Related papers: A Maxwell-Amp\`{e}re Nernst-Planck Framework for M…
We have developed efficient numerical algorithms for solving 3D steady-state Poisson-Nernst-Planck (PNP) equations with excess chemical potentials described by the classical density functional theory (cDFT). The coupled PNP equations are…
A macroscopic model to describe the dynamics of ion transport in ion channels is the Poisson-Nernst-Planck(PNP) equations. In this paper, we develop a finite-difference method for solving PNP equations, which is second-order accurate in…
Maxwell equations provide a complete description of the electromagnetic (EM) phenomena, which have been one of the key fundamental-theories of modern physics, such as electromagnetism, optics, quantum theories, etc. The vacuum permittivity…
In this paper, we propose a general framework for designing numerical schemes that have both well-balanced (WB) and asymptotic preserving (AP) properties, for various kinds of kinetic models. We are interested in two different parameter…
Classical molecular dynamics simulations have recently become a standard tool for the study of electrochemical systems. State-of-the-art approaches represent the electrodes as perfect conductors, modelling their responses to the charge…
The model reduction of a mesoscopic kinetic dynamics to a macroscopic continuum dynamics has been one of the fundamental questions in mathematical physics since Hilbert's time. In this paper, we consider a diagram of the diffusion limit…
We develop a wave packet molecular dynamics framework for modeling the structural properties of partially-ionized dense plasmas, based on a chemical model that explicitly includes bound state wavefunctions. Using hydrogen as a…
For charged systems in heterogeneous dielectric media, a key obstacle for molecular dynamics (MD) simulations is the need to solve the Poisson equation in the media. This obstacle can be bypassed using MD methods that treat the local…
We investigate the subtle effects of diffuse charge on interfacial kinetics by solving the governing equations for ion transport (Nernst-Planck) with realistic boundary conditions representing reaction kinetics (Butler-Volmer) and…
We consider in this paper a numerical approximation of Poisson-Nernst-Planck-Navier- Stokes (PNP-NS) system. We construct a decoupled semi-discrete and fully discrete scheme that enjoys the properties of positivity preserving, mass…
Radio-frequency-driven atmospheric pressure plasma jets (RF APPJs) play an essential role in many technological applications. This work studies the characteristics of these discharges in the so-called non-neutral regime where the…
Within the framework of the homogeneous non-linear Boltzmann equation, we present a new analytic method, without the intrinsic limitations of existing methods, for obtaining asymptotic solutions. This method permits extension of existing…
Understanding electron energy dynamics in low-temperature plasmas such as capacitively coupled plasmas (CCPs), including energy absorption, conversion, transport, and dissipation, is essential for interpreting discharge physics and process…
We develop an action principle to construct the field equations for a multi-fluid system containing charge-neutral fluids, plasmas, and dissipation (via resistive interactions), by combining the standard, Maxwell action and minimal coupling…
This article is concerned with the existence, status and description of the so-called emergent phenomena believed to occur in certain principally planar electronic systems. In fact, two distinctly different if inseparable tasks are…
A mechanism is proposed to describe the occurrence of distance-dependent dissipation peaks in the dynamics of an atomic force microscope tip oscillating over a surface characterized by a charge density wave state. The dissipation has its…
Koopman-based neural MPC models generate time-varying dynamics from historical data, but preserve convexity by enforcing that the system operator is independent of the current control input. This conditional independence constraint limits…
We study the free boundary problem for a plasma-vacuum interface in ideal incompressible magnetohydrodynamics. Unlike the classical statement when the vacuum magnetic field obeys the div-curl system of pre-Maxwell dynamics, to better…
In this paper we discuss the dissipative property of near-equilibrium classical solutions to the Cauchy problem of the Vlasov-Maxwell-Boltzmann System in the whole space $\R^3$ when the positive charged ion flow provides a spatially uniform…
We build a new mathematical model of shape optimization for maximizing ionic concentration governed by the multi-physical coupling steady-state Poisson-Nernst-Planck system. Shape sensitivity analysis is performed to obtain the Eulerian…