Related papers: Shock Reflection in Plane Symmetry
We present a detailed analysis of the general exact solution of Einstein's equation corresponding to a static and plane symmetric distribution of matter with density proportional to pressure. We study the geodesics in it and we show that…
The collapse of a vapor bubble near a flat solid boundary results in the formation of a jet that is directed towards the boundary. In more complex geometries such as corners, predictions of the collapse cannot be made in a straightforward…
We show that the spacetimes of domain wall solutions to the coupled Einstein-scalar field equations with a given scalar field potential fall into two classes, depending on whether or not reflection symmetry on the wall is imposed. Solutions…
Suppose we are given an environment consisting of axis-parallel and diagonal line segments with integer endpoints, each of which may be reflective or non-reflective, with integer endpoints, and an initial position for a light ray passing…
We study microlocally the transmission problem at the interface between an isotropic linear elastic solid and a linear inviscid fluid. We set up a system of evolution equations describing the particle displacement and velocity in the solid,…
We study a free boundary problem on the lattice whose scaling limit is a harmonic free boundary problem with a discontinuous Hamiltonian. We find an explicit formula for the Hamiltonian, prove the solutions are unique, and prove that the…
The process of gravitational accretion of initially homogeneous gas onto a solid ball is studied with methods of fluid dynamics. The fluid partial differential equations for polytropic flow can be solved exactly in an early stage, but this…
Understanding the contact between solid surfaces is a long standing problem which has a strong impact on the physics of many processes such as adhesion, friction, lubrication and wear. Experimentally, the investigation of solid/solid…
We study the 2D vortex-free XY model in a random field, a model for randomly pinned flux lines in a plane. We construct controlled RG recursion relations which allow for replica symmetry breaking (RSB). The fixed point previously found by…
In this article some of the hydrodynamical (HD) aspects of steady shocks as described by the steady-state shock model are reviewed and discussed. It is found that, at least in some of the contexts in which the steady-state model is used,…
Protection of topological surface states by reflection symmetry breaks down when the boundary of the sample is misaligned with one of the high symmetry planes of the crystal. We demonstrate that this limitation is removed in amorphous…
For a particle in orbit about a static spherically symmetric body, we study the change in self-force that results when the central body type (i.e., the choice of interior metric for the Schwarzschild exterior) is changed. While a straight…
A perfectly reflecting accelerating boundary produces thermal emission to an observer at $\mathscr{I}_L^+$ and a finite amount of energy to an observer at $\mathscr{I}_R^+$ by asymptotically traveling to the speed of light without an…
We present an exact solution for the time-dependent Stokes problem of an infinite cylinder of radius r=a in a fluid with harmonic boundary conditions at infinity. This is a 3-dimensional problem but, because of translational invariance…
Describing the phenomenon of total internal reflection in terms of a reflection coefficient of unit magnitude, we found that, not only can propagating plane waves be total internally reflected at the planar interface of two dissimilar,…
The commonly applied self-similar solution of the problem of the converging shock wave (shock) evolution with constant compression of the medium behind the shock front results in an unlimited increase of the medium velocity in the vicinity…
We study the time-reflection and time-refraction of waves caused by a spatial interface with a medium undergoing a sudden temporal change in permittivity. We show that monochromatic waves are transformed into a pulse by the permittivity…
Predicting the shape of a crater formed by high velocity impact is of interest in several fields. It can aid in design of more efficient protective structures, in forensic analysis of bullet holes, and in understanding the effects of…
Let $S$ be a smooth hypersurface properly embedded in $\mathbb R^N$ with $N \geq 3$ and consider its tubular neighborhood $\mathcal N$. We show that, if a heat flow over $\mathcal N$ with appropriate initial and boundary conditions has $S$…
We prove existence and uniqueness of a reaction-diffusion equation whose diffusivity is a non-linear functional of the boundary temperature. We do this by studying systems of one-dimensional reflecting diffusions whose noise is a function…