Related papers: Nonlinear wave interactions in geochemical modelin…
The multi-fluid modelling of high-frequency waves in partially ionized plasmas has shown that the behavior of magnetohydrodynamics waves in the linear regime is heavily influenced by the collisional interaction between the different species…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
On an example of the open nonlinear electrodynamic system - transverse non-homogeneous, isotropic, nonlinear (a Kerr-like dielectric nonlinearity) dielectric layer, the algorithms of solution of the diffraction problem of a plane wave on…
We propose a new regularization method for constructing a shock wave type solution with nonsmooth front (interaction of shock waves) for quasilinear equations in the one-dimensional case.
The study of geological systems requires the solution of complex geochemical relations. We present an implementation of a chemical solver which can handle various types of models, including surface chemistry. The implementation is done in…
We generalize the nonlinear one-dimensional equation for a fluid layer surface to any geometry and we introduce a new infinite order differential equation for its traveling solitary waves solutions. This equation can be written as a…
We establish nonlinear stability and asymptotic behavior of traveling periodic waves of viscous conservation laws under localized perturbations or nonlocalized perturbations asymptotic to constant shifts in phase, showing that long-time…
We derive a model to describe the interaction of an rf-SQUID (radio frequency superconducting quantum interference device) based metasurface with free space electromagnetic waves. The electromagnetic fields are described on the base of…
We study the ionic equilibria and interactions of neutral semi-permeable spherical shells immersed in electrolyte solutions, including polyions. Although the shells are uncharged, only one type of ions of the electrolyte can permeate them,…
We study the existence of solitary-wave solutions and some of their properties for a general multicomponent long-wave-short-wave interaction system. The system considered here describes the nonlinear interaction of multiple short waves with…
Recent measurements of microsphere interactions in diverse media suggest that the standard dielectric-continuum models of solution-phase interactions are fundamentally incomplete. Experiments indicate that the interactions of charged…
In this paper we consider the Benjamin equation, a partial differential equation that models one-way propagation of long internal waves of small amplitude along the interface of two fluid layers under the effects of gravity and surface…
The nonlinear interaction, due to quantum electrodynamical (QED) effects, between photons is investigated using a wave-kinetic description. Starting from a coherent wave description, we use the Wigner transform technique to obtain a set of…
The interaction between small-scale waves and a larger-scale flow can be described by a multi-scale theory that forms the basis for a new class of parameterizations of subgrid-scale gravity waves (GW) in weather and climate models. The…
A fully conservative sharp-interface method is developed for multiphase flows with phase change. The coupling between two phases is implemented via introducing the interfacial fluxes, which are obtained by solving a general Riemann problem…
The shear shallow water model is a higher order model for shallow flows which includes some shear effects that are neglected in the classical shallow models. The model is a non-conservative hyperbolic system which can admit shocks,…
Classifications of symmetries and conservation laws are presented for a variety of physically and analytically interesting wave equations with power onlinearities in n spatial dimensions: a radial hyperbolic equation, a radial Schrodinger…
We consider a non-linear system modelling the dynamics of a linearly elastic body immersed in an incompressible viscous fluid, without damping on the elastic part. We prove local existence of strong solutions and global existence and…
Ab initio modeling of electrochemical systems is becoming a key tool for understanding and predicting electrochemical behavior. Development and careful benchmarking of computational electrochemical methods are essential to ensure their…
The response of underwater structures to a near-field explosion is coupled with the dynamics of the explosion bubble and the surrounding water. This multiphase fluid-structure interaction process is investigated using a model problem that…