Nonlinear translational symmetric equilibria relevant to the L-H transition

Nonlinear z-independent solutions to a generalized Grad-Shafranov equation (GSE) with up to quartic flux terms in the free functions and incompressible plasma flow non parallel to the magnetic field are constructed quasi-analytically. Through an ansatz the GSE is transformed to a set of three ordinary differential equations and a constraint for three functions of the coordinate x, in cartesian coordinates (x,y), which then are solved numerically. Equilibrium configurations for certain values of the integration constants are displayed. Examination of their characteristics in connection with the impact of nonlinearity and sheared flow indicates that these equilibria are consistent with the L-H transition phenomenology. For flows parallel to the magnetic field one equilibrium corresponding to the H-state is potentially stable in the sense that a sufficient condition for linear stability is satisfied in an appreciable part of the plasma while another solution corresponding to the L-state does not satisfy the condition. The results indicate that the sheared flow in conjunction with the equilibrium nonlinearity play a stabilizing role.Comment: 26 pages, 16 figure

Discretization of the velocity space in solution of the Boltzmann equation

We point out an equivalence between the discrete velocity method of solving the Boltzmann equation, of which the lattice Boltzmann equation method is a special example, and the approximations to the Boltzmann equation by a Hermite polynomial expansion. Discretizing the Boltzmann equation with a BGK collision term at the velocities that correspond to the nodes of a Hermite quadrature is shown to be equivalent to truncating the Hermite expansion of the distribution function to the corresponding order. The truncated part of the distribution has no contribution to the moments of low orders and is negligible at small Mach numbers. Higher order approximations to the Boltzmann equation can be achieved by using more velocities in the quadrature

A causal statistical family of dissipative divergence type fluids

In this paper we investigate some properties, including causality, of a particular class of relativistic dissipative fluid theories of divergence type. This set is defined as those theories coming from a statistical description of matter, in the sense that the three tensor fields appearing in the theory can be expressed as the three first momenta of a suitable distribution function. In this set of theories the causality condition for the resulting system of hyperbolic partial differential equations is very simple and allow to identify a subclass of manifestly causal theories, which are so for all states outside equilibrium for which the theory preserves this statistical interpretation condition. This subclass includes the usual equilibrium distributions, namely Boltzmann, Bose or Fermi distributions, according to the statistics used, suitably generalized outside equilibrium. Therefore this gives a simple proof that they are causal in a neighborhood of equilibrium. We also find a bigger set of dissipative divergence type theories which are only pseudo-statistical, in the sense that the third rank tensor of the fluid theory has the symmetry and trace properties of a third momentum of an statistical distribution, but the energy-momentum tensor, while having the form of a second momentum distribution, it is so for a different distribution function. This set also contains a subclass (including the one already mentioned) of manifestly causal theories.Comment: LaTex, documentstyle{article

Strong Shock Waves and Nonequilibrium Response in a One-dimensional Gas: a Boltzmann Equation Approach

We investigate the nonequilibrium behavior of a one-dimensional binary fluid on the basis of Boltzmann equation, using an infinitely strong shock wave as probe. Density, velocity and temperature profiles are obtained as a function of the mixture mass ratio \mu. We show that temperature overshoots near the shock layer, and that heavy particles are denser, slower and cooler than light particles in the strong nonequilibrium region around the shock. The shock width w(\mu), which characterizes the size of this region, decreases as w(\mu) ~ \mu^{1/3} for \mu-->0. In this limit, two very different length scales control the fluid structure, with heavy particles equilibrating much faster than light ones. Hydrodynamic fields relax exponentially toward equilibrium, \phi(x) ~ exp[-x/\lambda]. The scale separation is also apparent here, with two typical scales, \lambda_1 and \lambda_2, such that \lambda_1 ~ \mu^{1/2} as \mu-->0$, while \lambda_2, which is the slow scale controlling the fluid's asymptotic relaxation, increases to a constant value in this limit. These results are discussed at the light of recent numerical studies on the nonequilibrium behavior of similar 1d binary fluids.Comment: 9 pages, 8 figs, published versio

Entropic force, noncommutative gravity and ungravity

After recalling the basic concepts of gravity as an emergent phenomenon, we analyze the recent derivation of Newton's law in terms of entropic force proposed by Verlinde. By reviewing some points of the procedure, we extend it to the case of a generic quantum gravity entropic correction to get compelling deviations to the Newton's law. More specifically, we study: (1) noncommutative geometry deviations and (2) ungraviton corrections. As a special result in the noncommutative case, we find that the noncommutative character of the manifold would be equivalent to the temperature of a thermodynamic system. Therefore, in analogy to the zero temperature configuration, the description of spacetime in terms of a differential manifold could be obtained only asymptotically. Finally, we extend the Verlinde's derivation to a general case, which includes all possible effects, noncommutativity, ungravity, asymptotically safe gravity, electrostatic energy, and extra dimensions, showing that the procedure is solid versus such modifications.Comment: 8 pages, final version published on Physical Review

Relativistic Dissipative Hydrodynamics: A Minimal Causal Theory

We present a new formalism for the theory of relativistic dissipative hydrodynamics. Here, we look for the minimal structure of such a theory which satisfies the covariance and causality by introducing the memory effect in irreversible currents. Our theory has a much simpler structure and thus has several advantages for practical purposes compared to the Israel-Stewart theory (IS). It can readily be applied to the full three-dimensional hydrodynamical calculations. We apply our formalism to the Bjorken model and the results are shown to be analogous to the IS.Comment: 25 pages, 2 figures, Phys. Rev. C in pres

On the kinetic systems for simple reacting spheres : modeling and linearized equations

Series: Springer Proceedings in Mathematics & Statistics, Vol. 75In this work we present some results on the kinetic theory of chemically reacting gases, concerning the model of simple reacting spheres (SRS) for a gaseous mixture undergoing a chemical reaction of type A1 +A2 A3 +A4. Starting from the approach developed in paper [11], we provide properties of the SRS system needed in the mathematical and physical analysis of the model. Our main result in this proceedings provides basic properties of the SRS system linearized around the equilibrium, including the explicit representations of the kernels of the linearized SRS operators.Fundação para a Ciência e a Tecnologia (FCT), PEst-C/MAT/UI0013/2011, SFRH/BD/28795/200

Fluid moment hierarchy equations derived from quantum kinetic theory

A set of quantum hydrodynamic equations are derived from the moments of the electrostatic mean-field Wigner kinetic equation. No assumptions are made on the particular local equilibrium or on the statistical ensemble wave functions. Quantum diffraction effects appear explicitly only in the transport equation for the heat flux triad, which is the third-order moment of the Wigner pseudo-distribution. The general linear dispersion relation is derived, from which a quantum modified Bohm-Gross relation is recovered in the long wave-length limit. Nonlinear, traveling wave solutions are numerically found in the one-dimensional case. The results shed light on the relation between quantum kinetic theory, the Bohm-de Broglie-Madelung eikonal approach, and quantum fluid transport around given equilibrium distribution functions.Comment: 5 pages, three figures, uses elsarticle.cl

Enhancing e-Infrastructures with Advanced Technical Computing: Parallel MATLAB® on the Grid

MATLAB® is widely used within the engineering and scientific fields as the language and environment for technical computing, while collaborative Grid computing on e-Infrastructures is used by scientific communities to deliver a faster time to solution. MATLAB allows users to express parallelism in their applications, and then execute code on multiprocessor environments such as large-scale e-Infrastructures. This paper demonstrates the integration of MATLAB and Grid technology with a representative implementation that uses gLite middleware to run parallel programs. Experimental results highlight the increases in productivity and performance that users obtain with MATLAB parallel computing on Grids

A Continuum Description of Rarefied Gas Dynamics (I)--- Derivation From Kinetic Theory

We describe an asymptotic procedure for deriving continuum equations from the kinetic theory of a simple gas. As in the works of Hilbert, of Chapman and of Enskog, we expand in the mean flight time of the constituent particles of the gas, but we do not adopt the Chapman-Enskog device of simplifying the formulae at each order by using results from previous orders. In this way, we are able to derive a new set of fluid dynamical equations from kinetic theory, as we illustrate here for the relaxation model for monatomic gases. We obtain a stress tensor that contains a dynamical pressure term (or bulk viscosity) that is process-dependent and our heat current depends on the gradients of both temperature and density. On account of these features, the equations apply to a greater range of Knudsen number (the ratio of mean free path to macroscopic scale) than do the Navier-Stokes equations, as we see in the accompanying paper. In the limit of vanishing Knudsen number, our equations reduce to the usual Navier-Stokes equations with no bulk viscosity.Comment: 16 page