On singularity-free spacetimes

We consider here the metric for the singularity-free family of fluid models. The metric is unique for cylindrically symmetric space-time with metric potentials being separable functions of radial and time coordinates in the comoving coordinates. It turns out that fluid models separate out into two classes, withρ ≠μp in general butρ = 3p in particular andp =ρ. It is shown that in both the cases radial heat flow can be incorporated without disturbing the singularity-free character of the spacetime. The geodesics of the singularity-free metric are studied and the geodesic completeness is established. Several previously known solutions are derived as particular cases.     

Plane Symmetric Inhomogeneous Cosmological Models with a Perfect Fluid in General Relativity

In this paper we investigate a class of solutions of Einstein equations for the plane- symmetric perfect fluid case with shear and vanishing acceleration. If these solutions have shear, they must necessarily be non-static. We examine the integrable cases of the field equations systematically. Among the cases with shear we find three classes of solutions. PACS No.: 04.20.-q.     

Explanation of the Motionless Electromagnetic Generator by Sachs's Theory of Electrodynamics

It is shown that the principles of general relativity as developed by Sachs [1] can be used to explain the principles of the motionless electromagnetic generator (MEG), which takes electromagnetic energy from Riemannian curved space-time and in consequence outputs about twenty times more energy than inputted [2]. Therefore, it is shown in the most general manner that electromagnetic energy can be extracted from vacuum and used to power working devices such as the MEG, devices which are reproducible and repeatable [2].     

A Maxwell Field Equations Class of Exact Solutions on Matter-Dominated Spatially Closed Friedman-Robertson-Walker Universe

Working in a spatially closed Friedman-Robertson-Walker universe with cosmological dust, we investigate a particular source-free Maxwell field generated by a rotationally-symmetric potential A with one of the components in the direction of and the other along . Using the (, , )-Euler coordinates on S ³ and a compact timelike coordinate f, we obtain a class of parametric solutions that allows us to write down the essential components of the Maxwell tensor as well as the induction and the electric field intensity pointing out, besides the non-propagating fundamental electric field, a burst of electromagnetic radiation.     

A new (2+1)-dimensional supersymmetric Boussinesq equation and its Lie symmetry study

According to the conjecture based on some known facts of integrable models, a new (2+1)-dimensional supersymmetric integrable bilinear system is proposed. The model is not only the extension of the known (2+1)-dimensional negative Kadomtsev--Petviashvili equation but also the extension of the known (1+1)-dimensional supersymmetric Boussinesq equation. The infinite dimensional Kac--Moody--Virasoro symmetries and the related symmetry reductions of the model are obtained. Furthermore, the traveling wave solutions including soliton solutions are explicitly presented.     

Boltzmann Equations For Mixtures of Maxwell Gases: Exact Solutions and Power Like Tails

We consider the Boltzmann equations for mixtures of Maxwell gases. It is shown that in certain limiting case the equations admit self-similar solutions that can be constructed in explicit form. More precisely, the solutions have simple explicit integral representations. The most interesting solutions have finite energy and power like tails. This shows that power like tails can appear not just for granular particles (Maxwell models are far from reality in this case), but also in the system of particles interacting in accordance with laws of classical mechanics. In addition, non-existence of positive self-similar solutions with finite moments of any order is proven for a wide class of Maxwell models.     

Anisotropic Harmonic Oscillator in a Static Electromagnetic Field

A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneousstatic electromagnetic field is studied. Several configurations of the electromagnetic field are considered. The Schrodingerequation is solved analytically in most of the cases. The energy levels and wave functions are obtained explicitly. Insome of the cases, the ground state obtained is not a minimum wave packet, though it is of the Gaussian type. Coherentand squeezed states and their time evolution axe discussed in detail.     

Anisotropic Harmonic Oscillator in a Static Electromagnetic Field

A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneous static electromagnetic field is studied. Several configurations of the electromagnetic field are considered. The Schrödinger equation is solved analytically in most of the cases. The energy levels and wave functions are obtained explicitly. In some of the cases, the ground state obtained is not a minimum wave packet, though it is of the Gaussian type. Coherent and squeezed states and their time evolution are discussed in detail.     

A Physical Application of Kerr-Schild Groups

The present work deals with the search of useful physical applications of some generalized groups of metric transformations. We put forward different proposals and focus our attention on the implementation of one of them. Particularly, the results show how one can control very efficiently the kind of spacetimes related by a Generalized Kerr-Schild (GKS) Ansatz through Kerr-Schild groups. Finally a preliminary study regarding other generalized groups of metric transformations is undertaken which is aimed at giving some hints in new Ansätz to finding useful solutions to Einstein's equations.     

Exact Potts Model Partition Functions for Strips of the Square Lattice

We present exact calculations of the Potts model partition function Z(G, q, v) for arbitrary q and temperature-like variable v on n-vertex square-lattice strip graphs G for a variety of transverse widths L _t and for arbitrarily great length L , with free longitudinal boundary conditions and free and periodic transverse boundary conditions. These have the form Z(G, q, v)= . We give general formulas for N _{Z, G, j} and its specialization to v=–1 for arbitrary L _t for both types of boundary conditions, as well as other general structural results on Z. The free energy is calculated exactly for the infinite-length limit of the graphs, and the thermodynamics is discussed. It is shown how the internal energy calculated for the case of cylindrical boundary conditions is connected with critical quantities for the Potts model on the infinite square lattice. Considering the full generalization to arbitrary complex q and v, we determine the singular locus , arising as the accumulation set of partition function zeros as L , in the q plane for fixed v and in the v plane for fixed q.     

Integrable KP Coupling and Its Exact Solution

The integrable coupling is one of the most important topics in the nonlinear physics. This paper creates a novel integrable KP coupling and solves it via a recently-developed dark parameterization procedure.     

Construction of positive exact (2+1)-dimensional shock wave solutions for two discrete Boltzmann models

It is proved that (2+1)-dimensional (spacex, y; timet) positive exact shock wave solutions of two discrete Boltzmann models exist. For each densityN _i, these solutions are linear combinations of three similarity shock waves,N _i =n _0i + _j n _ji /[1+d _j exp( _j y+y _j x+ _j t)],j=1,2,3. Two models with four independent densities are investigated: the square discrete-velocity Boltzmann model and the model with eight velocities oriented toward the eight corners of a cube.The positivity problem for the densities is nontrivial. Two classes of solutions are considered for which the two first similarity shock wave components depend on only one spatial dimension, _j=const· _j ,j=1,2. For the positivity, if ₁₂>0, it is sufficient to prove that the 16 asymptotic shock limitsn _0i ,n _0i +n _3i , _j=0 ² n _ji , _j=0 ³ n _ji are positive. The density solutions are built up with five arbitrary parameters and we prove that there exist subdomains of the arbitrary parameter space in which the 16 shock limits are positive. We study numerically two explicit shock wave solutions. We are interested in the movement of the shock front when the time is growing and in the possible appearance of bumps. In the space, at intermediate times, these bumps represent populations of particles which are larger than at initial time or at equilibrium time.