Related papers: Shock Reflection-Diffraction, von Neumann's Conjec…
Mathematical diffraction theory is concerned with the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and mixed spectra…
We study the formation and the dynamics of a shock wave originating from the collision between two ultracold clouds of strongly interacting fermions as observed at a lower temperature in an experiment by Joseph et al. [Phys. Rev. Lett. 106,…
In this paper, we characterize a class of solutions to the unsteady 2-dimensional flow of a van der Waals fluid involving shock waves, and derive an asymptotic amplitude equation exhibiting quadratic and cubic nonlinearities including…
From optics to hydrodynamics, shock and rogue waves are widespread. Although they appear as distinct phenomena, new theories state that transitions between extreme waves are allowed. However, these have never been experimentally observed…
This paper introduces a novel wave front tracking framework for reconstructing unknown flux functions in $2\times 2$ hyperbolic conservation laws, extending beyond the well-studied scalar case. By analyzing Riemann solutions at fixed…
The shock reflection problem is one of the most important problems in mathematical fluid dynamics, since this problem not only arises in many important physical situations but also is fundamental for the theory of multidimensional…
This paper studies the expansion into vacuum of a wedge of gas at rest. This problem catches several important classes of wave interactions in the context of 2D Riemann problems. When the gas at rest is a nonideal gas, the gas away from the…
The diffraction of a scalar plane wave from a doubly-periodic surface on which either the Dirichlet or Neumann boundary condition is imposed is studied by means of a rigorous numerical solution of the Rayleigh equation for the amplitudes of…
We consider the long-time behavior of irrotational solutions of the three-dimensional compressible Euler equations with shocks, hypersurfaces of discontinuity across which the Rankine-Hugoniot conditions for irrotational flow hold. Our…
This article considers the problem of diffraction by a wedge consisting of two semi-infinite periodic arrays of point scatterers. The solution is obtained in terms of two coupled systems, each of which is solved using the discrete…
Time reflection and refraction are temporal analogies of the spatial boundary effects derived from Fermat's principle. They occur when classical waves strike a time boundary where an abrupt change in the properties of the medium is…
For a class of nonconservative hyperbolic systems of partial differential equations endowed with a strictly convex mathematical entropy, we formulate the initial value problem by supplementing the equations with a kinetic relation…
The boundary problem of linear classical optics about the interaction of electromagnetic radiation with a thin dielectric film has been solved under explicit consideration of its discrete structure. The main attention has been paid to the…
Corrugation instabilities occurring for solutions of the Riemann problem in relativistic hydrodynamics in which the fluid moves with a non-zero velocity tangent to the initial discontinuity are studied numerically. We perform simulations…
The oblique collisions and dynamical interference patterns of two-dimensional dispersive shock waves are studied numerically and analytically via the temporal dynamics induced by wedge-shaped initial conditions for the…
The present study investigates the shock wave interactions involving stationary and moving wedges using a sharp interface immersed boundary method combined with a fifth order weighted essentially non oscillatory (WENO) scheme. Inspired by…
We analyze rarefaction wave interactions of self-similar transonic irrotational flow in gas dynamics for the two dimensional Riemann problems. We establish the existence result of the supersonic solution to the prototype nonlinear wave…
A system of hyperbolic conservation laws $$ \partial_t u + \partial_x \partial_u Q = 0, \quad Q = u_1^3 / 3 + u_1 u_2^2, \qquad u = u(x,t) \in\mR^2, $$ as well as its viscous regularization $$ \partial_t u + \partial_x \partial_u Q = \calM…
The reflection of a triple-shock configuration was studied numerically in two dimensions using the Navier-Stokes equations. The flow field was initialized using three shock theory, and the reflection of the triple point on a plane of…
Diffraction is one of the universal phenomena of physics, and a way to overcome it has always represented a challenge for physicists. In order to control diffraction, the study of structured waves has become decisive. Here, we present a…