Thermodynamics of interacting entropy-corrected holographic dark energy in a non-flat FRW universe

A so-called "entropy-corrected holographic dark energy" (ECHDE), was recently proposed to explain the dark energy-dominated universe with the help of quantum corrections to the entropy-area relation in the setup of loop quantum cosmology. Using this new definition, we investigate its thermodynamical features including entropy and energy conservation. We describe the thermodynamical interpretation of the interaction between ECHDE and dark matter in a non-flat universe. We obtain a relation between the interaction term of the dark components and thermal fluctuation. Our study further generalizes the earlier works [M.R. Setare and E.C. Vagenas, Phys. Lett. B 666 (2008) 111; B. Wang et al., Phys. Lett. B 662 (2008) 1] in this direction.Comment: 14 pages, no figure, accepted by Int. J. Mod. Phys.

Entropy Corrections for Schwarzschild and Reissner-Nordstr\"om Black Holes

Schwarzschild black hole being thermodynamically unstable, corrections to its entropy due to small thermal fluctuations cannot be computed. However, a thermodynamically stable Schwarzschild solution can be obtained within a cavity of any finite radius by immersing it in an isothermal bath. For these boundary conditions, classically there are either two black hole solutions or no solution. In the former case, the larger mass solution has a positive specific heat and hence is locally thermodynamically stable. We find that the entropy of this black hole, including first order fluctuation corrections is given by: {\cal S} = S_{BH} - \ln[\f{3}{R} (S_{BH}/4\p)^{1/2} -2]^{-1} + (1/2) \ln(4\p), where $S_{BH}=A/4$ is its Bekenstein-Hawking entropy and $R$ is the radius of the cavity. We extend our results to four dimensional Reissner-Nordstr\"om black holes, for which the corresponding expression is: {\cal S} = S_{BH} - \f{1}{2} \ln [ {(S_{BH}/\p R^2) ({3S_{BH}}/{\p R^2} - 2\sqrt{{S_{BH}}/{\p R^2 -\a^2}}) \le(\sqrt{{S_{BH}}/{\p R^2}} - \a^2 \ri)}/ {\le({S_{BH}}/{\p R^2} -\a^2 \ri)^2} ]^{-1} +(1/2)\ln(4\p). Finally, we generalise the stability analysis to Reissner-Nordstr\"om black holes in arbitrary spacetime dimensions, and compute their leading order entropy corrections. In contrast to previously studied examples, we find that the entropy corrections in these cases have a different character.Comment: 6 pages, Revtex. References added, minor changes. Version to appear in Class. Quant. Gra

Deformation of Codimension-2 Surface and Horizon Thermodynamics

The deformation equation of a spacelike submanifold with an arbitrary codimension is given by a general construction without using local frames. In the case of codimension-1, this equation reduces to the evolution equation of the extrinsic curvature of a spacelike hypersurface. In the more interesting case of codimension-2, after selecting a local null frame, this deformation equation reduces to the well known (cross) focusing equations. We show how the thermodynamics of trapping horizons is related to these deformation equations in two different formalisms: with and without introducing quasilocal energy. In the formalism with the quasilocal energy, the Hawking mass in four dimension is generalized to higher dimension, and it is found that the deformation of this energy inside a marginal surface can be also decomposed into the contributions from matter fields and gravitational radiation as in the four dimension. In the formalism without the quasilocal energy, we generalize the definition of slowly evolving future outer trapping horizons proposed by Booth to past trapping horizons. The dynamics of the trapping horizons in FLRW universe is given as an example. Especially, the slowly evolving past trapping horizon in the FLRW universe has close relation to the scenario of slow-roll inflation. Up to the second order of the slowly evolving parameter in this generalization, the temperature (surface gravity) associated with the slowly evolving trapping horizon in the FLRW universe is essentially the same as the one defined by using the quasilocal energy.Comment: Latex, 61 pages, no figures; v2, type errors corrected; v3, references and comments are added, English is improved, to appear in JHE

Static flow on complete noncompact manifolds I: short-time existence and asymptotic expansions at conformal infinity

In this paper, we study short-time existence of static flow on complete noncompact asymptotically static manifolds from the point of view that the stationary points of the evolution equations can be interpreted as static solutions of the Einstein vacuum equations with negative cosmological constant. For a static vacuum $(M^n,g,V),$ we also compute the asymptotic expansions of $g$ and $V$ at conformal infinity.Comment: 25 page

Geometric and thermodynamic properties in Gauss-Bonnet gravity

In this paper, the generalized second law (GSL) of thermodynamics and entropy is revisited in the context of cosmological models in Gauss-Bonnet gravity with the boundary of the universe is assumed to be enclosed by the dynamical apparent horizon. The model is best fitted with the observational data for distance modulus. The best fitted geometric and thermodynamic parameters such as equation of state parameter, deceleration parameter and entropy are derived. To link between thermodynamic and geometric parameters, the "entropy rate of change multiplied by the temperature" as a model independent thermodynamic state parameter is also derived. The results show that the model is in good agreement with the observational analysis.Comment: 13 pages, 13 figures, to be published in Astrophysics and Space Sc

Short-range interactions in a two-electron system: energy levels and magnetic properties

The problem of two electrons in a square billiard interacting via a finite-range repulsive Yukawa potential and subjected to a constant magnetic field is considered. We compute the energy spectrum for both singlet and triplet states, and for all symmetry classes, as a function of the strength and range of the interaction and of the magnetic field. We show that the short-range nature of the potential suppresses the formation of ``Wigner molecule'' states for the ground state, even in the strong interaction limit. The magnetic susceptibility $\chi(B)$ shows low-temperature paramagnetic peaks due to exchange induced singlet-triplet oscillations. The position, number and intensity of these peaks depend on the range and strength of the interaction. The contribution of the interaction to the susceptibility displays paramagnetic and diamagnetic phases as a function of $T$.Comment: 12 pages,6 figures; to appear in Phys. Rev.

Peristaltic Transport of a Couple Stress Fluid: Some Applications to Hemodynamics

The present paper deals with a theoretical investigation of the peristaltic transport of a couple stress fluid in a porous channel. The study is motivated towards the physiological flow of blood in the micro-circulatory system, by taking account of the particle size effect. The velocity, pressure gradient, stream function and frictional force of blood are investigated, when the Reynolds number is small and the wavelength is large, by using appropriate analytical and numerical methods. Effects of different physical parameters reflecting porosity, Darcy number, couple stress parameter as well as amplitude ratio on velocity profiles, pumping action and frictional force, streamlines pattern and trapping of blood are studied with particular emphasis. The computational results are presented in graphical form. The results are found to be in good agreement with those of Shapiro et. al \cite{r25} that was carried out for a non-porous channel in the absence of couple stress effect. The present study puts forward an important observation that for peristaltic transport of a couple stress fluid during free pumping when the couple stress effect of the fluid/Darcy permeability of the medium, flow reversal can be controlled to a considerable extent. Also by reducing the permeability it is possible to avoid the occurrence of trapping phenomenon

Optimised Method for the Production and Titration of Lentiviral Vectors Pseudotyped with the SARS-CoV-2 Spike

The use of recombinant lentivirus pseudotyped with the coronavirus Spike protein of SARS-CoV-2 would circumvent the requirement of biosafety-level 3 (BSL-3) containment facilities for the handling of SARS-CoV-2 viruses. Herein, we describe a fast and reliable protocol for the transient production of lentiviruses pseudotyped with SARS-CoV-2 Spike (CoV-2 S) proteins and green fluorescent protein (GFP) reporters. The virus titer is determined by the GFP reporter (fluorescent) expression with a flow cytometer. High titers (>1.00 E+06 infectious units/ml) are produced using codon-optimized CoV-2 S, harbouring the prevalent D614G mutation and lacking its ER retention signal. Enhanced and consistent cell entry is achieved by using permissive HEK293T/17 cells that were genetically engineered to stably express the SARS-CoV-2 human receptor ACE2 along with the cell surface protease TMPRSS2 required for efficient fusion. For the widespread use of this protocol, its reagents have been made publicly available. Graphic abstract: Production and quantification of lentiviral vectors pseudotyped with the SARS-CoV-2 Spike glycoprotein

Defect ferromagnetism induced by lower valence cation doping:Li-doped SnO(2)nanoparticles

To explore the role of Li in establishing room-temperature ferromagnetism in SnO2, the structural, electronic and magnetic properties of Li-doped SnO(2)compounds were studied for different size regimes, from nanoparticles to bulk crystals. Li-doped nanoparticles show ferromagnetic ordering plus a paramagnetic contribution for particle sizes in the range of 16-51 nm, while pure SnO(2)and Li-doped compounds below and above this particular size range are diamagnetic. The magnetic moment is larger for compositions where the Li substitutes for Sn than for compositions where Li prevalently occupies interstitial sites. The observed ferromagnetic ordering in Li-doped SnO(2)nanoparticles is mainly due to the holes created when Li substitutes at a Sn site. Conversely, Li acts as an electron donor and electrons from Li may combine with holes to decrease ferromagnetism when lithium mainly occupies interstitial sites in the SnO(2)lattice