Related papers: Shock wave formation in Rosenau's extended hydrody…
In this paper, we present a detailed derivation of relativistic first-order spin hydrodynamics using the Chapman-Enskog method to linearize the nonlocal collision term for massive fermions proposed in \cite{Weickgenannt:2021cuo}, which well…
The present paper is the last of a series studying the first-order Fermi acceleration processes at relativistic shock waves with the method of Monte Carlo simulations applied to shocks propagating in realistically modeled turbulent magnetic…
We construct a formally time-reversible, one-dimensional forced Burgers equation by imposing a global constraint of energy conservation, wherein the constant viscosity is modified to a fluctuating state-dependent dissipation coefficient.…
The extended electrodynamic theory introduced by Aharonov and Bohm (after an earlier attempt by Ohmura) and recently developed by Van Vlaenderen and Waser, Hively and Giakos, can be re-written and solved in a simple and effective way in the…
The classical system of shallow-water (Saint--Venant) equations describes long surface waves in an inviscid incompressible fluid of a variable depth. Although shock waves are expected in this quasilinear hyperbolic system for a wide class…
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…
Shockwaves provide a useful and rewarding route to the nonequilibrium properties of simple fluids far from equilibrium. For simplicity, we study a strong shockwave in a dense two-dimensional fluid. Here, our study of nonlinear transport…
We performed highly resolved one-dimensional fully compressible Navier-Stokes simulations of heat-release-induced compression waves in near-critical CO2. The computational setup, inspired by the experimental setup of Miura et al., Phys.…
A relativistic generalization of the inviscid Burgers equation was proposed by LeFloch, Makhlof, and Okutmustur and then investigated on a Schwarzschild background. Here, we extend their analysis to a Friedmann-Lemaitre-Robertson-Walker…
Shock waves are supersonic disturbances propagating in a fluid and giving rise to dissipation and drag. Weak shocks, i.e., those of small amplitude, can be well described within the hydrodynamic approximation. On the other hand, strong…
Large amplitude water waves on deep water has long been known in the sea faring community, and the cause of great concern for, e.g., oil platform constructions. The concept of such freak waves is nowadays, thanks to satellite and radar…
Experiments have shown that shear waves induced in brain tissue can develop into shock waves, thus providing a possible explanation of deep traumatic brain injuries. Here, we study the formation of shock waves in soft viscoelastic solids…
Presented here is the mathematical model describing the phenomenon of shock waves. The underlying concept is based on the time-space model of wave propagation.
One of the most profound questions of mathematical physics is that of establishing from first principles the hydrodynamic equations in large, isolated, strongly interacting many-body systems. This involves understanding relaxation at long…
In this paper, two kinds of occurrence mechanism on the phenomenon of concentration and the formation of delta shock wave in the flux approximation limit of Riemann solutions to the extended Chaplygin gas equations are analyzed and…
Observations of both gamma-ray burst sources and certain classes of active galaxy indicate the presence of relativistic shock waves and require the production of high energy particles to explain their emission. In this paper we review the…
We study the long-time behavior of scalar viscous conservation laws via the structure of $\omega$-limit sets. We show that $\omega$-limit sets always contain constants or shocks by establishing convergence to shocks for arbitrary monotone…
We consider propagation of density wave packets in a Bose-Einstein condensate. We show that the shape of initially broad, laser-induced, density perturbation changes in the course of free time evolution so that a shock wave front finally…
We investigate shock-wave solutions of the Einstein equations in the case when the speed of propagation is equal to the speed of light. The work extends the shock matching theory of Smoller and Temple, which characterizes solutions of the…
A second-order PDE is derived from Euler's equaitons under certain assumptions. It is shown that this PDE admits shock and rarefaction waves, and that a single point gradient blow-up admits a unique similarity extension after blow-up that…