Related papers: Partial-moment minimum-entropy models for kinetic …
We develop Electrochemical Mean-Field Kinetic Equations (EMFKE) to simulate electrochemical cells. We start from a microscopic lattice-gas model with charged particles, and build mean-field kinetic equations following the lines of earlier…
As motivated by studies of cellular motility driven by spatiotemporal chemotactic gradients in microdevices, we develop a framework for constructing approximate analytical solutions for the location, speed and cellular densities for cell…
We investigate the application of the method of moments approach for the one-dimensional population balance equation. We consider different types of moment closures, namely polynomial (P_N) closures, maximum entropy (M_N) closures and the…
In this paper we consider approximations of Neumann problems for the integral fractional Laplacian by continuous, piecewise linear finite elements. We analyze the weak formulation of such problems, including their well-posedness and…
We review some geometrical properties of models of moment closures of gas-kinetic equations, and consider a transport-projection splitting scheme for construction of solutions of such closures. The scheme, formulated in terms of a dual…
In this paper, we consider the quasi-gas-dynamic (QGD) model in a multiscale environment. The model equations can be regarded as a hyperbolic regularization and are derived from kinetic equations. So far, the research on QGD models has been…
We design a Mixed Virtual Element Method for the approximated solution to the first-order form of the acoustic wave equation. In absence of external load, the semi-discrete method exactly conserves the system energy. To integrate in time…
We use the method of Compensated Compactness and Kinteic Formulation to show that the almost everywhere limit of quasilinear viscous approximations is the unique entropy solution (in the sense of {\it F. Otto}) of the corresponding scalar…
The quasi--equilibrium or maximum entropy approximation is applied in order to derive constitutive equations from kinetic models of polymer dynamics. It is shown in general and illustrated for an example how canonical distribution functions…
Recently, a new connection between density functional theory and kinetic theory has been proposed. In particular, it was shown that the Kohn-Sham (KS) equations can be reformulated as a macroscopic limit of the steady-state solution of a…
The present work was inspired by the recent developments in laboratory experiments made on chip, where culturing of multiple cell species was possible. The model is based on coupled reaction-diffusion-transport equations with chemotaxis,…
Transported probability density function (PDF) methods are widely used to model turbulent flames characterized by strong turbulence-chemistry interactions. Numerical methods directly resolving the PDF are commonly used, such as the…
We derive the hydrodynamic limit of a kinetic equation with a stochastic, short range perturbation of the velocity operator. Under some mixing hypotheses on the stochastic perturbation, we establish a diffusion-approximation result: the…
We present the efficient and universal numerical method for simulation of interacting quantum gas kinetics on a finite momentum lattice, based on the Boltzmann equation for occupation numbers. Usually, the study of models with two-particle…
There are many mathematical models of biochemical cell signaling pathways that contain a large number of elements (species and reactions). This is sometimes a big issue for identifying critical model elements and describing the model…
Treatment with high energy ionizing radiation is one of the main methods in modern cancer therapy that is in clinical use. During the last decades, two main approaches to dose calculation were used, Monte Carlo simulations and…
Partial equilibrium approximation (PEA) and quasi-steady-state approximation (QSSA) are two classical methods for reducing complex macroscopic chemical reactions into simple computable ones. Previous studies mainly focus on the accuracy of…
The relativistic method of moments is one of the most successful approaches to extract second order viscous hydrodynamics from a kinetic underlying background. The equations can be systematically improved to higher order, and they have…
We study the dilute Fermi gas at unitarity using molecular dynamics with an effective quantum potential constructed to reproduce the quantum two-body density matrix at unitarity. Results for the equation of state, the pair correlation…
This paper presents a new narrow-stencil finite difference method for approximating the viscosity solution of second order fully nonlinear elliptic partial differential equations including Hamilton-Jacobi-Bellman equations. The proposed…