A neutrino universe with viscosity

A solution of the Einstein field equation corresponding to a distribution of fluid with equation of stateρ = 3p but with a nonvanishing shear viscosity is presented. The solution is spherical symmetric and the flow lines are geodetic.     

Exact solution for an open universe with viscosity

The derivation of exact cosmological solutions describing an open universe with a conformally flat metric and volume viscosity is discussed. The method used in the article permits the modeling of an open universe to be reduced to the problem of mechanical motion of a particle in a specified force field. The behavior of the equation of state, which changes as the universe evolves, is investigated. A new exact solution of the gravitation equations is found in a simple form corresponding to an equivalent, variable-frequency oscillator with linear damping.This work has been performed under the auspices of the Astronomy Joint Scientific and Engineering Program.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 79–83, January, 1995.     

Homogeneous rotating universe with flat space

The homogeneous, anisotropic cosmological model is considered. It satisfies three physically reasonable conditions: it is space homogeneous, possesses flat space like sections and is filled with expanding, rotating and shearing matter. The asymptotic solution is presented and general properties are discussed. The question how the rotation influences the behaviour of matter near the singularity is investigated.     

Sonically produced heat in a fluid with bulk viscosity and shear viscosity

In a viscous fluid, sound produces heat in a spatial pattern which, in general, depends on the relative magnitudes of the shear viscosity coefficient eta and the bulk viscosity coefficient B'. It is well known that when the particle velocity components ui relative to Cartesian coordinates xi are given for an arbitrary sound field, or any field of flow, the volume rate of heat production qv can be determined from a dissipation function in the form B'T1 + eta T2. Here, T1 and T2 are quadratic functions involving derivatives of the type delta ui/delta xj. In this paper, examples are discussed for continuous monofrequency sound fields, including crossed plane waves, as well as focused and unfocused fields. In these examples, spatial distributions of the time-averaged quantity [qv] for media in which the loss mechanism is primarily bulk viscosity are compared to those for media in which shear viscosity dominates.     

Exact solutions in Brans-Dicke theory with bulk viscosity

The effect of bulk viscosity on the evolution of the homogeneous and isotropic cosmological models in the Brans-Dicke theory of gravitation is studied. Solutions are found, with a baratropic equation of state, a time-independent bulk viscosity, the gravitational constant inversely proportional to the age of the universe, and the mass of the universe (in the closed model) proportional to the square of its age; the expansion factor is a linear function of the cosmological time. For flat space, power law expansions are found, among them one that is related to extended inflation.     

Cosmological models with particle creation and bulk viscosity

The effect of bulk viscosity on the evolution of the Friedmann models is investigated in the context of open thermodynamic systems, which allows for particle creation. It is seen that, by choosing an appropriate function,(t), for the particle creation, all the models presented exhibit inflationary expansion and a non-singular beginning.     

Nonlinear spinor fields in an anisotropic universe filled with viscous fluid: Exact solutions and qualitative analysis

A self-consistent system containing a nonlinear spinor field and a Bianchi type-I (BI) gravitational field is considered in the presence of a viscous fluid and the cosmological constant. Nonlinear terms in the Lagrangian spinor-field appear either due to a self-action, or as a result of interaction with a scalar field. They are given by power functions of the invariants I and J, constructed from the bilinear spinor forms S and P. As far as the viscosity is concerned, it is a function of the energy density ? exhibiting a power-law behavior. Self-consistent solutions of the spinor, scalar, and gravitational field equations are derived. The obtained solutions are expressed in terms of the function τ(t), where τ is the volume scale in the BI-type Universe. A system of equations for τ, H, and ? is derived, where H is the Hubble constant, and ? is the viscous-flow energy. Exact solutions of the system are found for some special choices of the nonlinearity and viscosity. A complete qualitative analysis of the evolution at the boundaries is performed, and numerical solutions are obtained in the most interesting cases. In particular, it is shown that the system has Big Rip type solutions, which is typical for systems containing a phantom matter.     

Hubble parameter in QCD Universe for finite bulk viscosity

We consider the influence of the perturbative bulk viscosity on the evolution of the Hubble parameter in the QCD era of the early Universe. For the geometry of the Universe we assume the homogeneous and isotropic Friedmann‐Lemaitre‐Robertson‐Walker metric, while the background matter is assumed to be characterized by barotropic equations of state, obtained from recent lattice QCD simulations, and heavy‐ion collisions, respectively. Taking into account a perturbative form for the bulk viscosity coefficient, we obtain the evolution of the Hubble parameter, and we compare it with its evolution for an ideal (non‐viscous) cosmological matter. A numerical solution for the viscous QCD plasma in the framework of the causal Israel‐Stewart thermodynamics is also obtained. Both the perturbative approach and the numerical solution qualitatively agree in reproducing the viscous corrections to the Hubble parameter, which in the viscous case turns out to be slightly different as compared to the non‐viscous case. Our results are strictly limited within a very narrow temperature‐ or time‐interval in the QCD era, where the quark‐gluon plasma is likely dominant.     

A nonlinear stability analysis of a double-diffusive magnetized ferrofluid with magnetic field-dependent viscosity

A rigorous nonlinear stability result is derived by introducing a suitable generalized energy functional for a magnetized ferrofluid layer heated and soluted from below with magnetic field-dependent (MFD) viscosity, for stress-free boundaries. The mathematical emphasis is on how to control the nonlinear terms caused by magnetic body and inertia forces. For ferrofluids, we find that there is possibility of existence of subcritical instabilities, however, it is noted that in case of non-ferrofluid, global nonlinear stability Rayleigh number is exactly the same as that for linear instability. For lower values of magnetic parameters, this coincidence is immediately lost. The effects of magnetic parameter, M₃, solute gradient, S₁ and MFD viscosity parameter, δ, on the subcritical instability region have also been analyzed.     

Entropy viscosity method for nonlinear conservation laws

A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method.     

Suitability of artificial bulk viscosity for large-eddy simulation of turbulent flows with shocks

The artificial bulk viscosity method to numerically capture shocks is investigated for large-eddy simulation (LES). Different variations of this method are tested on a turbulent flow over a cylinder at Reynolds number of 10,000 and free-stream Mach number of 0.85. The artificial bulk viscosity model by Cook and Cabot, which is parameterized by the strain rate magnitude, is found to provide unnecessary bulk viscosity in turbulent regions away from shocks. While developed turbulent structures are found unaffected, this extra bulk viscosity is shown to significantly damp the sound field. An alternative formulation of the model which is parameterized by the rate of dilatation is proposed. This formulation is shown to avoid the unnecessary bulk viscosity and enhance the sound-prediction capability of the model. It was found that standard LES combined with artificial bulk viscosity is a promising approach for simulation of turbulent flows with shocks. The formulation of the model on curvilinear coordinates is presented in the appendix.     

Phase space analysis of metamaterial-based optical systems

Phase space analysis of light refraction in optical systems consisting of slabs or thin lenses from either metamaterials with negative refractive indices or common materials is performed with the aim of finding the conditions of perfect imaging for metamaterial-based optical systems. The analysis in the paraxial approximation uses ABCD matrices, whereas full ray tracing is employed in the non-paraxial case. The phase space analysis reveals that the ideality of planar metamaterial lenses only occurs when the absolute value of the refractive index in metamaterials is the same as in the surrounding medium.     

The universe formation by space reduction cascades with random initial parameters

In this paper we discuss the creation of our universe using the idea of extra dimensions. The initial, multidimensional Lagrangian contains only metric tensor. We have found many sets of the numerical values of the Lagrangian parameters corresponding to the observed low-energy physics of our Universe. Different initial parameters can lead to the same values of fundamental constants by the appropriate choice of a dimensional reduction cascade. This result diminishes the significance of the search for the ‘unique’ initial Lagrangian. We also have obtained a large number of low-energy vacua, which is known as ‘landscape’ in the string theory.     

Hartree-Fock-Slater exchange for anisotropic occupation in momentum space

It is shown that the well-known expression of the Hartree-Fock-Slater exchange energy (usually calculated for an occupied Fermi sphere) becomes scaled by a dimensionless factor in the case of a simple (compact) Fermi body and of only one (partially filled) band. Analytical results are presented for the following occupied regions in momentum space: i) ellipsoid of revolution (prolate as well as oblate), ii) ellipsoid with three unequal axes.The authors would like to thank Prof. P. Ziesche, Dr. H. Eschrig, and Dr. W. John for helpful discussions. One of us (M. H.) acknowledges an IREX-fellowship where part of this work has been completed.