Related papers: Closure method for spatially averaged dynamics of …
We propose a method to analyze the dynamics of systems exhibiting slow relaxation which is based on mesoscopic non-equilibrium thermodynamics. The method allows us to obtain kinetic equations of the Fokker-Planck type for the probability…
We present the Multi-Particle-Collision (MPC) dynamics approach to simulate properties of low-dimensional systems. In particular, we illustrate the method for a simple model: a one-dimensional gas of point particles interacting through…
We use a macroscopic description of a system of relativistic particles based on adding a nonequilibrium tensor to the usual hydrodynamic variables. The nonequilibrium tensor is linked to relativistic kinetic theory through a nonlinear…
The requirement for large-scale global simulations of plasma is an ongoing challenge in both space and laboratory plasma physics. Any simulation based on a fluid model inherently requires a closure relation for the high order plasma…
Structural and thermodynamic consistency of coarse-graining models across multiple length scales is essential for the predictive role of multi-scale modeling and molecular dynamic simulations that use mesoscale descriptions. Our approach is…
Electrokinetic phenomena in nanopore sensors and microfluidic devices require accurate simulation of coupled fluid-electrostatic interactions in geometrically complex domains with irregular boundaries and adaptive mesh refinement. We…
The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations. In this work, we derive and investigate a neural…
A general, variational approach to derive low-order reduced systems for nonlinear systems subject to an autonomous forcing, is introduced. The approach is based on the concept of optimal parameterizing manifold (PM) that substitutes the…
In the modelling of stochastic phenomena, such as quasi-reaction systems, parameter estimation of kinetic rates can be challenging, particularly when the time gap between consecutive measurements is large. Local linear approximation…
Smoothed Dissipative Particle Dynamics (SDPD) is a mesoscopic method which allows to select the level of resolution at which a fluid is simulated. In this work, we study the consistency of the resulting thermodynamic properties as a…
The moments of spatial probabilistic systems are often given by an infinite hierarchy of coupled differential equations. Moment closure methods are used to approximate a subset of low order moments by terminating the hierarchy at some order…
We propose a trajectory-based quasiclassical method for approximating dynamics in condensed phase systems. Building upon the previously developed Optimized Mean Trajectory (OMT) approximation that has been used to compute linear and…
In this paper we approximate the radiative transfer equations by the method of moments, constructing mesoscopic approximations of arbitrary order of the otherwise microscopic system. To define the necessary closure a minimum entropy…
A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a…
The well-posedness of a non-local advection-selection-mutation problem deriving from adaptive dynamics models is shown for a wide family of initial data. A particle method is then developed, in order to approximate the solution of such…
We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity,…
A multi-scale meshfree particle method for macroscopic mean field approximations of generalized interacting particle models is developed and investigated. The method is working in a uniform way for large and small interaction radii. The…
Entropy-based (M_N) moment closures for kinetic equations are defined by a constrained optimization problem that must be solved at every point in a space-time mesh, making it important to solve these optimization problems accurately and…
We use a linear system of Langevin spins with disordered interactions as an exactly solvable toy model to investigate a procedure, recently proposed by Coolen and Sherrington, for closing the hierarchy of macroscopic order parameter…
In this paper we establish a new efficient method for simulating polymer-solvent systems which combines a lattice Boltzmann approach for the fluid with a continuum molecular dynamics (MD) model for the polymer chain. The two parts are…