Related papers: Shock Reflection in Plane Symmetry
We present a parabolic approximation that incorporates reflection. With this approximation, there is no need to solve the parabolic equation for a coupled pair of solutions consisting of the incident and reflected waves. Rather, this…
Symmetry detection and discrimination are of fundamental meaning in science, technology, and engineering. This paper introduces reflection invariants and defines the directional moment to detect symmetry for shape analysis and object…
We consider a spectral problem associated with steady water waves of extreme form on the free surface of a rotational flow. It is proved that the spectrum of this problem contains arbitrary large negative eigenvalues and they are simple.…
We consider the problem of recovering the initial condition in the one-dimensional one-phase Stefan problem for the heat equation from the knowledge of the position of the melting point. We first recall some properties of the free boundary…
We examine the role discrete symmetries, time-reversal and mirror symmetries, play in the context of geophysical waves and instabilities. By looking at three special cases from the two-layer quasi-geostrophic model as well as developing a…
We consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain…
Analytical modeling of the evolution of cylindrical and spherical shock waves (shocks) during an implosion in water is presented for an intermediate range of convergence radii. Up to now this range is determined only in experiments…
The emergence of a shock from a medium with a free surface is an important process in various astrophysical phenomena. It generates the first light associated with explosions like supernovae and Gamma Ray Bursts. Most previous works…
The properties of the interface between solid and melt are key to solidification and melting, as the interfacial free energy introduces a kinetic barrier to phase transitions. This makes solidification happen below the melting temperature,…
We consider holographic theories at finite temperature in which a continuous global symmetry in the bulk is spontaneously broken. We study the linear response of operators in a regime which is dual to time dependent, long wavelength…
The goal of this work is to study the electromagnetic scattering problem of time-domain Maxwell's equations in an unbounded structure. An exact transparent boundary condition is developed to reformulate the scattering problem into an…
An exact formulation of the propagation of a monochromatic wave packet impinging upon a transparent, homogeneous, isotropic and parallel slab at oblique incidence is presented. Approximate formulas are derived for low divergence Gaussian…
This brief note addresses the free boundary problem arising from the steady two-dimensional seepage flow through a rectangular dam. The flow problem consists in finding the free boundary location, and the velocity and pressure fields. The…
We study the localization in the one-dimensional trap model in terms of statistical mechanics of trajectories. By numerically investigating overlap between trajectories of two particles on a common disordered potential, we find that there…
In this paper, we consider a moving rigid solid immersed in a potential fluid. The fluid-solid system fills the whole two dimensional space and the fluid is assumed to be at rest at infinity. Our aim is to study the inverse problem,…
This paper is concerned with the problem of scattering of time-harmonic acoustic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral equation…
We consider the inverse scattering problem of retrieving the structural parameters of a stratified medium consisting of dispersive materials, given knowledge of the complex reflection coefficient in a finite frequency range. It is shown…
Parametric and semiparametric tests of circular reflective symmetry about an unknown central direction are developed that are locally and asymptotically optimal in the Le Cam sense against asymmetric $k$-sine-skewed alternatives. The…
We consider the existence of radially symmetric stationary solutions of the compressible viscous and heat-conductive polytropic ideal fluid on the unbounded exterior domain of a sphere where the boundary and far-field conditions are…
We consider a cylindrical film of fluid adhering to a rigid cylinder of fixed radius. The main result is to give the critical (maximum) length for which such a film of given thickness can be stable. The problem is considered both when the…