Related papers: Fundamentals of Non-relativistic Collisionless Sho…
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…
A direct numerical simulation of a strong relativistic collisionless shock propagating into an unmagnetized medium has been performed in two spatial dimensions. It is found that: (i) collisionless shock exists, (ii) particle acceleration is…
In this paper, we study the nonlinear dispersive waves including the rarefaction and dispersive shock waves in the discrete modified KdV equation through the numerical simulations of the dispersive Riemann problems. In particular, we…
We perform a linear stability analysis for corrugations of a Newtonian shock, with particle pressure included, for an arbitrary diffusion coefficient. We study first the dispersion relation for homogeneous media, showing that, besides the…
We consider dispersive shock wave to the focusing nonlinear Schr\"odinger equation generated by a discontinuous initial condition which is periodic or quasi-periodic on the left semi-axis and zero on the right semi-axis. As an initial…
A two-dimensional (2D) shock-rest-frame model for particle simulations is developed. Then full kinetic dynamics of a perpendicular collisionless shock is examined by means of a 2D full particle simulation. We found that in the 2D simulation…
Propagation of elastic waves in damaged media (concrete, rocks) is studied theoretically and numerically. Such materials exhibit a nonlinear behavior, with long-time softening and recovery processes (slow dynamics). A constitutive model…
We discuss high-resolution simulations of one-dimensional, plane-parallel shock waves with mean speeds between 150 and 240 km/s propagating into gas with Alfven velocities up to 40 km/s and outline the conditions under which these radiative…
Models of steady-state plane-parallel shock waves propagating through the unperturbed hydrogen gas of temperature T=6000K and density rho = 1e-10 gm/cm^3 are computed for upstream velocities from 15 km/s to 70 km/s. The shock wave structure…
The KdV-Burgers equation is a canonical model describing the interplay between nonlinearity, viscosity and dispersion, and it admits viscous-dispersive shocks as traveling wave solutions. In this paper, we establish an $L^2$-contraction…
Stagnation of a cold plasma streaming to the center or axis of symmetry via an expanding accretion shock wave is ubiquitous in inertial confinement fusion (ICF) and high-energy-density plasma physics, the examples ranging from plasma flows…
The research is aimed at the study of the properties of solutions for parallel MHD shock waves in collisionless plasma with heat fluxes, using 8-moment MHD approximation. Restrictions have been established on the upstream shock parameters…
We study the nonlinear propagation of electrostatic wave packets in a collisional plasma composed of strongly coupled ions and relativistically degenerate electrons. The equilibrium of ions is maintained by an effective temperature…
Ideal gas dynamics can develop shock-like singularities with discontinuous density. Viscosity typically regularizes such singularities and leads to a shock structure. On the other hand, in 1d, singularities in the Hopf equation can be…
When a plane shock hits a wedge head on, it experiences a reflection-diffraction process, and then a self-similar reflected shock moves outward as the original shock moves forward in time. The complexity of reflection-diffraction…
We study the long term evolution of magnetic fields generated by an initially unmagnetized collisionless relativistic $e^+e^-$ shock. Our 2D particle-in-cell numerical simulations show that downstream of such a Weibel-mediated shock,…
Astrophysical plasmas in accretion discs are usually treated in the framework of fluid or MHD approaches but there are some situations where these treatments become inadequate and one needs to revert to the more fundamental underlying…
We investigate the acceleration of light particles in perpendicular shocks for plasmas consisting of a mixture of leptonic and hadronic particles. Starting from the full set of conservation equations for the mixed plasma constituents, we…
We study the longitudinal stability of beam-plasma systems in the presence of a density inhomogeneity in the background plasma. Previous works have focused on the non-relativistic regime where hydrodynamical models are used to evolve…
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…