Related papers: Long wave interaction with a partially immersed bo…
Two-dimensional free-surface potential flows of an ideal fluid over a strongly inhomogeneous bottom are investigated with the help of conformal mappings. Weakly-nonlinear and exact nonlinear equations of motion are derived by the…
In this work, we investigate mathematical models for electromagnetic wave propagation in dispersive isotropic media. We emphasize the link between physical requirements and mathematical properties of the models. A particular attention is…
A new derivation of the Bernoulli equation for water waves in three-dimensional rotating and translating coordinate systems is given. An alternative view on the Bateman-Luke variational principle is presented. The variational principle…
The standing surface waves in a rectangular vertically oscillating vessel filled with water (Faraday waves) in the presence of a floating elastic sheet are studied experimentally and theoretically. The threshold amplitude of the instability…
The Lagrangian formulation for the irrotational wave motion is straightforward and follows from a Lagrangian functional which is the difference between the kinetic and the potential energy of the system. In the case of fluid with constant…
The solution of a momentum conservation equation for the gas and liquid stream in the flowing element is obtained on the basis of the modern approach to a problem on contact interaction of bodies and mediums. A flowing element, system are:…
We study the scattering of a matter-wave from an interacting system of bosons in an optical lattice, focusing on the strong-interaction regime. Analytical expressions for the many-body scattering cross section are derived from a…
Three-dimensional central symmetric bodies different from spheres that can float in all orientations are considered. For relative density rho=1/2 there are solutions, if holes in the body are allowed. For rho different from 1/2 the body is…
A boundary integral equation formulation is presented for the electromagnetic transmission problem where an incident electromagnetic wave is scattered from a bounded dielectric object. The formulation provides unique solutions for all…
The scattering of electromagnetic waves by an obstacle is analyzed through a set of partial differential equations combining the Maxwell's model with the mechanics of fluids. Solitary type EM waves, having compact support, may easily be…
We study a partially ionized hydrogen plasma by means of quantum molecular dynamics, which is based on wave packets. We introduce a new model which distinguishes between free and bound electrons. The free electrons are modelled as Gaussian…
In this work we present a further analytical development and a numerical implementation of the recently suggested theoretical model for highly nonlinear potential long-crested water waves, where weak three-dimensional effects are included…
Consider the set of equations modeling the motion of a rigid body enclosed in sea ice. Using Hibler's viscous-plastic model for describing sea ice, it is shown by a certain decoupling approach that this system admits a unique, local strong…
The complex formations exhibited by schooling fish have long been the object of fascination for biologists and physicists. However, the physical and sensory mechanisms leading to organized collective behavior remain elusive. On the physical…
The description of gravity waves propagating on the water surface is considered from a historical point of view, with specific emphasis on the development of a theoretical framework and equations of motion for long waves in shallow water.…
The evolution of adiabatic waves with autoresonant trapped particles is described within the Lagrangian model developed in Paper I, under the assumption that the action distribution of these particles is conserved, and, in particular, that…
This paper introduces novel bulk-surface splitting schemes of first and second order for the wave equation with kinetic and acoustic boundary conditions of semi-linear type. For kinetic boundary conditions, we propose a reinterpretation of…
The main purpose of this work is to address the question of the utility of "effective constitutive relations" for problems in dynamics. This is done in the context of longitudinal shear waves in an elastic medium that is periodically…
This paper explores an idealized model of the ocean surface in which widely separated surface-wave packets and point vortices interact in two horizontal dimensions. We start with a Lagrangian which, in its general form, depends on the…
The goal of this work is to study waves interacting with partially immersed objects allowed to move freely in the vertical direction, and in a regime in which the propagation of the waves is described by the one dimensional…