Related papers: Shock Dynamics in Layered Periodic Media
We present a streamlined account of recent developments in the stability theory for planar viscous shock waves, with an emphasis on applications to physical models with ``real,'' or partial viscosity. The main result is the establishment of…
In this paper we study large time behaviors toward shock waves and rarefaction waves under periodic perturbations for 1-D convex scalar conservation laws. The asymptotic stabilities and decay rates of shock waves and rarefaction waves under…
Shock waves constitute discontinuities in matter which are relevant in studying the plasma behaviour in astrophysical scenarios and in heavy-ion collision. They can produce conical emission in relativistic collisions and are also thought to…
In order to understand the nonlinear stability of many types of time-periodic travelling waves on unbounded domains, one must overcome two main difficulties: the presence of embedded neutral eigenvalues and the time-dependence of the…
Dispersive shock waves and solitons are fundamental nonlinear excitations in dispersive media, but dispersive shock wave studies to date have been severely constrained. Here we report on a novel dispersive hydrodynamics testbed: the…
We review the latest progress and properties of the families of bright and dark one-dimensional periodic waves propagating in saturable Kerr-type and quadratic nonlinear media. We show how saturation of the nonlinear response results in…
The combination of fast propagation speeds and highly localized nature has hindered the direct observation of the evolution of shock waves at the molecular scale. To address this limitation, an experimental system is designed by tuning a…
For a model of nonlinear elastodynamics, we construct a finite volume scheme which is able to capture nonclassical shocks (also called undercompressive shocks). Those shocks verify an entropy inequality but are not admissible in the sense…
We introduce and systematically investigate the generation of dispersive shock waves, which arise naturally in physical settings such as optical waveguide arrays and superfluids confined within optical lattices. The underlying physically…
It is well-known that shock will form in finite time for hyperbolic conservation laws from initial nonlinear compression no matter how small and smooth the data are. Classical results, including Lax [14], Liu [22], Li-Zhou-Kong [16],…
Many astrophysical flows occur in inhomogeneous (clumpy) media. We present results of a numerical study of steady, planar shocks interacting with a system of embedded cylindrical clouds. Our study uses a two-dimensional geometry. Our…
Non-linear sound is an extreme phenomenon typically observed in solids after violent explosions. But granular media are different. Right when they jam, these fragile and disordered solids exhibit a vanishing rigidity and sound speed, so…
This paper develops the basic sets of equations which lead to the conservation laws describing collisionless plasma shock waves. We discuss the evolution of shock waves by wave steepening, derive the Rankine-Hugoniot conditions for…
The paper investigates shock-induced vortical flows within inhomogeneous media of nonuniform thermodynamic properties. Numerical simulations are performed using an Eularian type mathematical model for compressible multi-component flow…
In this paper, the asymptotic-time behavior of solutions to an initial boundary value problem in the half space for 1-D isentropic Navier-Stokes system is investigated. It is shown that the viscous shock wave is stable for an impermeable…
Molecular Dynamic (MD) approach is applied to study the converging cylindrical shock waves in a dense Lennard-Jones (LJ) fluid. MD method is based on tracking of the atom motions and hence it has an fundamental advantages over hydrodynamic…
We study the dynamical stability of stationary galactic spiral shocks. The steady-state equilibrium flow contains a shock of the type derived by Roberts in the tightly wound approximation. We find that boundary conditions are critical in…
We use time-dependent, axisymmetric, hydrodynamic simulations to study the linear stability of the stalled, spherical accretion shock that arises in the post-bounce phase of core-collapse supernovae. We show that this accretion shock is…
This paper shows that for the three-dimensional compressible isentropic Navier-Stokes equations, the planar viscous shocks are time-asymptotically stable to suitably small initial perturbations with zero masses. In particular, the…
This paper investigates the time asymptotic stability of composite waves formed by two shock waves within the context of one-dimensional relaxed compressible Navier-Stokes equations. We demonstrate that the composite waves consisting of two…