Effective Dissipation and Turbulence in Spectrally Truncated Euler Flows

A new transient regime in the relaxation towards absolute equilibrium of the conservative and time-reversible 3-D Euler equation with high-wavenumber spectral truncation is characterized. Large-scale dissipative effects, caused by the thermalized modes that spontaneously appear between a transition wavenumber and the maximum wavenumber, are calculated using fluctuation dissipation relations. The large-scale dynamics is found to be similar to that of high-Reynolds number Navier-Stokes equations and thus to obey (at least approximately) Kolmogorov scaling.Comment: 4 pages, 5 figures new version with only 4 figures; title changed; manuscript changed; accepted by PR

Fokker-Planck type equations for a simple gas and for a semi-relativistic Brownian motion from a relativistic kinetic theory

A covariant Fokker-Planck type equation for a simple gas and an equation for the Brownian motion are derived from a relativistic kinetic theory based on the Boltzmann equation. For the simple gas the dynamic friction four-vector and the diffusion tensor are identified and written in terms of integrals which take into account the collision processes. In the case of Brownian motion, the Brownian particles are considered as non-relativistic whereas the background gas behaves as a relativistic gas. A general expression for the semi-relativistic viscous friction coefficient is obtained and the particular case of constant differential cross-section is analyzed for which the non-relativistic and ultra relativistic limiting cases are calculated.Comment: To appear in PR

Nonlocal observables and lightcone-averaging in relativistic thermodynamics

The unification of relativity and thermodynamics has been a subject of considerable debate over the last 100 years. The reasons for this are twofold: (i) Thermodynamic variables are nonlocal quantities and, thus, single out a preferred class of hyperplanes in spacetime. (ii) There exist different, seemingly equally plausible ways of defining heat and work in relativistic systems. These ambiguities led, for example, to various proposals for the Lorentz transformation law of temperature. Traditional 'isochronous' formulations of relativistic thermodynamics are neither theoretically satisfactory nor experimentally feasible. Here, we demonstrate how these deficiencies can be resolved by defining thermodynamic quantities with respect to the backward-lightcone of an observation event. This approach yields novel, testable predictions and allows for a straightforward-extension of thermodynamics to General Relativity. Our theoretical considerations are illustrated through three-dimensional relativistic many-body simulations.Comment: typos in Eqs. (12) and (14) corrected, minor additions in the tex

Stationary Cylindrical Anisotropic Fluid

We present the whole set of equations with regularity and matching conditions required for the description of physically meaningful stationary cylindrically symmmetric distributions of matter, smoothly matched to Lewis vacuum spacetime. A specific example is given. The electric and magnetic parts of the Weyl tensor are calculated, and it is shown that purely electric solutions are necessarily static. Then, it is shown that no conformally flat stationary cylindrical fluid exits, satisfying regularity and matching conditions.Comment: 17 pages Latex. To appear in Gen.Rel.Gra

Improved Holographic QCD

We provide a review to holographic models based on Einstein-dilaton gravity with a potential in 5 dimensions. Such theories, for a judicious choice of potential are very close to the physics of large-N YM theory both at zero and finite temperature. The zero temperature glueball spectra as well as their finite temperature thermodynamic functions compare well with lattice data. The model can be used to calculate transport coefficients, like bulk viscosity, the drag force and jet quenching parameters, relevant for the physics of the Quark-Gluon Plasma.Comment: LatEX, 65 pages, 28 figures, 9 Tables. Based on lectures given at several Schools. To appear in the proceedinds of the 5th Aegean School (Milos, Greece

Matching stationary spacetimes

Using the quasi-Maxwell formalism, we derive the necessary and sufficient conditions for the matching of two stationary spacetimes along a stationary timelike hypersurface, expressed in terms of the gravitational and gravitomagnetic fields and the 2-dimensional matching surface on the space manifold. We prove existence and uniqueness results to the matching problem for stationary perfect fluid spacetimes with spherical, planar, hyperbolic and cylindrical symmetry. Finally, we find an explicit interior for the cylindrical analogue of the NUT spacetime.Comment: 13 pages; v2: references added, typos corrected, matches final published version; v3: statement about higher genus stars corrected, reference added; v4: footnote 3 made more precis

CXCR3 Antagonism of SDF-1(5-67) Restores Trabecular Function and Prevents Retinal Neurodegeneration in a Rat Model of Ocular Hypertension

Glaucoma, the most common cause of irreversible blindness, is a neuropathy commonly initiated by pathological ocular hypertension due to unknown mechanisms of trabecular meshwork degeneration. Current antiglaucoma therapy does not target the causal trabecular pathology, which may explain why treatment failure is often observed. Here we show that the chemokine CXCL12, its truncated form SDF-1(5-67), and the receptors CXCR4 and CXCR3 are expressed in human glaucomatous trabecular tissue and a human trabecular cell line. SDF-1(5-67) is produced under the control of matrix metallo-proteinases, TNF-α, and TGF-β2, factors known to be involved in glaucoma. CXCL12 protects in vitro trabecular cells from apoptotic death via CXCR4 whereas SDF-1(5-67) induces apoptosis through CXCR3 and caspase activation. Ocular administration of SDF-1(5-67) in the rat increases intraocular pressure. In contrast, administration of a selective CXCR3 antagonist in a rat model of ocular hypertension decreases intraocular pressure, prevents retinal neurodegeneration, and preserves visual function. The protective effect of CXCR3 antagonism is related to restoration of the trabecular function. These data demonstrate that proteolytic cleavage of CXCL12 is involved in trabecular pathophysiology, and that local administration of a selective CXCR3 antagonist may be a beneficial therapeutic strategy for treating ocular hypertension and subsequent retinal degeneration