Related papers: Spline Moment Models for the one-dimensional Boltz…
The size-modified Poisson-Boltzmann equation (SMPBE) is one important variant of the popular dielectric model, the Poisson-Boltzmann equation (PBE), to reflect ionic size effects in the prediction of electrostatics for a biomolecule in an…
The lattice Boltzmann equation describes the evolution of the velocity distribution function on a lattice in a manner that macroscopic fluid dynamical behavior is recovered. Although the equation is a derivative of lattice gas automata, it…
Nonlinear kinetic equations are reviewed for a wide audience of specialists and postgraduate students in physics, mathematical physics, material science, chemical engineering and interdisciplinary research. Contents: The Boltzmann equation,…
In this paper, we propose a new stabilizer free and pressure robust WG method for the Stokes equations with super-convergence on polytopal mesh in the primary velocity-pressure formulation. Convergence rates with one order higher than the…
A hybrid lattice Boltzmann method (LBM) for binary mixtures based on the free-energy approach is proposed. Non-ideal terms of the pressure tensor are included as a body force in the LBM kinetic equations, used to simulate the continuity and…
The paper establishes the strong convergence rates of a spatio-temporal full discretization of the stochastic wave equation with nonlinear damping in dimension one and two. We discretize the SPDE by applying a spectral Galerkin method in…
This article extends a recently introduced kinetic closure of turbulence by developing its theoretical framework, operational realizations, and validation. In contrast with filtered Navier--Stokes formulations, filtering the Boltzmann…
In this work, we present an asymptotic-preserving semi-Lagrangian discontinuous Galerkin scheme for the Boltzmann equation that effectively handles multi-scale transport phenomena. The main challenge lies in designing appropriate moments…
The influence and validity of wall boundary conditions for non-equilibrium fluid flows described by the Boltzmann equation remains an open problem. The substantial computational cost of directly solving the Boltzmann equation has limited…
This paper investigates a Stochastic Partial Differential Equation (SPDE) derived from the Fokker-Planck equation associated with Score-based Generative Models. We modify the standard Fokker-Planck equation to better represent practical…
This paper develops a class of robust weak Galerkin methods for the stationary incompressible convective Brinkman-Forchheimer equations. The methods adopt piecewise polynomials of degrees $m\ (m\geq1)$ and $m-1$ respectively for the…
I review single-molecule experiments (SME) in biological physics. Recent technological developments have provided the tools to design and build scientific instruments of high enough sensitivity and precision to manipulate and visualize…
Improvement of numerical methods for calculating charge transport quantities of materials from the Boltzmann transport equation (BTE) is important for prediction of material properties. In particular, techniques which allow for more…
The discretized equilibrium distributions of the lattice Boltzmann method are presented by using the coefficients of the Lagrange interpolating polynomials that pass through the points related to discrete velocities and using moments of the…
Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method…
New exact completely closed homogeneous Generalized Master Equations (GMEs), governing the evolution in time of equilibrium two-time correlation functions for dynamic variables of a subsystem of s particles (s<N) selected from N>>1…
In the task of predicting spatio-temporal fields in environmental science using statistical methods, introducing statistical models inspired by the physics of the underlying phenomena that are numerically efficient is of growing interest.…
The Gauss Galerkin Method/Quadrature method of moments (GG-QMoM) closure scheme, introduced by Dawson, closes a truncated set of moment equations of an SDE by a Galerkin approximation of its law in the space of probability measures. Here,…
In this paper, we investigate steady states of shallow water moment equations including bottom topographies. We derive a new hyperbolic shallow water moment model based on linearized moment equations that allows for a simple assessment of…
We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining…