Related papers: Pseudospectral implementation of the Einstein-Maxw…
The state of art of charge-conserving electromagnetic finite element particle-in-cell has grown by leaps and bounds in the past few years. These advances have primarily been achieved for leap-frog time stepping schemes for Maxwell solvers,…
This paper investigates the asymptotic behaviors of global solutions to fourth-order parabolic and hyperbolic equations with Dirichlet boundary conditions. The equations model Micro-Electro-Mechanical Systems (MEMS) and are depending on a…
Including the effect of the molecular environment in the numerical modeling of time-resolved electronic spectroscopy remains an important challenge in computational spectroscopy. In this contribution, we present a general approach for the…
The response of the system, consisting of two kinds of opposite-charged fermions and their bound states (hydrogen-like atoms), to the perturbation by the external electromagnetic field in low particle kinetic energies region is studied.…
A basic model for describing plasma dynamics is given by the Euler-Maxwell system, in which compressible ion and electron fluids interact with their own self-consistent electromagnetic field. In this paper we consider the "one-fluid"…
Charge dynamics play essential role in many practical applications such as semiconductors, electrochemical devices and transmembrane ion channels. A Maxwell-Amp\`{e}re Nernst-Planck (MANP) model that describes charge dynamics via…
In this article we consider an inverse boundary value problem for the time-harmonic Maxwell equations. We show that the electromagnetic material parameters are determined by boundary measurements where part of the boundary data is measured…
Pseudo-Hermitian operators appear in the solution of Maxwell's equations for stationary non-dispersive media with arbitrary (space-dependent) permittivity and permeability tensors. We offer an extension of the results in this direction to…
Within loop quantum gravity we construct a coarse-grained approximation for the Einstein-Maxwell theory that yields effective Maxwell equations in flat spacetime comprising Planck scale corrections. The corresponding Hamiltonian is defined…
Applying a simple harmonic map method to the cylindrically symmetric Einstein-Maxwell system, we obtain exact solutions representing strong nonlinear interaction between gravitational waves and electromagnetic waves in the case without any…
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;…
Our study of abstract quasi-linear parabolic problems in time-weighted L_p-spaces, begun in [17], is extended in this paper to include singular lower order terms, while keeping low initial regularity. The results are applied to…
We consider the problem of how many samples from a Gaussian multi-index model are required to weakly reconstruct the relevant index subspace. Despite its increasing popularity as a testbed for investigating the computational complexity of…
Maxwell's equations describe the evolution of electromagnetic fields, together with constraints on the divergence of the magnetic and electric flux densities. These constraints correspond to fundamental physical laws: the nonexistence of…
The study of parameter-dependent partial differential equations (parametric PDEs) with countably many parameters has been actively studied for the last few decades. In particular, it has been well known that a certain type of parametric…
We consider a coupled system of Maxwell's equations and the equations of elasticity, which is commonly used to model piezo-electric material behavior. The boundary influence is encoded as a separate dynamics on the boundary data spaces…
We develop a unified framework for semilinear elliptic equations with gradient-dependent nonlinearities and singular weights in strictly convex domains. Considering large solutions of \[ -\Delta u + b(x)\,h(|\nabla u|) + a(x)\,u = f(x)…
Recently, no-go theorems for the existence of solitonic solutions in Einstein-Maxwell-scalar (EMS) models have been established in arXiv:1902.07721. Here we discuss how these theorems can be circumvented by a specific class of non-minimal…
We introduce a new micro/macro decomposition of collisional kinetic equations which naturally incorporates the exact space boundary conditions. The idea is to write the distribution fonction $f$ in all its domain as the sum of a Maxwellian…
We present new exact solutions for the Einstein-Maxwell system in static spherically symmetric interior spacetimes. For a particular form of the gravitational potentials and the electric field intensity, it is possible to integrate the…