Modeling Galactic Halos with Predominantly Quintessential Matter

This paper discusses a new model for galactic dark matter by combining an anisotropic pressure field corresponding to normal matter and a quintessence dark energy field having a characteristic parameter ω _q such that -1 < w_q < -\frac13-1<\omega_{q}< -\frac{1}{3}. Stable stellar orbits together with an attractive gravity exist only if ω _q is extremely close to -\frac13-\frac{1}{3}, a result consistent with the special case studied by Guzman et al. (Rev. Mex. Fis. 49:303, 2003). Less exceptional forms of quintessence dark energy do not yield the desired stable orbits and are therefore unsuitable for modeling dark matter.     

Higher Dimensional Bianchi Type I Universe in Creation-field Cosmology

We have studied the Hoyle-Narlikar C-field cosmology with Bianchi type-I space-time in higher dimensions. Using methods of Narlikar and Padmanabhan (Phys. Rev. D 32:1928, 1985), the solutions have been studied when the creation field C is a function of time t only. The geometrical and physical aspects for model are also studied.     

Bianchi Type-III Cosmological Models with Anisotropic Dark Energy (DE) in Lyra Geometry

The main purpose of this paper is to explore the solutions of Bianchi type-III cosmological model in Lyra geometry in the background of anisotropic dark energy. The general form of the anisotropy parameter of the expansion for Bianchi type-III space time is obtained in the presence of a single imperfect fluid with a dynamical anisotropic equation of state parameter and a dynamical energy density in Lyra geometry. A special law is assumed for the anisotropy of the fluid with reduces the anisotropy parameter of the expansion to a simple form $\Delta \propto \frac{1}{H^{2}V^{2}}$ . The exact solutions of the field equations, under the assumption on the anisotropy of the fluid, are obtained for exponential and power law volumetric expansion. The isotropy of the fluid, space and expansion are discussed. It is observed that the universe can approach to isotropy monotonically even in the presence of an anisotropic fluid. The anisotropy of the fluid also isotropizes at later times for accelerating models. The expression for the look-back time, proper distance, luminosity distance and angular diameter distance are also derived.     

Statistics of Advective Stretching in Three-dimensional Incompressible Flows

We present a method to quantify kinematic stretching in incompressible, unsteady, isoviscous, three-dimensional flows. We extend the method of Kellogg and Turcotte (J. Geophys. Res. 95:421–432, 1990) to compute the axial stretching/thinning experienced by infinitesimal ellipsoidal strain markers in arbitrary three-dimensional incompressible flows and discuss the differences between our method and the computation of Finite Time Lyapunov Exponent (FTLE). We use the cellular flow model developed in Solomon and Mezic (Nature 425:376–380, 2003) to study the statistics of stretching in a three-dimensional unsteady cellular flow. We find that the probability density function of the logarithm of normalised cumulative stretching (log S) for a globally chaotic flow, with spatially heterogeneous stretching behavior, is not Gaussian and that the coefficient of variation of the Gaussian distribution does not decrease with time as t^-\frac12t^{-\frac{1}{2}} . However, it is observed that stretching becomes exponential log S∼t and the probability density function of log S becomes Gaussian when the time dependence of the flow and its three-dimensionality are increased to make the stretching behaviour of the flow more spatially uniform. We term these behaviors weak and strong chaotic mixing respectively. We find that for strongly chaotic mixing, the coefficient of variation of the Gaussian distribution decreases with time as t^-\frac12t^{-\frac{1}{2}} . This behavior is consistent with a random multiplicative stretching process.     

Anisotropic Plane Symmetric Magnetized Model with Cosmological Constant

In this paper, we have obtained the solutions of perfect fluid cosmological model in Cylindrically-symmetric space time (Marder in Proc. R. Soc. A 246:133, 1958) with varying cosmological constant in the presence of electromagnetic field. To get determinate model of the universe we assumed that the scalar of expansion in the model is proportional to the eigen-value of the shear tensor which lead to the condition A=(BC) ⁿ . The magnetic field is due to an electric current produced along x-axis. Thus the magnetic field is in yz-plane and F ₂₃ is the only non-vanishing component of electromagnetic field tensor F _ij . Various physical and geometrical features of the model have been discussed.     

General Dynamical Equations for Dingle’s Space-Times Filled with a Charged Non-perfect Fluid

In this paper we have assumed charged non-perfect fluid as the material content of the space-time. The expression for the “mass function-M(r,y,z,t)” is obtained for the general situation and the contributions from the Ricci tensor in the form of material energy density ρ, pressure anisotropy [\fracp₂+p₃2-p₁][\frac{p_{2}+p_{3}}{2}-p_{1}] , electromagnetic field energy ℰ and the conformal Weyl tensor, viz. energy density of the free gravitational field ε (=\frac-3Y₂4p)(=\frac{-3\Psi_{2}}{4\pi}) are made explicit. This work is an extension of the work obtained earlier by Rao and Hasmani (Math. Today XIIA:71, 1993; New Directions in Relativity and Cosmology, Hadronic Press, Nonantum, 1997) for deriving general dynamical equations for Dingle’s space-times described by this most general orthogonal metric,

Revisiting Deng et al.’s Multiparty Quantum Secret Sharing Protocol

The multiparty quantum secret sharing protocol [Deng et al. in Chin. Phys. Lett. 23: 1084–1087, 2006] is revisited in this study. It is found that the performance of Deng et al.’s protocol can be much improved by using the techniques of block-transmission and decoy single photons. As a result, the qubit efficiency is improved 2.4 times and only one classical communication, a public discussion, and two quantum communications between each agent and the secret holder are needed rather than n classical communications, n public discussions, and \frac3n2\frac{3n}{2} quantum communications required in the original scheme.     

Axially Symmetric Universe in Creation-Field Cosmology

Axially symmetric space-time is considered in the Hoyle-Narlikar C-field cosmology. Using methods of Narlikar and Padmanabhan (Phys. Rev. D 32:1928, 1985), the solutions have been studied when the creation field C is a function of time t only. The geometrical and physical aspects for models are also studied.     

Higher Dimensional Cosmological Model with Quark and Strange Quark Matter

We study higher dimensional homogeneous cosmological model in the presence of quark and strange quark matter. The dynamical behavior of the model for the strange quark matter equation of state of the form p = \frac13 (r- 4 B_c)p= \frac{1}{3} (\rho- 4 B_{c}) are studied.     

Statistical Mechanics of Hard Spheres: Application of the Improved Scaled Particle Theory to the Hard Sphere Crystal

In a previous article (Baeyens and Verschelde in J. Math. Phys. 36:201, 1995), an improved approach to the scaled particle theory of Reiss et al. was presented. We used a generalized series expansion of the contact correlation function G(y,r). Truncating it after the third term, we obtained a Padé-like expression for the compressibility factor of the system. That expression contains two parameters which we were able to calculate, not only for the fluid state, but also for the known glassy states (Baeyens and Verschelde in Z. Phys. B 102:255, 1997). The resulting equations of state are in good agreement with the simulation data. Yet in the case of the hard sphere crystal our improved scaled particle theory fails, which is one of the reasons why an extension of it is desirable.     

Scale Transformation,Modified Gravity,and Brans-Dicke Theory

A model of Einstein-Hilbert action subject to the scale transformation is studied. By introducing a dilaton field as a means of scale transformation a new action is obtained whose Einstein field equations are consistent with traceless matter with non-vanishing modified terms together with dynamical cosmological and gravitational coupling terms. The obtained modified Einstein equations are neither those in f(R) metric formalism nor the ones in f(ℛ) Palatini formalism, whereas the modified source terms are formally equivalent to those of f(R)=\frac12R²f({\mathcal{R}})=\frac{1}{2}{\mathcal{R}}^{2} gravity in Palatini formalism. The correspondence between the present model, the modified gravity theory, and Brans-Dicke theory with w = -\frac32\omega=-\frac{3}{2} is explicitly shown, provided the dilaton field is condensated to its vacuum state.     

Kaluza-Klein Cosmological Model in f(R,T) Gravity

A five dimensional Kaluza-Klein space-time is considered in the presence of perfect fluid source in f(R,T) gravity proposed by Harko et al. ( [gr-qc], 2011). A cosmological model with a negative constant deceleration parameter with an appropriate choice of a function f(T) is presented. To find a determinate solution of the field equations it is assumed that scalar of expansion is proportional to the shear scalar of the space time. The physical behavior of the model is also studied.     

HOW TO EXTEND ANY DYNAMICAL SYSTEM SO THAT IT BECOMES ISOCHRONOUS,ASYMPTOTICALLY ISOCHRONOUS OR MULTI-PERIODIC

We indicate how one can extend any dynamical system (namely, any system of nonlinearly coupled autonomous ordinary differential equations) so that the extended dynamical system thereby obtained is either isochronous or asymptotically isochronous or multi-periodic, namely its generic solutions are either completely periodic with a fixed period or tend asymptotically, in the remote future, to such completely periodic functions or are multi-periodic (or become multi-periodic only asymptotically, in the remote future). In all cases the scale of the periodicity can be arbitrarily assigned. Moreover, the solutions of the extended systems are generally well approximated by those of the original, unmodified, systems, up to a constant rescaling of the independent variable (time), as long as their evolution is considered over time intervals short with respect to the (arbitrarily assigned) periodicities characterizing the extended systems. Several examples are displayed. In some cases the general solution of these dynamical systems is also exhibited; in others, this is impossible inasmuch as the models being manufactured are extensions of dynamical systems displaying chaotic evolutions, such as, for instance, the well-known Lorenz model of 3 nonlinearly coupled ODEs.     

Bianchi I in scalar and scalar-tensor cosmologies

We study how the constants G and Λ may vary in different theoretical models (general relativity (GR) with a perfect fluid, scalar cosmological models (SM) (“quintessence”) with and without interacting scalar and matter fields and three scalar-tensor theories (STT) with a dynamical Λ) in order to explain some observational results. We apply the program outlined in section II to study the Bianchi I models, under the self-similarity hypothesis. We put special emphasis on calculating exact power-law solutions which allow us to compare the different models. In all the studied cases we conclude that the solutions are isotropic and noninflationary. We also arrive at the conclusion that in the GR model with time-varying constants, Λ vanishes while G is constant. In the SM all the solutions are massless i.e. the potential vanishes and all the interacting models are inconsistent from the thermodynamical point of view. The solutions obtained in the STT collapse to the perfect fluid one obtained in the GR model where G is a true constant and Λ vanishes as in the GR and SM frameworks.     

Dissipative Future Universe Without Big Rip

The present study deals with dissipative future universe without big rip in context of Eckart formalism. The generalised Chaplygin gas, characterised by equation of state p=-\fracAr^\frac1ap=-\frac{A}{\rho^{\frac{1}{\alpha}}}, has been considered as a model for dark energy due to its dark-energy-like evolution at late time. It is demonstrated that, if the cosmic dark energy behaves like a fluid with equation of state p=ωρ; ω<−1 as well as Chaplygin gas simultaneously then the big rip problem does not arise and the scale factor is found to be regular for all time.     

Bianchi type III models with anisotropic dark energy

The general form of the anisotropy parameter of the expansion for Bianchi type-III metric is obtained in the presence of a single diagonal imperfect fluid with a dynamically anisotropic equation of state parameter and a dynamical energy density in general relativity. A special law is assumed for the anisotropy of the fluid which reduces the anisotropy parameter of the expansion to a simple form (D μ H^-2V^-2{\Delta\propto H^{-2}V^{-2}}, where Δ is the anisotropy parameter, H is the mean Hubble parameter and V is the volume of the universe). The exact solutions of the Einstein field equations, under the assumption on the anisotropy of the fluid, are obtained for exponential and power-law volumetric expansions. The isotropy of the fluid, space and expansion are examined. It is observed that the universe can approach to isotropy monotonically even in the presence of an anisotropic fluid. The anisotropy of the fluid also isotropizes at later times for accelerating models and evolves into the well-known cosmological constant in the model for exponential volumetric expansion.     

Upper Bounds for Coarsening for the Deep Quench Obstacle Problem

The deep quench obstacle problem models phase separation at low temperatures. During phase separation, domains of high and low concentration are formed, then coarsen or grow in average size. Of interest is the time dependence of the dominant length scales of the system. Relying on recent results by Novick-Cohen and Shishkov (Discrete Contin. Dyn. Syst. B 25:251–272, 2009), we demonstrate upper bounds for coarsening for the deep quench obstacle problem, with either constant or degenerate mobility. For the case of constant mobility, we obtain upper bounds of the form t ^1/3 at early times as well as at times t for which E(t) ￡ \frac(1-[`(u)]<sup>2</sup>)4E(t)\le\frac{(1-\overline{u}^{2})}{4}, where E(t) denotes the free energy. For the case of degenerate mobility, we get upper bounds of the form t <sup>1/3</sup> or t <sup>1/4</sup> at early times, depending on the value of E(0), as well as bounds of the form t <sup>1/4</sup> whenever E(t) ￡ \frac(1-[`(u)]²)4E(t)\le\frac{(1-\overline{u}^{2})}{4}.     

Bianchi Type-III Cosmological Model with Negative Constant Deceleration Parameter in Brans Dicke Theory of Gravitation

Bianchi type-III space time is considered in the presence of perfect fluid source in the scalar-tensor theory of gravitation proposed by Brans and Dicke (Phys. Rev. 124:925, 1961). With the help of special law of variation for Hubble’s parameter proposed by Bermann (Nuovo Cimento 74B:182, 1983) a cosmological model with negative constant deceleration parameter is obtained in the presence of perfect fluid with disordered radiation. Some physical and kinematical properties of the model are also discussed.     

Curvature Induced Acceleration and Reheating of the Universe

We present some solutions in a modified theory of gravity with R ² and \frac1R\frac{1}{R} terms in the Einstein-Hilbert action with an ideal fluid in FLRW spacetime. Graceful exit from early inflation to radiation dominated era is obtained in the strong curvature regime preceding a fluctuation of effective equation of state parameter at the end of inflation. In the weak curvature regime the universe evolves through a radiation era that subsequently turns to a matter era and finally transits to late time accelerating era.