Related papers: Exact moment models for conservation laws in phase…
In this paper, we propose a moment method to numerically solve the Vlasov equations using the framework of the NRxx method developed in [6, 8, 7] for the Boltzmann equation. Due to the same convection term of the Boltzmann equation and the…
We extend the phase field crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of…
The method of moments is widely used for the reduction of kinetic equations into fluid models. It consists in extracting the moments of the kinetic equation with respect to a velocity variable, but the resulting system is a priori…
In this paper we study the problem of model reduction by moment matching for stochastic systems. We characterize the mathematical object which generalizes the notion of moment to stochastic differential equations and we find a class of…
Geophysical flow simulations using hyperbolic shallow water moment equations require an efficient discretization of a potentially large system of PDEs, the so-called moment system. This calls for tailored model order reduction techniques…
The aim of this work is to investigate the application of partial moment approximations to kinetic chemotaxis equations in one and two spatial dimensions. Starting with a kinetic equation for the cell densities we apply a…
We derive diffusive macroscopic equations for the particle and energy density of a system whose time evolution is described by a kinetic equation for the one particle position and velocity function f(r,v,t) that consists of a part that…
Power moments, modified moments, and optimized moments are powerful tools for solving microscopic models of macroscopic systems; however the expansion of the density of states as a continued fraction does not converge to the macroscopic…
We present a novel theoretical formulation for performing quantum dynamics in terms of moments within the single-particle description. By expressing the quantum dynamics in terms of increasing orders of moments, instead of single-particle…
We propose a novel reformulation of the Vlasov-Amp{\`e}re equations for plasmas. This reformulation exposes discrete symmetries to achieve simultaneous conservation of mass, momentum, and energy; preservation of Gauss's law involution;…
We present a new algorithm for the discretization of the Vlasov-Maxwell system of equations for the study of plasmas in the kinetic regime. Using the discontinuous Galerkin finite element method for the spatial discretization, we obtain a…
Mixed-moment models, introduced before for one space dimension, are a modification of the method of moments applied to a (linear) kinetic equation, by choosing mixtures of different partial moments. They are well-suited to handle such…
We describe a new model for the study of weakly-collisional, magnetized plasmas derived from exploiting the separation of the dynamics parallel and perpendicular to the magnetic field. This unique system of equations retains the particle…
We introduce Spline Moment Equations (SME) for kinetic equations using a new weighted spline ansatz of the distribution function and investigate the ansatz, the model, and its performance by simulating the one-dimensional Boltzmann-BGK…
In many applications, for instance when describing dynamics of fluids or gases, hyperbolic conservation laws arise naturally in the modeling of conserved quantities of a system, like mass or energy. These types of equations exhibit highly…
Models phrased though moment conditions are central to much of modern inference. Here these moment conditions are embedded within a nonparametric Bayesian setup. Handling such a model is not probabilistically straightforward as the…
Validity of fluid models breaks down for non-thermal or weakly collisional plasmas which often occur e.g. in the solar wind. In these regimes one has to resort to modelling through the first-principle Vlasov-Maxwell system, but its…
Stable numerical simulations for a hyperbolic system of conservation laws of relaxation type but not in divergence form are obtained by incorporating the physical entropy into the simulations. The entropy balance is utilized as an…
Stable distribution is one of the attractive models that well describes fat-tail behaviors and scaling phenomena in various scientific fields. The approach based upon the method of moments yields a simple procedure for estimating stable law…
Relativistic hydrodynamics of classic plasmas is derived from the microscopic model in the limit of ideal plasmas. The chain of equations is constructed step by step starting from the concentration evolution. It happens that the energy…