the first time the asymptotic representation of the solution to the space dependent variable order fractional diffusion and Fokker-Planck equations. We identify a new advection term that causes ultra-slow spatial aggregation of…
We study the asymptotic behavior of Fokker-Planck equations with spatially inhomogeneous nonlinear diffusion, based on the energy dissipation law. First, we consider the Fokker-Planck equation with porous-medium-type nonlinear diffusion…
Kinetic equations model the position-velocity distribution of particles subject to transport and collision effects. Under a diffusive scaling, these combined effects converge to a diffusion equation for the position density in the limit of…
The stochastic differential equations for a model of dissipative particle dynamics with both total energy and total momentum conservation in the particle-particle interactions are presented. The corresponding Fokker-Planck equation for the…
We present a new splitting method for time-dependent convection-dominated diffusion problems. The original convection diffusion system is split into two sub-systems: a pure convection system and a diffusion system. At each time step, a…
This paper presents numerical cross-comparisons and benchmark results for two different kinetic numerical methods, capable of describing relativistic dissipative fluid dynamics in a wide range of kinematic regimes, typical of relevant…
The dissolution and microfluidic mass transfer of carbon dioxide in water at high-pressure conditions are crucial for a myriad of technological applications, including microreactors, extractions, and carbon capture, utilization, and…
We analyze the fluctuation-driven escape of particles from a metastable state under the influence of a weak periodic force. We develop an asymptotic method to solve the appropriate Fokker-Planck equation with mixed natural and absorbing…
Motivated by recent work on approximation of diffusion equations by deterministic interacting particle systems, we develop a nonlocal approximation for a range of linear and nonlinear diffusion equations and prove convergence of the method…
We present a novel simulation-free framework for training continuous-time diffusion processes over very general objective functions. Existing methods typically involve either prescribing the optimal diffusion process -- which only works for…
Dipolar dissociation processes in the electron collisions with carbon monoxide have been studied using time of flight (TOF) mass spectroscopy in combination with the highly differential velocity slice imaging (VSI) technique. Probing…
A stochastic model is presented for a super-position of uncorrelated pulses with a random distribution of amplitudes, sizes, velocities and arrival times. The pulses are assumed to move radially with fixed shape and amplitudes decaying…
We present a theoretical framework to model the electric response of cell aggregates. We establish a coarse representation for each cell as a combination of membrane and cytoplasm dipole moments. Then we compute the effective conductivity…
In plasma turbulence theory, due to the complexity of the system with many non-linearly interacting waves, the dynamics of the phases is often disregarded and the so-called random-phase approximation (RPA) is used assuming the existence of…
We propose a prescription based on the Fokker-Planck equation in the Stratonovich approach, with the diffusion coefficient dependent on temporal and spatial coordinates, for describing heat conduction by phonons in small structures. This…
We introduce a fractional Fokker-Planck equation with a temporal power-law dependence on the drift force fields. For this case, the moments of the tracer from the force-force correlation in terms of the time-dependent drift force fields are…