Some Exact Bianchi Type V Perfect Fluid Solutions with Heat Flow

The variation law for generalized mean Hubble’s parameter is discussed in a spatially homogeneous and anisotropic Bianchi type V space-time with perfect fluid along with heat-conduction. The variation law for Hubble’s parameter, that yields a constant value of deceleration parameter, generates two types of solutions for the average scale factor, one is of power-law type and other one of exponential form. Using these two forms of the average scale factor, exact solutions of Einstein field equations with a perfect fluid and heat conduction are presented for a Bianchi type V space-time, which represent expanding singular and non-singular cosmological models. We find that the constant value of deceleration parameter is reasonable for the present day universe. The physical and geometrical properties of the models are also discussed in detail.     

Exact Bianchi Type-I Cosmological Models in a Scalar-Tensor Theory

In this paper, a spatially homogeneous and anisotropic Bianchi type-I space-time filled with perfect fluid is investigated within the framework of a scalar-tensor theory proposed by Saez and Ballester. Two different physically viable models of the universe are obtained by using a special law of variation for Hubble’s parameter that yields a constant value of deceleration parameter. One of the models is found to generalize a model recently investigated by Reddy et al. (Astrophys. Space Sci. 306:171, 2006). The Einstein’s field equations are solved exactly and the solutions are found to be consistent with the recent observations of type Ia supernovae. A detailed study of physical and kinematical properties of the models is carried out.     

Exact spatially homogeneous cosmologies

We consider perfect fluid spatially homogeneous cosmological models. Starting with a new exact solution of Blanchi type VIII, we study generalizations which lead to new classes of exact solutions. These new solutions are discussed and classified in several ways. In the original type VIII solution, the ratio of matter shear to expansion is constant, and we present a theorem which delimits those space-times for which this condition holds.     

Kaluza-Klein cosmology: Phenomenology and exact solutions with three-component matter

We explain the general fact that Friedmann models in Kaluza-Klein cosmologies, in which ordinary space-time is supplemented by internal factor spaces, are equivalent to the motion of tensorial-mass particle in a scalar field. We find exact solutions for an important class of three-component matter in the case of one internal space of dimensiond. The three components in question are the curvature of the internal space, the Zeldovich matter, and dust of the protoradiation type. The method includes one-component solutions for all the different models of compactification discussed so far.     

LRS Bianchi type I perfect fluid solutions generated from known solutions

Some LRS Bianchi type I perfect fluid solutions are generated from known solutions of this type. The solutions represent spatially homogeneous and anisotropic cosmological models which would give essentially empty space for large time. The physical and kinematic properties of the models are discussed.     

Some Generalized Scalar Field Models with Abundant Soliton-Like configurations

Some generahed scalar field models are presented. It is shown that there exist generally three types of soliton solutions for the extended models. The form of the first type of the soliton solutions is model-independent. An arbitrary constant can be included in the second type of the soliton excitations which is model-dependent. The third type of the soliton solutions is also modeldependent but with no arbitrary constant. The extended φ⁴ model and sine-Gordon model are studied in detail.     

Hydrodynamical model for bulk and surface plasmons in cylindrical wires

In this paper, we study the electrostatic surface and volume modes of a cylindrical wire using the hydrodynamical model of plasmon excitation, which allows an analytical study of dispersion effects. We solve the hydrodynamical equations for a cylindrical wire geometry, obtaining new analytical expressions for the bulk and surface modes. New dispersion relations are obtained for each type of mode and numerical solutions are given. We analyze in detail the characteristics of the solutions and their differences with previous treatments based on non-dispersive models. These differences become important for wires of small radii, particularly in the range of few nanometers.     

Absence of static solutions in source-free Yang-Mills theory

The vanishing of self-stress for static systems excludes finite energy time-independent solutions of source-free Yang-Mills models (with compact gauge groups), except in five dimensions. Static solutions of Abelian self-interacting models of the Born-Infeld type are also forbidden.     

Some Anisotropic Universes in the Presence of Imperfect Fluid Coupling with Spatial Curvature

We consider Bianchi VI spacetime, which also can be reduced to Bianchi types VI₀-V-III-I. We initially consider the most general form of the energy-momentum tensor which yields anisotropic stress and heat flow. We then derive an energy-momentum tensor that couples with the spatial curvature in a way so as to cancel out the terms that arise due to the spatial curvature in the evolution equations of the Einstein field equations. We obtain exact solutions for the universes indefinitely expanding with constant mean deceleration parameter. The solutions are beriefly discussed for each Bianchi type. The dynamics of the models and fluid are examined briefly, and the models that can approach to isotropy are determined. We conclude that even if the observed universe is almost isotropic, this does not necessarily imply the isotropy of the fluid (e.g., dark energy) affecting the evolution of the universe within the context of general relativity.     

Non-existence of a massive scalar field for the Marder universe in Lyra and Riemannian geometries

In this paper, we have studied a massive scalar field for a Marder type universe in the context of Lyra and Riemannian geometries. From the exact solutions obtained we show that the massive scalar field does not survive in Lyra and Riemannian geometries for an anisotropic Marder type universe. Therefore we have solved the massless scalar field problem in Lyra and Riemann geometries for two cases. Also we have obtained vacuum solutions for homogeneous and anisotropic Marder space-time in Lyra geometry and the solutions obtained are compared by considering Lyra and Riemann geometries. Finally, some physical and kinematical properties are discussed by using graphics.     

A Modified Gravity Theory: Null Aether

General quantum gravity arguments predict that Lorentz symmetry might not hold exactly in nature. This has motivated much interest in Lorentz breaking gravity theories recently. Among such models are vector-tensor theories with preferred direction established at every point of spacetime by a fixed-norm vector field. The dynamical vector field defined in this way is referred to as the "aether". In this paper, we put forward the idea of a null aether field and introduce, for the first time, the Null Aether Theory(NAT) — a vector-tensor theory. We first study the Newtonian limit of this theory and then construct exact spherically symmetric black hole solutions in the theory in four dimensions, which contain Vaidya-type non-static solutions and static Schwarzschild-(A)dS type solutions, Reissner-Nordstr?m-(A)dS type solutions and solutions of conformal gravity as special cases. Afterwards, we study the cosmological solutions in NAT:We find some exact solutions with perfect fluid distribution for spatially flat FLRW metric and null aether propagating along the x direction. We observe that there are solutions in which the universe has big-bang singularity and null field diminishes asymptotically. We also study exact gravitational wave solutions — AdS-plane waves and pp-waves — in this theory in any dimension D ≥ 3. Assuming the Kerr-Schild-Kundt class of metrics for such solutions, we show that the full field equations of the theory are reduced to two, in general coupled, differential equations when the background metric assumes the maximally symmetric form. The main conclusion of these computations is that the spin-0 aether field acquires a "mass" determined by the cosmological constant of the background spacetime and the Lagrange multiplier given in the theory.     

Hořava–Witten stability: eppur si muove

We construct exact time-dependent solutions of the supergravity equations of motion in which two initially non-singular branes, one with positive and the other with negative tension, move together and annihilate each other in an all-enveloping spacetime singularity. Among our solutions are the Hořava–Witten solution of heterotic M-theory and a Randall–Sundrum I type solution, both of which are supersymmetric, i.e. BPS, in the time-independent case. In the absence of branes our solutions are of Kasner type, and the source of instability may ascribed to a failure to stabilise some of the modulus fields of the compactification. It also raises questions about the viability of models based on some sorts of negative tension brane.     

Generation of LRS Bianchi type I universes filled with perfect fluids

A generating technique is presented which converts known LRS Bianchi type I models into new models of the same type. Starting from the general Kasner solutions new classes of models are obtained which add to the rare perfect-fluid solutions not satisfying the equation of state. The physical and kinematical properties of cosmological models are studied.     

Development of intermolecular potential models for electrolyte solutions using an electrolyte SAFT-VR Mie equation of state

ABSTRACT

We present a theoretical framework and parameterisation of intermolecular potentials for aqueous electrolyte solutions using the statistical associating fluid theory based on the Mie interaction potential (SAFT-VR Mie), coupled with the primitive, non-restricted mean-spherical approximation (MSA) for electrolytes. In common with other SAFT approaches, water is modelled as a spherical molecule with four off-centre association sites to represent the hydrogen-bonding interactions; the repulsive and dispersive interactions between the molecular cores are represented with a potential of the Mie (generalised Lennard-Jones) form. The ionic species are modelled as fully dissociated, and each ion is treated as spherical: Coulombic ion–ion interactions are included at the centre of a Mie core; the ion–water interactions are also modelled with a Mie potential without an explicit treatment of ion–dipole interaction. A Born contribution to the Helmholtz free energy of the system is included to account for the process of charging the ions in the aqueous dielectric medium. The parameterisation of the ion potential models is simplified by representing the ion–ion dispersive interaction energies with a modified version of the London theory for the unlike attractions. By combining the Shannon estimates of the size of the ionic species with the Born cavity size reported by Rashin and Honig, the parameterisation of the model is reduced to the determination of a single ion–solvent attractive interaction parameter. The resulting SAFT-VRE Mie parameter sets allow one to accurately reproduce the densities, vapour pressures, and osmotic coefficients for a broad variety of aqueous electrolyte solutions; the activity coefficients of the ions, which are not used in the parameterisation of the models, are also found to be in good agreement with the experimental data. The models are shown to be reliable beyond the molality range considered during parameter estimation. The inclusion of the Born free-energy contribution, together with appropriate estimates for the size of the ionic cavity, allows for accurate predictions of the Gibbs free energy of solvation of the ionic species considered. The solubility limits are also predicted for a number of salts; in cases where reliable reference data are available the predictions are in good agreement with experiment.     

Solvable statistical mechanics models on group lattices

We define a new type of lattice which is associated with a group G. Field theories on group lattices are considered and in certain cases the models are exactly solvable. The statistical mechanics of such systems is analyzed: the partition function and correlation functions are computed. The solutions utilize the irreducible matrix representations of G.     

非Abel对偶超导理论中的涡旋管研究

首次讨论了非Abel对偶超导理论中的涡旋管性质。 在Cho等工作的基础上进一步研究了非Abel情况下的动力学, 并推导出了哈密顿量和运动方程。 重点讨论了限制规范势对应的非Abel对偶超导理论性质, 并给出了D型及N型两类整数涡旋的具体数值解。 通过与传统的Abel对偶超导理论的对比分析,发现两者的运动方程形式及涡旋解基本一致, 这表明利用Abel对偶超导模型研究夸克色禁闭问题是合理的。 We have discussed vortices in the non Abelian dual superconductor theory. Based on the work of Cho et al., the Hamiltonian and the equations of motion of non Abelian model were discussed in details. The non Abelian dual superconductor theory related to the restricted guage potential was underlined and solutions of D type and N type integer vortices were obtained. Comparing with the traditional Abelian dual superconductor theory, we found that the the equations of motion and solutions of vortices in two models are almost same, which indicates it is reasonable to study quark confinement based on the Abelian dual superconductor theory.     

Homogeneous Bianchi type VI0 perfect fluid space-times

An algorithm is presented for generating new exact solutions of the Einstein equations for spatially homogeneous cosmological models of Bianchi type VI₀. The energy-momentum tensor is of perfect fluid type. Starting from Dunn and Tupper's dust-filled universe, new classes of solutions are obtained. The solutions represent anisotropic universes filled with perfect fluid not satisfying the equation of state. Some of their physical properties are studied.     

Inhomogeneous mixmaster universes: Some exact solutions

Algorithms for generating new exact solutions of the Einstein-Klein-Gordon field equations, which describe inhomogeneous universes with S³ topology of spatial sections, are developed. The known exact vacuum and stiff-fluid solutions with S³ topology are used as an input. The methods developed are further applied to derive inhomogenous generalizations of Bianchi type IX solutions and inhomogeneous S³ Gowdy models with gravitational and scalar waves. It is shown that the new solutions, which are generalizations of the Bianchi type IX models, permit identification of the scalar field with the velocity potential of the stiff irrotational fluid. The latter result is further used to study the growth rate of density perturbations of the isotropic and anisotropic Bianchi type IX universes in a fully nonlinear relativistic regime. The role of anisotropy of the rate of growth of density perturbations is studied in detail.