Related papers: Critical Point from Shock Waves Solution in Relati…
In the limit of small values of the aspect ratio parameter (or wave steepness) which measures the amplitude of a surface wave in units of its wave-length, a model equation is derived from the Euler system in infinite depth (deep water)…
The acceleration of relativistic particles due to repeated scattering across a shock wave remains the most attractive model for the production of energetic cosmic rays. This process has been analyzed extensively during the past two decades…
This report addresses the solution of Riemann problems for hyperbolic equations when the nonlinear characteristic fields loose their genuine nonlinearity. In this context, exact solvers for nonconvex 1D Riemann problems are developed. First…
In this note, we study the hydrodynamic limit, in the hyperbolic space-time scaling, for a one-dimensional unpinned chain of quantum harmonic oscillators with random masses. To the best of our knowledge, this is among the first examples,…
The runup of tsunami waves on the coasts of the barrow bays, channels and straits is studied in the framework of the nonlinear shallow water theory. Using the narrowness of the water channel, the one-dimensional equations are applied; they…
The response of inviscid incompressible unbounded fluid subject to a localized external perturbation is studed. The physically relevant hypotheses on the mode coupling mechanisma is justified by renormalization group method. The scaling…
We extend the effective theory approach to the ideal fluid limit where the polarization of the fluid is non-zero. After describing and motivating the equations of motion, we expand them around the hydrostatic limit, obtaining the sound wave…
A new class of accelerating, exact, explicit and simple solutions of relativistic hydrodynamics is presented. Since these new solutions yield a finite rapidity distribution, they lead to an advanced estimate of the initial energy density…
Shock wave theory was first studied for gas dynamics, for which shocks appear as compression waves. A shock wave is characterized as a sharp transition, even discontinuity in the flow. In fact, shocks appear in many different physical…
A shock waveform is proposed based on the mechanical mechanism of shock generation in a structure. The parameters in the shock waveform have clear mechanical meanings about the generation and development of the shock. A shock signal…
We present results from simulations of axisymmetric relativistic rotational core collapse. The general relativistic hydrodynamic equations are formulated in flux-conservative form and solved using a high-resolution shock-capturing scheme.…
This paper shows that in second-order hyperbolic systems of partial differential equations proposed in authors' earlier paper (J. Math. Phys. 59 (2018)) for modelling the relativistic dynamics of barotropic fluids in the presence of…
Several phenomena related to the critical behaviour of non-interacting electrons in a disordered 2d tight-binding system with a magnetic field are studied. Localization lengths, critical exponents and density of states are computed using…
We have used second order relativistic hydrodynamics equipped with equation of state which includes the critical point to study the propagation of perturbation in a relativistic QCD fluid. Dispersion relation for the sound wave has been…
We review recent interest in the relativistic Riemann problem as a method for generating a non-equilibrium steady state. In the version of the problem under con- sideration, the initial conditions consist of a planar interface between two…
We prove local higher-order asymptotics for extreme water waves with vorticity near stagnation points. We obtain that the behaviour of solutions and their regularity depend substantially on the vorticity. In particular, we show that extreme…
We have generalised the exact solution of the Riemann problem in special relativistic hydrodynamics for arbitrary tangential flow velocities. The solution is obtained by solving the jump conditions across shocks plus an ordinary…
This paper deals with the collapse and expansion of relativistic anisotropic self-gravitating source. The field equations for non-radiating and non-static plane symmetric anisotropic source have been evaluated. The non-radiating property of…
The classical equations of irrotational water waves have recently been reformulated as a system of two equations, one of which is an explicit non-local equation for the wave height and for the velocity potential evaluated on the free…
The magnetohydrodynamic equations system for heavy fluid over an arbitrary surface in shallow water approximation is studied in the present paper. It is shown that simple wave solutions exist only for underlying surfaces that are slopes of…