The First Principle Formula of the Relativistic Heat Conductivity of Coulomb Electronic Plasmas

Making use of the relativistic BBGKY technique,the relativistic generalization of Landau collision integral is botained.Furthermore,we calculate the relativistic hydrodynamic modes up to the second order in the hydrodynamic wave number.Combining Resibois‘ method,we present the first principle formula of the relativistic heat conductivity of Coulumb electronic plasmas for low-order corrections.     

The space–time CESE method for solving special relativistic hydrodynamic equations

The special relativistic hydrodynamic equations are more complicated than the classical ones due to the nonlinear and implicit relations that exist between conservative and primitive variables. In this article, a space–time conservation element and solution element (CESE) method is proposed for solving these equations in one and two space dimensions. The CESE method has capability to capture sharp propagating wavefront of the relativistic fluids without excessive numerical diffusion or spurious oscillations. In contrast to the existing upwind finite volume schemes, the Riemann solver and reconstruction procedure are not the building blocks of the suggested method. The method differs from previous techniques because of global and local flux conservation in a space–time domain without resorting to interpolation or extrapolation. The scheme is efficient, robust, and gives results comparable to those obtained with more sophisticated algorithms, even in highly relativistic two-dimensional test problems.     

Relativistic hydrodynamic scaling from the dynamics of quantum field theory

Relativistic hydrodynamic scaling or boost invariance is a particularly important hydrodynamic regime, describing collective flows of relativistic many body systems and is used in the interpretation of experiments from high-energy cosmic rays to relativistic heavy-ion collisions. We show evidence for the emergence of hydrodynamic scaling from the dynamics of relativistic quantum field theory. We consider a scalar lambdaphi(4) model in 1+1 dimensions in the Hartree approximation and study the relativistic collisions of two kinks and the decay of a localized high-energy density region. We find that thermodynamic scalar isosurfaces show approximate boost invariance at high-energy densities.     

Relativistic Hydrodynamics and Essentially Non-oscillatory Shock Capturing Schemes

Numerical solutions of relativistic hydrodynamic equations are obtained with essentially non-oscillatory (ENO) finite differencing schemes. The method is explicit, conservative, consistent with the entropy condition, and high order accurate in space and time. The present implementation is applicable to the most general, three-dimensional problems with an arbitrary equation of state. Numerical experiments, including computations of multi-dimensional flows, demonstrate that the method delivers sharp, non-oscillatory shock transitions without sacrificing high resolution of the smooth regions. This extends results already established for the Euler gas dynamics to the relativistic regime, suggesting the usefulness of ENO schemes for modelling relativistic nuclear collisions.     

Quantum ion-acoustic solitary waves in weak relativistic plasma

Small amplitude quantum ion-acoustic solitary waves are studied in an unmagnetized two- species relativistic quantum plasma system, comprised of electrons and ions. The one-dimensional quantum hydrodynamic model (QHD) is used to obtain a deformed Korteweg–de Vries (dKdV) equation by reductive perturbation method. A linear dispersion relation is also obtained taking into account the relativistic effect. The properties of quantum ion-acoustic solitary waves, obtained from the deformed KdV equation, are studied taking into account the quantum mechanical effects in the weak relativistic limit. It is found that relativistic effects significantly modify the properties of quantum ion-acoustic waves. Also the effect of the quantum parameter H on the nature of solitary wave solutions is studied in some detail.     

The laws of relativistic thermodynamics: I. The macroscopic quantities

The physical quantities which occur in the laws of relativistic thermodynamics are defined as statistical expressions of relativistic kinetic theory. The role of the hydrodynamic velocity field is discussed.     

Relativistic aspects of HMO

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Coarse-graining scale and effectiveness of hydrodynamic modeling

We review our work on the application of the renormalization-group method to obtain first- and second-order relativistic hydrodynamics from the relativistic Boltzmann equation (RBE) as a dynamical system, with some corrections and new unpublished results. For the first-order equation, we explicitly obtain the distribution function in the asymptotic regime as the invariant manifold of the dynamical system, which turns out to be nothing but the matching condition defining the energy frame, i.e., the Landau-Lifshitz one. It is argued that the frame on which the flow of the relativistic hydrodynamic equation is defined must be the energy frame, if the dynamics should be consistent with the underlying RBE. A sketch is also given for derivation of the second-order hydrodynamic equation, i.e., extended thermodynamics, which is accomplished by extending the invariant manifold so that it is spanned by excited modes as well as the zero modes (hydrodynamic modes) of the linearized collision operator. On the basis of thus constructed resummed distribution function, we propose a novel ansatz for the functional form to be used in Grad moment method; it is shown that our theory gives the same expressions for the transport coefficients as those given in the Chapman-Enskog theory as well as the novel expressions for the relaxation times and lengths allowing natural interpretation.