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

Explicit coercivity estimates for the linearized Boltzmann and Landau operators

We prove explicit coercivity estimates for the linearized Boltzmann and Landau operators, for a general class of interactions including any inverse-power law interactions, and hard spheres. The functional spaces of these coercivity estimates depend on the collision kernel of these operators. They cover the spectral gap estimates for the linearized Boltzmann operator with Maxwell molecules, improve these estimates for hard potentials, and are the first explicit coercivity estimates for soft potentials (including in particular the case of Coulombian interactions). We also prove a regularity property for the linearized Boltzmann operator with non locally integrable collision kernels, and we deduce from it a new proof of the compactness of its resolvent for hard potentials without angular cutoff.Comment: 32 page

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

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

Boltzmann equation and hydrodynamic fluctuations

We apply the method of invariant manifolds to derive equations of generalized hydrodynamics from the linearized Boltzmann equation and determine exact transport coefficients, obeying Green-Kubo formulas. Numerical calculations are performed in the special case of Maxwell molecules. We investigate, through the comparison with experimental data and former approaches, the spectrum of density fluctuations and address the regime of finite Knudsen numbers and finite frequencies hydrodynamics.Comment: This is a more detailed version of a related paper: I.V. Karlin, M. Colangeli, M. Kroger, PRL 100 (2008) 214503, arXiv:0801.2932. It contains comparison between predictions and experiment, in particular. 11 pages, 6 figures, 2 table

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

Bioreactor mechanically guided 3D mesenchymal stem cell chondrogenesis using a biocompatible novel thermo-reversible methylcellulose-based hydrogel

Autologous chondrocyte implantation for cartilage repair represents a challenge because strongly limited by chondrocytes' poor expansion capacity in vitro. Mesenchymal stem cells (MSCs) can differentiate into chondrocytes, while mechanical loading has been proposed as alternative strategy to induce chondrogenesis excluding the use of exogenous factors. Moreover, MSC supporting material selection is fundamental to allow for an active interaction with cells. Here, we tested a novel thermo-reversible hydrogel composed of 8% w/v methylcellulose (MC) in a 0.05 M Na 2 SO 4 solution. MC hydrogel was obtained by dispersion technique and its thermo-reversibility, mechanical properties, degradation and swelling were investigated, demonstrating a solution-gelation transition between 34 and 37 °C and a low bulk degradation (<20%) after 1 month. The lack of any hydrogel-derived immunoreaction was demonstrated in vivo by mice subcutaneous implantation. To induce in vitro chondrogenesis, MSCs were seeded into MC solution retained within a porous polyurethane (PU) matrix. PU-MC composites were subjected to a combination of compression and shear forces for 21 days in a custom made bioreactor. Mechanical stimulation led to a significant increase in chondrogenic gene expression, while histological analysis detected sulphated glycosaminoglycans and collagen II only in loaded specimens, confirming MC hydrogel suitability to support load induced MSCs chondrogenesis