Bianchi Type-I Universe with wet dark fluid

The Bianchi Type-I Universe filled with dark energy from a wet dark fluid has been considered. A new equation of state for the dark energy component of the Universe has been used. It is modeled on the equation of state p = γ(ρ − ρ*) which can describe a liquid, for example water. The exact solutions to the corresponding field equations are obtained in quadrature form. The solution for constant deceleration parameter have been studied in detail for both power-law and exponential forms. The cases γ = 1 and γ = 0 have also been analysed.      

Spherically symmetric static solutions of the Einstein-Maxwell equations

We report a new formalism to obtain solutions of Einstein-Maxwell’s equations for static spheres assuming the matter content to be a charged perfect fluid of null-conductivity. Defining three new variablesu=4πεr ²,ν=4πpr ^{2 2} andw=(4π/3)(ρ+ε)r ² whereε, ρ andε denote respectively energy densities of the electric, matter and free gravitational fields whereasp is the fluid pressure, Einstein’s field equations are rewritten in an elegant form. The solutions given by Bonnor [1], Nduka [2], Cooperstock and De la Cruz [3], Mehra [4], Tikekar [5,6], Xingxiang [7], Patino and Rago [8] are all shown to possess simple relations betweenu, v, andw whereas Pant and Sah’s [9] solution for which all the three functions,u, v, andw are constants is a trivial case of the present formalism, We have presented six new solutions with ε = 2ρ. For the first three solutionsw andu are constants withv as a variable whereas the remaining three solutions satisfy the equation of state for isothermal gas;v =kw =-ku where (i)k is an arbitrary constant but not equal to 1 or 1/3 (ii)k = 1 and (iii)k = 1/3. We also obtained a generalization of Cooperstock and De la Cruz’s [3] solution which is regular for 2ρ > ε but singular for 2ρ ≤ ε.     

Scalar field dynamics on a brane

The dynamics of a flat isotropic brane Universe with two-component matter source —perfect fluid with the equation of statep = (γ − 1)ρ and a scalar field with a power-law potentialV ∼ φ^α is investigated. We describe solutions for which the scalar field energy density scales as a power-law of the scale factor. We also describe solutions existing in regions of the parameter space where these scaling solutions are unstable or do not exist.     

Shock profiles for the asymmetric simple exclusion process in one dimension

The asymmetric simple exclusion process (ASEP) on a one-dimensional lattice is a system of particles which jump at ratesp and 1-p (herep > 1/2) to adjacent empty sites on their right and left respectively. The system is described on suitable macroscopic spatial and temporal scales by the inviscid Burgers’ equation; the latter has shock solutions with a discontinuous jump from left density ρ- to right density ρ+, ρ-< ρ +, which travel with velocity (2p−1 )(1−ρ₊−p ₋). In the microscopic system we may track the shock position by introducing a second class particle, which is attracted to and travels with the shock. In this paper we obtain the time-invariant measure for this shock solution in the ASEP, as seen from such a particle. The mean density at lattice siten, measured from this particle, approachesp _± at an exponential rate asn→ ±∞, witha characteristic length which becomes independent ofp when . For a special value of the asymmetry, given byp/(1−p)=p ₊(1−p ₋)/p ₋(1−p ₊), the measure is Bernoulli, with densityρ ₋ on the left andp ₊ on the right. In the weakly asymmetric limit, 2p−1 → 0, the microscopic width of the shock diverges as (2p+1)^-1. The stationary measure is then essentially a superposition of Bernoulli measures, corresponding to a convolution of a density profile described by the viscous Burgers equation with a well-defined distribution for the location of the second class particle.     

Early Universe with Variable Gravitational and Cosmological Constants

Einstein field equations are considered in zero-curvature Robertson–Walker (R–W) cosmology with perfect fluid source and time-dependent gravitational and cosmological “constants.” Exact solutions of the field equations are obtained by using the ’gamma-law' equation of state p = (γ − 1)ρ in which γ varies continuously with cosmological time. The functional form of γ (R) is used to analyze a wide range of cosmological solutions at early universe for two phases in cosmic history: inflationary phase and Radiation-dominated phase. The corresponding physical interpretations of the cosmological solutions are also discussed.     

Charged sphere of shear-free fluids with $$\frac{\partial}{\rho} \partial r \leq 0$$

The Einstein-Maxwell equations for non-static charged shear-free spherically symmetric perfect fluid distribution reduce to a second-order non-linear differential equation in the radial parameter. Several solutions of this equation have been obtained in earlier work without considering the general requirement for physical relevance of the solutions. Generally physically acceptable relativistic fluid models demand that the solutions satisfy the reality conditions ρ ≥ 0, p ≥ 0, ρ _r ≤ 0, etc. throughout the fluid model. In this article the expression for density gradient ρ _x (or ρ _r ) has been utilized to produce charged shear-free relativistic fluid models with non-positive density gradient (NDG)ρ _r ≤ 0. Eventually, we have found that none of the Riccati solutions have NDG including Vaidya metric. Also, the solutions with NDG neither possess Lie-symmetries nor Painlevé property. Further, it is observed that the solutions with NDG have no uncharged analogue.     

Relativistic compact objects in isotropic coordinates

We present a matrix method for obtaining new classes of exact solutions for Einstein’s equations representing static perfect fluid spheres. By means of a matrix transformation, we reduce Einstein’s equations to two independent Riccati-type differential equations for which three classes of solutions are obtained. One class of the solutions corresponding to the linear barotropic-type fluid with an equation of statep =γρ is discussed in detail.     

An isotropic cosmological model in general scalar tensor theory

An isotropic homogeneous cosmological model with Robertson-Walker line element is studied in general scalar tensor theory where the parameterω is a function of the scalar field. The model consists of perfect fluid with the equation of statep=ερ. Exact solutions are obtained in Dicke’s conformally transformed units forε=1 andε=1/3 assuming a functional relationship betweenω and the scalar fieldφ. The properties are compared with vacuum models in this theory.     

FRW Bulk Viscous Cosmology in Multi Dimensional Space-Time

The exact solutions of the field equations are obtained by using the gamma law equation of state p=(γ−1)ρ in which the parameter γ depends on scale factor R. The fundamental form of γ(R) is used to analyze a wide range of phases in cosmic history: inflationary phase and radiation-dominated phase. The corresponding physical interpretations of cosmological solutions are also discussed in the framework of (n+2) dimensional space time.     

Dark Energy with Generalized Equation of State in Bianchi Type-I Cosmological Model

Dark energy with the usually used equation of state p=γρ, where γ=const<0 is hydrodynamically unstable. To overcome this drawback we consider the cosmology of a perfect fluid with a linear equation of state of a more general form p=α(ρ−ρ ₀), where the constants α and ρ ₀ are free parameters. The anisotropic Bianchi type-I cosmological model filled with dark energy has been considered. A generalized equation of state for the dark energy component of the universe has been used. The exact solutions to the corresponding Einstein field equations and the statefinder diagnostic pair i.e. {r,s} parameters have been obtained in three interesting cases (i) when ρ _Λ>0 and A>0 (ii) when ρ _Λ>0 and A<0 and (iii) when ρ _Λ<0 and A>0 at the singularities i.e. t→0 and t→±∞.     

Magnetoresistivity and acoustoelectronic effects in a tilted magnetic field in <Emphasis Type="Italic">p</Emphasis>-Si/SiGe/Si structures with an anisotropic <Emphasis Type="Italic">g</Emphasis> factor

Magnetoresistivity ρ _xx and ρ _xy and the acoustoelectronic effects are measured in p-Si/SiGe/Si with an impurity concentration p = 1.99 × 10¹¹ cm⁻² in the temperature range 0.3–2.0 K and an tilted magnetic field up to 18 T. The dependence of the effective g factor on the angle of magnetic field tilt θ to the normal to the plane of a two-dimensional p-Si/SiGe/Si channel is determined. A first-order ferromagnet-paramagnet phase transition is observed in the magnetic fields corresponding to a filling factor ν = 2 at θ ≈ 59°–60°.     

Classification of the FRW universe with a cosmological constant and a perfect fluid of the equation of state <Emphasis Type="Italic">p</Emphasis> = <Emphasis Type="Italic">w</Emphasis><Emphasis Type="Italic">ρ</Emphasis>

We systematically study the evolution of the Friedmann–Robertson–Walker (FRW) universe coupled with a cosmological constant Λ and a perfect fluid that has the equation of state p = w ρ, where p and ρ denote, respectively, the pressure and energy density of the fluid, and w is an arbitrary real constant. Depending on the specific values of w, Λ, and the curvature k of 3-dimensional space, we separate all of the solutions into various cases. In each case the main properties of the evolution are given in detail, including the periods of deceleration and/or acceleration, and the existence of big bang, big crunch, and big rip singularities. In some cases, errors in classification and interpretation appearing in standard textbooks have been corrected.     

<Emphasis Type="Italic">ρρ</Emphasis>N and <Emphasis Type="Italic">ρρ</Emphasis>Δ molecules with J<Superscript>P</Superscript> = 5/2<Superscript>+</Superscript> and J<Superscript>P</Superscript> = 7/2<Superscript>+</Superscript>

The ρρN and ρρΔ three-body systems have been studied within the framework of the fixed center approximation of Faddeev equation. The ρρ interaction in isospin I = 0 , spin S = 2 is strongly attractive, and so are the N ρ, ρΔ interactions. This leads to bound states of both ρρN and ρρΔ. We find peaks of the modulus squared of the scattering matrix around 2227 MeV for ρρN, and 2372 MeV for ρρΔ. Yet, the strength of the peak for the ρρN amplitude is much smaller than for ρρΔ, weakening the case for a ρρN bound state, or a dominant ρρN component. A discussion is made on how these states can be searched for in present programs looking for multimeson final states in different reactions.     

Bulk viscous cosmology in early Universe

The effect of bulk viscosity on the early evolution of Universe for a spatially homogeneous and isotropic Robertson-Walker model is considered. Einstein’s field equations are solved by using ‘gamma-law’ equation of state p = (γ − 1)ρ, where the adiabatic parameter gamma (γ) depends on the scale factor of the model. The ‘gamma’ function is defined in such a way that it describes a unified solution of early evolution of the Universe for inflationary and radiation-dominated phases. The fluid has only bulk viscous term and the coefficient of bulk viscosity is taken to be proportional to some power function of the energy density. The complete general solutions have been given through three cases. For flat space, power-law as well as exponential solutions are found. The problem of how the introduction of viscosity affects the appearance of singularity, is briefly discussed in particular solutions. The deceleration parameter has a freedom to vary with the scale factor of the model, which describes the accelerating expansion of the Universe.      

Possible manifestation of spin fluctuations in the temperature behavior of the resistivity of Sm<Subscript>1.85</Subscript>Ce<Subscript>0.15</Subscript>CuO<Subscript>4</Subscript> thin films

A pronounced step-like (kink) behavior in the temperature dependence of resistivity ρ(T) is observed in the optimally doped Sm_1.85Ce_0.15CuO₄ thin films around T _sf = 87 K and attributed to the manifestation of strong-spin fluctuations induced by Sm³⁺ moments with the energy ħω_sf = k _B T _sf ≃ 7 meV. The experimental data are found to be well fitted by the residual (zero-temperature) ρ_res, electron-phonon ρ_e-ph(T) = AT, and electron-electron ρ_e-e(T) = BT ² contributions in addition to the fluctuation-induced contribution ρ_sf(T) due to thermal broadening effects (of the width ω_sf). According to the best fit, the plasmon frequency, impurity scattering rate, electron-phonon coupling constant, and Fermi energy are estimated as ω_p = 2.1 meV, τ ₀ ⁻¹ = 9.5 × 10⁻¹⁴ s⁻¹, λ = 1.2, and E _F = 0.2 eV, respectively. The text was submitted by the authors in English.     

Higher Dimensional Bianchi Type-V Cosmological Models with Perfect Fluid and Dark Energy

We have studied the Bianchi type-V cosmological models with binary mixture of perfect fluid and dark energy in five dimensions. The perfect fluid is obeying the equation of state p=γρ with γ∈[0,1]. The dark energy is considered to be either the quintessence or the Chaplygin gas. The exact solutions of the Einstein’s field equations are obtained in quadrature form.     

<Emphasis Type="Italic">ρN</Emphasis>-resonance dynamics in the proton nucleus reaction

The strong coupling of rho meson to the nucleon produces s- and p-wave rho-meson-nucleon (ρN) resonances. In a nucleus, the ρN-resonance-hole polarization generates the optical potential or self-energy for the ρ meson. The scattering of ρ meson due to this potential provides valuable information about the ρN-resonance dynamics in a nucleus. To investigate it, we use this potential to calculate the mass distribution spectrumfor the ρ meson produced coherently in the proton-nucleus reaction. The cross sections arising due to s- and ρ-wave ρN resonances have been presented. The coherent and incoherent contributions to the cross sections due to these resonances are compared. In addition, the calculated results due to nonrelativistic and relativistic ρ-meson self-energy are illustrated.     

Five Dimensional Axially Symmetric String Cosmological Models with Bulk Viscous Fluid

Bulk viscous fluid distribution with massive strings in LRS Bianchi type-1 space time is studied. The exact solutions of the field equations are obtained by using the equation of state ρ=−λ and ρ=λ. We observed that the bulk viscous fluid does not survive for ρ=−λ whereas it survives for ρ=λ. Some physical and geometrical properties of the models are discussed.