Related papers: Revisiting the Strong Shock Problem: Converging an…
We investigate the properties of a special class of singular solutions for a self-gravitating perfect fluid in general relativity: the singular isothermal sphere. For arbitrary constant equation-of-state parameter $w=p/\rho$, there exist…
Evolution of scalar perturbations in a universe containing solid matter with positive pressure is studied. Solution for pure solid is found and matched with solution for ideal fluid, including the case when the pressure to energy density…
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…
Hele-Shaw flow at vanishing surface tension is ill-defined. In finite time, the flow develops cusp-like singularities. We show that the ill-defined problem admits a weak {\it dispersive} solution when singularities give rise to a graph of…
We show the existence of a new class of initially smooth spherically symmetric self-similar solutions to the non-isentropic Euler-Poisson system. These solutions exhibit supersonic gravitational implosion in the sense that the density…
The collapse of cavities under shock is a key problem in various fields ranging from erosion of material, ignition of explosive, to sonoluminescence, etc. We study such processes using the material-point-method developed recently in the…
We establish rigorously the existence of a three-parameter family of self-similar,globally bounded, and continuous weak solutions in two space dimensions to the compressible Euler equations with axisymmetry for gamma-law polytropic gases…
Simulations of hot, pressure supported, tilted black hole accretion flows, in which the angular momentum of the flow is misaligned with the black hole spin axis, can exhibit two non-axisymmetric shock structures in the inner regions of the…
The collision of a plane parallel shock wave with a plane parallel cloud of uniform density is analysed for the case in which magnetic fields and radiative losses are not considered. General analytic solutions are discussed for the case in…
The shock reflection problem is one of the most important problems in mathematical fluid dynamics, since this problem not only arises in many important physical situations but also is fundamental for the theory of multidimensional…
We present the generalization of the Sedov-Taylor self-similar strong spherical shock solution for the case of a central energy source varying in time, $E=A t^k$, where $A$ and $k$ are constants. The known Sedov-Taylor solution corresponds…
Strong non-relativistic shocks are known to accelerate particles up to relativistic energies. However, for Diffusive Shock Acceleration electrons must have a highly suprathermal energy, implying a need for very efficient pre-acceleration.…
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…
The unique confinement of shock waves inside isolated liquid volumes amplifies the density of shock-liquid interactions. We investigate this universal principle through an interdisciplinary study of shock-induced cavitation inside liquid…
Relativistic shocks are present in all high-energy astrophysical processes involving relativistic plasma outflows interacting with their ambient medium. While a well understood process in the context of relativistic hydrodynamics and ideal…
We investigate the gravitational collapse of a spherically symmetric, perfect fluid with equation of state P = (Gamma -1)rho. We restrict attention to the ultrarelativistic (``kinetic-energy-dominated'', ``scale-free'') limit where black…
In this paper we extend the Sedov - Taylor - Von Neumann model for a strong explosion to account for small angular and radial variations in the density. We assume that the density profile is given by…
The general problem of shock formation in three space dimensions was solved by D. Christodoulou in his 2007 monograph: 'The Formation of Shocks in 3-dimensional Fluids'. In this work also a complete description of the maximal development of…
We examine the stability of self-similar solutions for an accelerating relativistic blast wave which is generated by a point explosion in an external medium with a steep radial density profile of a power-law index > 4.134. These…
We investigate spherically symmetric continuously self-similar (CSS) solutions in the SU(2) sigma model coupled to gravity. Using mixed numerical and analytical methods, we provide evidence for the existence (for small coupling) of a…