Hydrostatic Equilibrium of a Perfect Fluid Sphere with Exterior Higher-Dimensional Schwarzschild Spacetime

We discuss the question of how the number of dimensions of space and time can influence the equilibrium configurations of stars. We find that dimensionality does increase the effect of mass but not the contribution of the pressure, which is the same in any dimension. In the presence of a (positive) cosmological constant the condition of hydrostatic equilibrium imposes a lower limit on mass and matter density. We show how this limit depends on the number of dimensions and suggest that >0 is more effective in 4D than in higher dimensions. We obtain a general limit for the degree of compactification (gravitational potential on the boundary) of perfect fluid stars in D dimensions. We argue that the effects of gravity are stronger in 4D than in any other number of dimensions. The generality of the results is also discussed.     

Flux vacua in DBI type Einstein–Maxwell theory

We study compactification of extra dimensions in a theory of Dirac–Born–Infeld type gravity. We investigate the solution for Minkowski spacetime with an S ² extra space as well as that for de Sitter spacetime (S ⁴) with an S ² extra space. They are derived by the effective potential method in the presence of the magnetic flux on the extra sphere. We also consider the higher-dimensional generalization of the solutions. We find that, in a certain model, the radius of the extra space has a minimum value independent of the higher-dimensional Newton constant.     

Hydrostatic equilibrium and Tsallis’ equilibrium for self-gravitating systems

Self-gravitating systems are generally thought to behavior non-extensively due to the long-range nature of gravitational forces. We discuss a relation between the nonextensive parameter q of Tsallis statistics, the temperature gradient and the gravitational potential based on the equation of hydrostatic equilibrium for self-gravitating systems. It is suggested that the nonextensive parameter in Tsallis statistics has a clear physical meaning with regard to the non-isothermal nature of the systems with long-range interactions. Tsallis’ equilibrium distribution for the self-gravitating systems describes the property of hydrostatic equilibrium of the systems.     

Non-ℤ<Subscript>2</Subscript> symmetric braneworlds in scalar tensorial gravity

We obtain, via the Gauss–Codazzi formalism, the expression of the effective Einstein–Brans–Dicke projected equations in a non-ℤ₂ symmetric braneworld scenario which presents hybrid compactification. It is shown that the functional form of such equations resembles the one in the Einstein case, except for the fact that they bring about extra information in the context of exotic compactifications.     

Instability of the Randall-Sundrum Model and Exact Bulk Solutions

Five dimensional geodesic equation is used to study the gravitational force acted on a test particle in the bulk of the Randall-Sundrum two-brane model. This force could be interpreted as the gravitational attraction from matters on the two branes and may cause the model to be unstable. By analogy with star models in astrophysics, a fluid RS model is proposed in which the bulk is filled with a fluid and this fluid has an anisotropic pressure to balance the gravity from the two branes. Thus a class of exact bulk solutions is obtained which shows that any 4D Einstein solution with a perfect fluid source can be embedded in y = constant hypersurfaces in the bulk to form an equilibrium state of the brane model. By requiring a 4D effective curvature to have a minimum, the compactification size of the extra dimension is discussed.     

Spectral Analysis of Weakly Coupled Stochastic Lattice Ginzburg–Landau Models

We consider the relaxation to equilibrium of solutions , t>0, , of stochastic dynamical Langevin equations with white noise and weakly coupled Ginzburg–Landau interactions. Using a Feynman–Kac formula, which relates stochastic expectations to correlation functions of a spatially non-local imaginary time quantum field theory, we obtain results on the joint spectrum of H, , where H is the self-adjoint, positive, generator of the semi-group associated with the dynamics, and P ^j , j= 1, …, d are the self-adjoint generators of the group of lattice spatial translations. We show that the low-lying energy-momentum spectrum consists of an isolated one-particle dispersion curve and, for the mass spectrum (energy-momentum at zero-momentum), besides this isolated one-particle mass, we show, using a Bethe–Salpeter equation, the existence of an isolated two-particle bound state if the coefficient of the quartic term in the polynomial of the Ginzburg–Landau interaction is negative and d= 1, 2; otherwise, there is no two-particle bound state. Asymptotic values for the masses are obtained. Received: 27 September 2000 / Accepted: 16 January 2001     

IR spectral analysis of the chemical composition of the lichen <Emphasis Type="Italic">Hypogymnia physodes</Emphasis> to assess atmospheric pollution

We have studied the level of atmospheric pollution in different urban recreational areas using analysis of the chemical composition of the lichen Hypogymnia physodes by Fourier transform IR (FTIR) spectroscopy. We have developed a procedure for determining the dominant pollutant, its concentration, and the degree of its impact on the structure of the lichen. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 3, pp. 446–452, May–June, 2009.     

Relativistic compact stars with charged anisotropic matter

In this article, we perform a detailed theoretical analysis of new exact solutions with anisotropic fluid distribution of matter for compact objects subject to hydrostatic equilibrium. We present a family solution to the Einstein-Maxwell equations describing a spherically symmetric, static distribution of a fluid with pressure anisotropy. We implement an embedding class one condition to obtain a relation between the metric functions. We generalize the properties of a spherical star with hydrostatic equilibrium using the generalised Tolman-Oppenheimer-Volkoff (TOV) equation. We match the interior solution to an exterior Reissner-Nordström one, and study the energy conditions, speed of sound, and mass-radius relation of the star. We also show that the obtained solutions are compatible with observational data for the compact object Her X-1. Regarding our results, the physical behaviour of the present model may serve for the modeling of ultra compact objects.     

Exact Solutions of Einstein's Field Equations

We examine various well known exact solutions available in the literature to investigate the recent criterion obtained in Negi and Durgapal [Gravitation and Cosmology 7, 37 (2001)] which should be fulfilled by any static and spherically symmetric solution in the state of hydrostatic equilibrium. It is seen that this criterion is fulfilled only by (i) the regular solutions having a vanishing surface density together with pressure, and (ii) the singular solutions corresponding to a non-vanishing density at the surface of the configuration. On the other hand, the regular solutions corresponding to a non-vanishing surface density do not fulfill this criterion. Based upon this investigation, we point out that the exterior Schwarzschild solution itself provides necessary conditions for the types of the density distributions to be considered inside the mass, in order to obtain exact solutions or equations of state compatible with the state of hydrostatic equilibrium in general relativity. The regular solutions with finite centre and non-zero surface densities which do not fulfill the criterion given by Negi and Durgapal (2001), in fact, cannot meet the requirement of the‘actual mass’, set up by exterior Schwarzschild solution. The only regular solution which could be possible in this regard is represented by uniform (homogeneous) density distribution. This criterion provides a necessary and sufficient condition for any static and spherical configuration (including core-envelope models) to be compatible with the structure of general relativity [that is, the state of hydrostatic equilibrium in general relativity]. Thus, it may find application to construct the appropriate core-envelope models of stellar objects like neutron stars and may be used to test various equations of state for dense nuclear matter and the models of relativistic star clusters with arbitrary large central redshifts. PACS :04.20.Jd; 04.40.Dg; 97.60.Jd.     

Gauss–Codazzi formalism to brane-world within Brans–Dicke theory

We apply the Gauss–Codazzi formalism to brane-worlds within the framework of Brans–Dicke gravity. The compactification is taken from six to five dimensions in order to formalize brane-world models with hybrid compactification in scalar tensor theories. PACS  04.50.+h; 98.80.Cq     

One-Dimensional Hard-Rod Caricature of Hydrodynamics: “Navier–Stokes Correction” for Local Equilibrium Initial States

A one-dimensional system, consisting of identical hard-rod particles of length $a$ is studied in the hydrodynamical limit. A “Navier–Stokes correction” to the Euler equation is found for an initial local equilibrium family of states , of constant density. The correction is given, at , by a non-linear second order differential operator acting on f(q,v), the hydrodynamical density at a point of the “species” of fluid with velocity . Received: 14 October 1996 / Accepted: 13 February 1997     

Multi-soliton complexes in mode-locked fiber lasers

We numerically investigate the formation of soliton pairs (bound states) in mode-locked fiber ring lasers in the normal dispersion domain. In the distributed mathematical model (complex cubic-quintic Ginzburg–Landau equation), we observe a discrete family of soliton pairs with equidistantly increasing peak separation. We show that stabilization of previously unstable bound states can be achieved when the finite relaxation time of the saturable absorber is taken into account. The domain of stability can be controlled by varying this relaxation time. Furthermore, we investigate the parameter domain where the region of stable bound states does not shrink to zero for vanishing absorber recovery time corresponding to a laser with an instantaneous saturable absorber. For a certain domain of the small-signal gain, we obtain a robust first level bound state with almost constant separation where the phase of the two pulses evolves independently. Moreover, their phase difference can evolve either periodically or chaotically depending on the small signal gain. Interestingly, higher level bound states exhibit a fundamentally different dynamics. They represent oscillating solutions with a phase difference alternating between zero and π.     

Open-Closed Moduli Spaces and Related Algebraic Structures

We set up a Batalin–Vilkovisky Quantum Master Equation (QME) for open-closed string theory and show that the corresponding moduli spaces give rise to a solution, a generating function for their fundamental chains. The equation encodes the topological structure of the compactification of the moduli space of bordered Riemann surfaces. The moduli spaces of bordered J-holomorphic curves are expected to satisfy the same equation, and from this viewpoint, our paper treats the case of the target space equal to a point. We also introduce the notion of a symmetric Open-Closed Topological Conformal Field Theory (OC TCFT) and study the L _∞ and A _∞ algebraic structures associated to it.     

Perfect fluid bianchi Type-I cosmological models with time varying <Emphasis Type="Italic">G</Emphasis> and Λ

Bianchi Type-I cosmological models containing perfect fluid with time varying G and Λ have been presented. The solutions obtained represent an expansion scalar θ bearing a constant ratio to the anisotropy in the direction of space-like unit vector λ ⁱ . Of the two models obtained, one has negative vacuum energy density, which decays numerically. In this model, we obtain Λ ∼ H ², Λ ∼ R ₄₄/R and Λ ∼ T ⁻² (T is the cosmic time) which is in accordance with the main dynamical laws for the decay of Λ. The second model reduces to a static solution with repulsive gravity.      

Phase transition in three-dimensional quantum electrodynamics at <Emphasis Type="Italic">T</Emphasis> ≠ 0

Dynamic mass generation in 3D quantum electrodynamics (QED₃) is considered at T ≠ 0. To solve the Schwinger–Dyson equation for the Matsubara electron Green’s function, the ladder approximation is used and the corresponding photonic function is taken in the Landau gauge. In this case, the instant approximation is used for the photonic function. It is established that the process of dynamical mass generation in QED₃ at T ≠ 0 is accompanied by a phase transition. Formal analogy of transitions in the coupling constant is revealed at T ≠ 0 in QED₃, at T = 0 in QED₄, and in graphene theory. Critical values of the coupling constant and temperature, calculated numerically based on an approximate analytical solution of the Schwinger–Dyson equation are of the same orders of magnitude.     

Coplanar (<Emphasis Type="Italic">e</Emphasis>, 3<Emphasis Type="Italic">e</Emphasis>) differential cross-section of He atom

We present in this paper the results of our calculation of five-fold differential cross-section (FDCS) for (e,3e) process on He atom in low momentum transfer and high electron impact energy in shake-off mechanism. The formalism has been developed in Born approximation using plane waves, Byron and Joachain as well as Le Sech and correlated BBK-type wave functions respectively for incident and scattered, bound and ejected electrons. The angular distribution of FDCS of our calculation is presented in various modes of coplanar geometry and comparison is made with the available experimental data. We observe that the present calculation is able to reproduce the trend of the experimental data. However, it differs in magnitude from the experiment. The present theory does not predict four-peak structure insummed mutual angle mode for lower excess ejected electron energies. We also discuss the importance of momentum transfer, post-collision interaction (PCI) and ion participation in the (e,3e) process in constant θ₁₂ mode     

Homogenization and two-scale models for liquid phase epitaxy

We consider models for liquid phase epitaxy without and with elasticity. The models are based on continuum models for fluid flow and transport of adatoms in the liquid solution and a BCF–model for the growth of the solid phase. Using homogenization by formal asymptotic expansion, we obtain two–scale models that are appropriate to describe the evolution of microstructures in the solid phase for processes of technically relevant macroscopic length scales. The two–scale models consist of macroscopic equations for fluid flow and solute transport in the liquid and microscopic cell problems for the growth and elastic deformation of the solid. For the case without elasticity and a phase field approximation of the BCF–model, an estimate of the model error is presented.     

A new class of exact hairy black hole solutions

We present a new class of black hole solutions with a minimally coupled scalar field in the presence of a negative cosmological constant. We consider an one-parameter family of self-interaction potentials parametrized by a dimensionless parameter g. When g = 0, we recover the conformally invariant solution of the Martinez–Troncoso–Zanelli (MTZ) black hole. A non-vanishing g signals the departure from conformal invariance. Thermodynamically, there is a critical temperature at vanishing black hole mass, where a higher-order phase transition occurs, as in the case of the MTZ black hole. Additionally, we obtain a branch of hairy solutions which undergo a first-order phase transition at a second critical temperature which depends on g and it is higher than the MTZ critical temperature. As g → 0, this second critical temperature diverges.     

Approximate analytical lower bounds on ‘double asymptotic scaling’ variables and physics at HERA

We analytically examine the asymptotic solution of gluon evolution equation in terms of the ‘double scaling variables’ρ andσ of perturbative QCD and find the approximate lower bounds on these, above which the solution is considered to be valid. Comparison of this asymptotic solution is made with the fit obtained from data and the estimated lower bound onρ is nearly equal to our analytical finding. To analyze the data below the lower bound onρ, other analytical solutions of gluon evolution equation are to be used which depend highly on the inputx-distributions of gluon to study the physics at low-x of HERA range.     

Study of ion–solvent interactions and activation energy of LiBr in DMSO,H<Subscript>2</Subscript>O and DMSO–H<Subscript>2</Subscript>O mixtures at various temperatures

The Jones–Dole B coefficients of the electrolyte Lithium bromide (LiBr), reference salts tetra butyl ammonium tetra phenyl borate (BU₄NBPh₄), tetra butyl ammonium bromide (BU₄NBr), and potassium chloride (KCl) in dimethylsulfoxide (DMSO), water, and DMSO–water mixtures were obtained at different temperatures range from 25 to 45 °C For this, the relative viscosities were measured for Lithium bromide (LiBr) and reference salts in DMSO, water, and DMSO–water mixtures at above-mentioned temperatures. The B coefficients of these electrolytes were behaved as structure makers in DMSO, while in H₂O and DMSO–H₂O mixtures, the B-coefficient values were less positive showing the weak structure-making effect. Ionic viscosity B coefficients allow us to assess the behavior of ions in the solvent mixtures. In this study it was observed that all the values of ionic B coefficient of (Li⁺) were positive and small showing the weak structure-making effects. It was also observed that Br⁻ ions maintain negative B coefficient values in all DMSO–H₂O mixtures, except in 60% DMSO mole fraction. From this it can be concluded that Br⁻ ion behaved as a structure breaker in water and in all DMSO–H₂O mixtures except in 60% DMSO mole fraction mixtures. The low B _± values of alkali metal ions and Br⁻ ions in water are due to the breakdown of the tetrahedral structural of water and the formation of strongly structured solvated ion. It is also observed that the values of the energy of activation of the flow for LiBr are greater in DMSO–water mixtures and in pure water than in DMSO. This may be due the presence of a network of hydrogen bonds which cause the hindrance in the flow of the solution of LiBr in DMSO–water mixtures and in pure water than in DMSO.