Relativistic shocks in the systems containing domains with anomalous equation of state and quark baryonic matter hadronization

Theoretical basis for general stability criterion of relativistic shocks in baryonic matter is proposed. Different formulations of shock mechanical stability are considered and applied to the analysis of rarefaction shock hadronization transition.     

Relativistic shocks in the systems containing domains with anomalous equation of state and quark baryonic matter hadronization

Theoretical basis for general stability criterion of relativistic shocks in baryonic matter is proposed. Different formulations of shock mechanical stability are considered and applied to the analysis of rarefaction shock hadronization transition.     

Shock stability criterion in relativistic hydrodynamics and quark-gluon plasma hadronization

The shock stability condition in the relativistic hydrodynamics is found. This criterion is applied to a quark-gluon plasma shock-like hadronization transition.     

Criterion for long-wavelength electromagnetic instability of a homogeneous relativistic plasma

Electromagnetic instability of an unmagnetized homogeneous relativistic plasma with an anisotropic velocity distribution having a center of symmetry is analyzed. A stability criterion is derived for slowly varying long-wavelength perturbations. The criterion is formulated as a set of equalities that are not valid for ellipsoidal velocity distributions, but can be satisfied for other anisotropic distributions. The relativistic case is special only in that the rest mass is replaced with the relativistic one.     

Criterion for existence of shock waves in relativistic magnetohydrodynamics with a general equation of state

Relativistic stationary shock waves in an ideal conducting fluid are studied for the general equation of state. We use small viscosity arguments to obtain a criterion that selects physically admissible shock transitions without any supposition about convexity of the Poisson adiabats. The relations between the magnetosound speeds and the speed of the shock obtained as a consequence of this criterion reveal specific differences between relativistic considerations versus classical ones.     

Ondes de choc et hypothèses de compressibilité en magnétohydrodynamique relativiste

The principal purpose of this paper is to show that the normals to the hypersurfaces in space-time which represent the shock waves of relativistic magnetohydrodynamics are spacelike when the caloric equation of state of the medium satisfies the conditions of compressibility previously given in references [5] and [6]. Thus, the velocities of these waves are less than the local velocity of light and the theory is consistent with the postulates of a relativistic theory. A theorem previously given in reference [5] concerning the stability of Alfven shock waves, is corrected in this paper.     

A New Type of Conserved Quantity of Mei Symmetry for Relativistic Variable Mass Mechanical System in Phase Space

In this paper, a new type of conserved quantity directly deduced from the Mei symmetry for relativistic variable mass system in phase space is studied. The definition and the criterion of the Mei symmetry for the system are given. The conditions for existence and the form of the new conserved quantity are obtained. Finally, an example is given to illustrate the application of the results.     

A new type of conserved quantity of Mei symmetry for relativistic nonholonomic mechanical system in phase space

In this paper, a new type of conserved quantity induced directly from the Mei symmetry for a relativistic nonholonomic mechanical system in phase space is studied. The definition and the criterion of the Mei symmetry for the system are given. The conditions for the existence and form of the new conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.     

强磁场中相互作用费米气体的相对论稳定性

由单粒子的弱相互作用能谱及泊松公式,导出了强磁场中相互作用费米气体的相对论热力学势函数,求解了系统力学稳定性的判别式,分析了相互作用、磁场及相对论效应对系统稳定性的影响机理.结果表明,强磁场中弱相互作用费米气体的力学稳定性会受到弱相互作用的影响,强磁场对这种影响具有调节作用,而相对论效应对相互作用的影响基本没有调节作用.     

强磁场中相互作用费米气体的相对论稳定性

由单粒子的弱相互作用能谱及泊松公式,导出了强磁场中相互作用费米气体的相对论热力学势函数,求解了系统力学稳定性的判别式,分析了相互作用、磁场及相对论效应对系统稳定性的影响机理。结果表明,强磁场中弱相互作用费米气体的力学稳定性会受到弱相互作用的影响,强磁场对这种影响具有调节作用,而相对论效应对相互作用的影响基本没有调节作用。     

Structure and evolution of shock waves in relativistic magnetohydrodynamics

We derive the existence conditions for relativistic shock waves propagating in a perfectly conducting fluid with a general equation of state that guarantees that the stationary wave has a continuous profile in the presence of weak viscosity. To this end we study the one-dimensional solutions of the magnetohydrodynamic equations with a relativistic viscosity tensor. We allow for anomalous regions of thermodynamic variables and do not use the well-known condition for the convexity of Poisson adiabats. The results lead to relationships among the velocities of magnetoacoustic, Alfvén, and shock waves in front of and behind the discontinuity that prove to be more stringent than the corollaries of the evolution conditions. In the nonrelativistic case and in parallel and perpendicular shock waves, any difference between the two conditions disappears. Zh. éksp. Teor. Fiz. 114, 881–891 (September 1998)     

Symmetry Properties and Reduction of the Generalized Nonlinear System of Two-Phase Liquid Equations

Abstract

We consider discontinuous flows of relativistic magnetic fluid with a general equation of state that is not supposed to be normal in the sense of Bethe and Weyl. The criteria of admissibility of the shock waves without a supposition of the relativistic version of the convexity condition are obtained. The results are used to analyze the cases of perpendicular and parallel shock waves.     

On the role of dissipation in structure formation for dilute relativistic gases: the fluctuating static background case

A correction to the Jeans stability criterion due to dissipation is established for the case of dilute high temperature gases. This effect is only relevant in the relativistic scenario and includes additional terms due to a density gradient driven heat flux, a non-vanishing bulk viscosity and the space-time dependent gravitational potential first order fluctuations. The result is obtained by thoroughly analyzing the exponentially growing modes present in the dynamics of density fluctuations in the linearized relativistic Navier–Stokes regime. The corrections to the corresponding Jeans mass and wavenumber are explicitly obtained and are compared to the non-relativistic and non-dissipative values using the transport coefficients obtained in the BGK approximation.     

Models of spherical shells as sources of Majumdar–Papapetrou type spacetimes

By starting with a seed Newtonian potential–density pair we construct relativistic thick spherical shell models for a Majumdar–Papapetrou type conformastatic spacetime. As a simple example, we considerer a family of Plummer–Hernquist type relativistic spherical shells. As a second application, these structures are then used to model a system composite by a dust disk and a halo of matter. We study the equatorial circular motion of test particles around such configurations. Also the stability of the orbits is analyzed for radial perturbation using an extension of the Rayleigh criterion. The models considered satisfying all the energy conditions.     

Supersonic Shock Wave with Landau Quantization in a Relativistic Degenerate Plasma

A three-dimensional(3D)BurgersJ equation adopting perturbative methodology is derived to study the evolution of a shock wave with Landau quantized magnetic field in relativistic quantum plasma.The characteristics of a shock wave in such a plasma under the influence of magnetic quantization,relativistic parameter and degenerate electron density are studied with assistance of steady state solution.The magnetic field has a noteworthy control,especially on the shock wave's amplitude in the lower range of the electron density,whereas the amplitude in the higher range of the electron density reduces remarkably.The rate of increase of shock wave potential is much higher(lower)with a magnetic Held in the lower(higher)range of electron density.With the relativistic factor,the shock wave's amplitude increases significantly and the rate of increase is higher(lower)for lower(higher)electron density.The combined effect of the increase of relativistic factor and the magnetic field on the strength of the shock wave,results in the highest value of the wave potential in the lower range of the degenerate electron density.     

Stability of Covariant Relativistic Quantum Theory

In this paper we study the relativistic quantum-mechanical interpretation of the solution of the inhomogeneous Euclidean Bethe-Salpeter equation. Our goal is to determine conditions on the input to the Euclidean Bethe-Salpeter equation so the solution can be used to construct a model Hilbert space and a dynamical unitary representation of the Poincaré group. We prove three theorems that relate the stability of this construction to properties of the kernel and driving term of the Bethe-Salpeter equation. The most interesting result is that the positivity of the Hilbert space norm in the non-interacting theory is not stable with respect to Euclidean covariant perturbations defined by Bethe-Salpeter kernels. The long-term goal of this work is to understand which model Euclidean Green functions preserve the underlying relativistic quantum theory of the original field theory. Understanding the constraints imposed on the Green functions by the existence of an underlying relativistic quantum theory is an important consideration for formulating field-theory motivated relativistic quantum models.This work supported in part by the U.S. Department of Energy, under contract DE-FG02-86ER40286     

E-H Type Mach Configuration and its Stability

This paper is devoted to the study of the classification and stability of Mach configurations. In the Mach reflection of a shock wave by a rigid wall the flow behind the reflected shock front can be supersonic or subsonic. Correspondingly, the Mach configuration can be classified as E-E type and E-H type. In this paper we proved the stability of E-H type Mach configurations provided the reflected shock is weak. The result is the complement of the stability of E-E type Mach configurations in our earlier work.The stability of E-H Mach configurations is reduced to a generalized Tricomi problem of a nonlinear mixed type equation. The linearization of this problem is a generalized Tricomi problem of a linear Lavrentiev-Bitsadze’s mixed type equation. In order to prove the existence of such a problem we first use the equation in the hyperbolic region and a condition on the reflected shock to establish a relation of the unknown function and its normal derivative on the sonic line. Then the generalized Tricomi problem is reduced to a nonlocal boundary value problem in the elliptic region. Careful analysis gives necessary estimates and the solvability of the linearized problem. It leads to the existence of the solution to the corresponding nonlinear problem, which implies the required stability of E-H Mach configurations.     

Nonlinear Dynamical Stability of Newtonian Rotating and Non-rotating White Dwarfs and Rotating Supermassive Stars

We prove general nonlinear stability and existence theorems for rotating star solutions which are axi-symmetric steady- state solutions of the compressible isentropic Euler-Poisson equations in 3 spatial dimensions. We apply our results to rotating white dwarf and high density supermassive (extreme relativistic) stars, stars which are in convective equilibrium and have uniform chemical composition. Also, we prove nonlinear dynamical stability of non-rotating white dwarfs with general perturbation without any symmetry restrictions. This paper is a continuation of our earlier work ([26]).     

Ion acoustic shock waves in a relativistic electron-positron-ion plasmas

The Korteweg-de Vries-Burger (KdVB) equation is derived for ion acoustic shock waves in a weakly relativistic electron-positron-ion plasma. Electrons, positrons are considered isothermal and ions are relativistic. The travelling wave solution has been acquired by employing the tangent hyperbolic method. The vivid display of the graphical results is presented and analyzed. It is observed that amplitude and steepness of the shock wave decrease with increase of the relativistic streaming factor, the positron concentration and they increase with the increase of the coefficient of kinematic viscosity and vice versa. It is determined that at low temperature the shock wave propagates, whereas at very high temperature the solitary wave propagates in the system. The results may have relevance in astrophysical plasmas as well as in inertial confinement fusion plasmas.     

Chaos in the relativistic two-electron atom

Chaotic autoionization of the relativistic two-electron atom is investigated. A theoretical analysis of chaotic dynamics of the relativistic outer electron under the periodic perturbation due to the inner electron, assumed to be on a circular orbit, based on the Chirikov criterion, is given. The diffusion coefficient, the ionization rate, and time are calculated. (c) 2002 American Institute of Physics.