Related papers: Shock wave formation in Rosenau's extended hydrody…
Extended thermodynamics commonly uses polynomial moments to model non-equilibrium transportation, but faces a crisis due to sub-shocks, which are anomalous discontinuities in gas properties when predicting shock waves. The cause of…
In this paper we provide bound estimates for the two fastest wave speeds emerging from the solution of the Riemann problem for three well-known hyperbolic systems, namely the Euler equations of gas dynamics, the shallow water equations and…
We derive the second-order hydrodynamic equation and the microscopic formulae of the relaxation times as well as the transport coefficients systematically from the relativistic Boltzmann equation. Our derivation is based on a novel…
The piston shock problem is a prototypical example of strongly nonlinear fluid flow that enables the experimental exploration of fluid dynamics in extreme regimes. Here we investigate this problem for a nominally dissipationless, superfluid…
The thermomagnetic instability of the critical state in superconductors is analysed with account of the dissipation and dispersion. The possibility is demonstrated of the existance of a nonlinear shok wave describing the final stage of the…
The KdV equation can be derived in the shallow water limit of the Euler equations. Over the last few decades, this equation has been extended to include higher order effects. Although this equation has only one conservation law, exact…
We derive a retained-spin micropolar hydrodynamic closure from the Boltzmann--Curtiss equation using a generalized Chapman--Enskog construction in which the local mean spin is retained as a quasi-slow variable. Starting from the…
We report on the formation of a dispersive shock wave in a nonlinear optical medium. We monitor the evolution of the shock by tuning the incoming beam power. The experimental observations for the position and intensity of the solitonic edge…
In this article, we provide notes that complement the lectures on the relativistic Euler equations and shocks that were given by the second author at the program Mathematical Perspectives of Gravitation Beyond the Vacuum Regime, which was…
The solution of self-similar shock dynamics satisfying the inviscid Burgers equation are provided in closed form for planar, cylindrical and spherical problems. The approach follows Lee's method for obtaining self-similar solutions for the…
Integrable systems feature an infinite number of conserved charges and on hydrodynamic scales are described by generalised hydrodynamics (GHD). This description breaks down when the integrability is weakly broken and sufficiently large…
The objective of this paper is to construct geometrically Riemann $k$-wave solutions of the general form of first-order quasilinear hyperbolic systems of partial differential equations. To this end, we adapt and combine elements of two…
This paper deals with the convergence/divergence issue of the Chapman-Enskog series expansion of the shear and normal stresses for a granular gas of inelastic hard spheres. From the exact solution of a simple kinetic model in the uniform…
The basis for a hydrodynamic description of granular gases is discussed for a low density gas of smooth, inelastic hard spheres. The more fundamental mesoscopic description is taken to be the nonlinear Boltzmann kinetic equation. Two…
We revisit and derive the shock-change equations relating the dynamics of a shock wave with the partial derivatives describing the motion of a reactive fluid with general equation of state in a stream-tube with arbitrary area variation. We…
In the hydrodynamic approximation we obtain analytic solutions to the Gross-Pitaevskii equation with positive scattering length which describe expansions of the Bose-Einstein condensates in quasi-one and quasi-two dimensional geometries.…
A new formulation of second-order viscous hydrodynamics, based on an expansion around a locally anisotropic momentum distribution, is presented. It generalizes the previously developed formalism of anisotropic hydrodynamics (aHydro) to…
The origin of the X-ray plateau phase observed in a large fraction of gamma-ray burst afterglows remains debated. We present a novel analytic framework for the hydrodynamics of ultra-relativistic, radially stratified outflows interacting…
Wave-driven outflows and non-disruptive explosions have been implicated in pre-supernova outbursts, supernova impostors, LBV eruptions, and some narrow-line and superluminous supernovae. To model these events, we investigate the dynamics of…
A possibility of the hydrodynamic description of ultracold fermions via the microscopic derivation of the model is described. Differently truncated hydrodynamic models are derived and compared. All models are based on the microscopic…