Higher Dimensional Dark Energy Investigation with?Variable Λ and G

Two phenomenological models of Λ, viz. L ~ ([(a)\dot]/a)²\Lambda \sim (\dot{a}/a)^{2} and L ~ [(a)\ddot]/a\Lambda \sim \ddot{a}/a are studied under the assumption that G is a time-variable parameter. Both models show that G is inversely proportional to time as suggested earlier by others including Dirac. The models considered here can be matched with observational results by properly tuning the parameters of the models. Our analysis shows that L ~ [(a)\ddot]/a\Lambda \sim \ddot{a}/a model corresponds to a repulsive situation and hence correlates with the present status of the accelerating Universe. The other model L ~ ([(a)\dot]/a)²\Lambda \sim (\dot{a}/a)^{2} is, in general, attractive in nature. Moreover, it is seen that due to the combined effect of time-variable Λ and G the Universe evolved with acceleration as well as deceleration. This later one indicates a Big Crunch.     

Phenomenology of Λ-CDM Model: A?Possibility of?Accelerating Universe with Positive Pressure

Among various phenomenological Λ models, a time-dependent model [(L)\dot] ~ H³\dot{\Lambda}\sim H^{3} is selected here to investigate the Λ-CDM cosmology. The model can follow from dynamics, underlying the origin of Λ. Using this model the expressions for the time-dependent equation of state parameter ω and other physical parameters are derived. It is shown that in H ³ model accelerated expansion of the Universe takes place at negative energy density, but with a positive pressure. It has also been possible to obtain the change of sign of the deceleration parameter q during cosmic evolution.     

Domain Wall with Strange Quark Matter in Kaluza-Klein Type Cosmological Model

In this study we have analyzed the Kaluza-Klein type Robertson Walker (RW) cosmological model by considering variable cosmological constant term Λ of the form: , and Λ∼ρ in the presence of strange quark matter with domain wall. The various physical aspects of the model are also discussed.     

Bulk Viscous Bianchi Type I Barotropic Fluid Cosmological Model with Varying <Emphasis Type="Bold">Λ</Emphasis> and Functional Relation on Hubble Parameter

Bianchi Type I bulk viscous barotropic fluid cosmological with varying Λ is investigated. We have also assumed a functional relation on Hubble parameter as H(R)=a(R ⁻ⁿ +1), n>1, a>0, H the Hubble constant, R being scale factor and H = [(R)\dot]/RH = \dot{R}/R. The physical and geometrical aspects of the model related with astronomical observations are discussed.     

Scenario of Inflationary Cosmology from the Phenomenological Λ Models

Choosing the three phenomenological models of the dynamical cosmological term Λ, viz., , and Λ∼ρ where a is the cosmic scale factor, it has been shown by the method of numerical analysis for the considered non-linear differential equations that the three models are equivalent for the flat Universe k=0 and for arbitrary non-linear equation of state. The evolution plots for dynamical cosmological term Λ vs. time t and also the cosmic scale factor a vs. t are drawn here for k=0,+1. A qualitative analysis has been made from the plots which supports the idea of inflation and hence expanding Universe.     

Unifying dark energy and dark matter with the modified Ricci model

In this paper, two modified Ricci models are considered as the candidates of unified dark matter–dark energy. In model one, the energy density is given by r_MR=3M_pl(aH²+b[(H)\dot])\rho_{\mathrm{MR}}=3M_{\mathrm{pl}}(\alpha H^{2}+\beta\dot{H}), whereas, in model two, by r_MR=3M_pl(\fraca6 R+g[(H)\ddot]H^-1)\rho_{\mathrm{MR}}=3M_{\mathrm{pl}}(\frac{\alpha}{6} R+\gamma\ddot{H}H^{-1}). We find that they can explain both dark matter and dark energy successfully. A constant equation of state of dark energy is obtained in model one, which means that it gives the same background evolution as the wCDM model, while model two can give an evolutionary equation of state of dark energy with the phantom divide line crossing in the near past.     

Solar System planetary tests of $${\dot c/c}$$

Analytical and numerical calculations show that a putative temporal variation of the speed of light c, with the meaning of space-time structure constant c _ST, assumed to be linear over timescales of about one century, would induce a secular precession of the longitude of the pericenter v{\varpi} of a test particle orbiting a spherically symmetric body. By comparing such a predicted effect to the corrections D[(v)\dot]{\Delta\dot\varpi} to the usual Newtonian/Einsteinian perihelion precessions of the inner planets of the Solar System, recently estimated by E.V. Pitjeva by fitting about one century of modern astronomical observations with the standard classical/relativistic dynamical force models of the EPM epehemerides, we obtained [(c)\dot]/c = (0.5±2)×10^-7 yr^-1{\dot c/c =(0.5\pm 2)\times 10^{-7} {\rm yr}^{-1}} . Moreover, the possibility that [(c)\dot]/c 1 0{\dot c/c\neq 0} over the last century is ruled out at 3−12σ level by taking the ratios of the perihelia for different pairs of planets. Our results are independent of any measurement of the variations of other fundamental constants which may be explained by a variation of c itself (with the meaning of electromagnetic constant c _EM). It will be important to repeat such tests if and when other teams of astronomers will estimate their own corrections to the standard Newtonian/Einsteinian planetary perihelion precessions with different ephemerides.     

Kaluza-Klein Type Robertson Walker Cosmological Model with Dynamical Cosmological Term Λ

In this paper we have analyzed the Kaluza-Klein type Robertson Walker (RW) cosmological models by considering three different forms of variable Λ: , and Λ∼ρ. It is found that, the connecting free parameters of the models with cosmic matter and vacuum energy density parameters are equivalent, in the context of higher dimensional space time. The expression for the look back time, luminosity distance and angular diameter distance are also derived. This work has thus generalized to higher dimensions the well-known results in four dimensional space time. It is found that there may be significant difference in principle at least, from the analogous situation in four dimensional space time.     

Critical Rotational Speeds in the Gross-Pitaevskii Theory on a Disc with Dirichlet Boundary Conditions

We study the two-dimensional Gross-Pitaevskii theory of a rotating Bose gas in a disc-shaped trap with Dirichlet boundary conditions, generalizing and extending previous results that were obtained under Neumann boundary conditions. The focus is on the energy asymptotics, vorticity and qualitative properties of the minimizers in the parameter range |log ε|≪Ω≲ε ⁻²|log ε|⁻¹ where Ω is the rotational velocity and the coupling parameter is written as ε ⁻² with ε≪1. Three critical speeds can be identified. At \varOmega = \varOmega_c1 ~ |loge|\varOmega=\varOmega_{\mathrm{c_{1}}}\sim |\log\varepsilon| vortices start to appear and for |loge| << \varOmega < \varOmega_c2 ~ e^-1|\log\varepsilon|\ll\varOmega< \varOmega_{\mathrm{c_{2}}}\sim \varepsilon^{-1} the vorticity is uniformly distributed over the disc. For \varOmega 3 \varOmega _c2\varOmega\geq\varOmega _{\mathrm{c_{2}}} the centrifugal forces create a hole around the center with strongly depleted density. For Ω≪ε ⁻²|log ε|⁻¹ vorticity is still uniformly distributed in an annulus containing the bulk of the density, but at \varOmega = \varOmega_c3 ~ e^-2|loge|^-1\varOmega=\varOmega_{\mathrm {c_{3}}}\sim\varepsilon ^{-2}|\log\varepsilon |^{-1} there is a transition to a giant vortex state where the vorticity disappears from the bulk. The energy is then well approximated by a trial function that is an eigenfunction of angular momentum but one of our results is that the true minimizers break rotational symmetry in the whole parameter range, including the giant vortex phase.     

Single flexible and semiflexible polymers at high shear: Non-monotonic and non-universal stretching response

Using Brownian hydrodynamic simulation techniques, we study single polymers in shear. We investigate the effects of hydrodynamic interactions, excluded volume, chain extensibility, chain length and semiflexibility. The well-known stretching behavior with increasing shear rate [(g)\dot] \dot{{\gamma}} is only observed for low shear [(g)\dot] \dot{{\gamma}} < [(g)\dot]^max \dot{{\gamma}}^{{\max}}_{} , where [(g)\dot]^max \dot{{\gamma}}^{{\max}}_{} is the shear rate at maximum polymer extension. For intermediate shear rates [(g)\dot]^max \dot{{\gamma}}^{{\max}}_{} < [(g)\dot] \dot{{\gamma}} < [(g)\dot]^min \dot{{\gamma}}^{{\min}}_{} the radius of gyration decreases with increasing shear with minimum chain extension at [(g)\dot]^min \dot{{\gamma}}^{{\min}}_{} . For even higher shear [(g)\dot]^min \dot{{\gamma}}^{{\min}}_{} < [(g)\dot] \dot{{\gamma}} the chain exhibits again shear stretching. This non-monotonic stretching behavior is obtained in the presence of excluded-volume and hydrodynamic interactions for sufficiently long and inextensible flexible polymers, while it is completely absent for Gaussian extensible chains. We establish the heuristic scaling laws [(g)\dot]^max \dot{{\gamma}}^{{\max}}_{} ∼ N ^-1.4 and [(g)\dot]^min \dot{{\gamma}}^{{\min}}_{} ∼ N ^0.7 as a function of chain length N , which implies that the regime of shear-induced chain compression widens with increasing chain length. These scaling laws also imply that the chain response at high shear rates is not a universal function of the Weissenberg number Wi = [(g)\dot] \dot{{\gamma}} t \tau anymore, where t \tau is the equilibrium relaxation time. For semiflexible polymers a similar non-monotonic stretching response is obtained. By extrapolating the simulation results to lengths corresponding to experimentally studied DNA molecules, we find that the shear rate [(g)\dot]^max \dot{{\gamma}}^{{\max}}_{} to reach the compression regime is experimentally realizable.     

Coevolution of competing systems: local cooperation and global inhibition

Using a set of heterogeneous competing systems with intra-system cooperation and inter-system aggression, we show how the coevolution of the system parameters (degree of organization and conditions for aggression) depends on the rate of supply of resources [(S)\dot]\dot{S}. The model consists of a number of units grouped into systems that compete for the resource S; within each system several units can be aggregated into cooperative arrangements whose size is a measure of the degree of organization in the system. Aggression takes place when the systems release inhibitors that impair the performance of other systems. Using a mean field approximation we show that i) even in the case of identical systems there are stable inhomogeneous solutions; ii) a system steadily producing inhibitors needs large perturbations to leave this regime; and iii) aggression may give comparative advantages. A discrete model is used in order to examine how the particular configuration of the units within a system determines its performance in the presence of aggression. We find that full-scale, one sided aggression is only profitable for less-organized systems, and that systems with a mixture of degrees of organization exhibit robustness against aggression. By using a genetic algorithm we find that, in terms of the full-occupation resource supply rate [(S)\dot]_F\dot{S}_{F}, the coevolution of the set of systems displays the following behavior: i) for [(S)\dot] < [(S)\dot]_F/10\dot{S}< \dot{S}_{F}/10 aggressions are irrelevant and most systems exhibit a high degree of organization; ii) For [(S)\dot]_F/10 < [(S)\dot] < [(S)\dot]_F/3\dot{S}_{F}/10 < \dot{S} < \dot{S}_{F}/3 aggressions are frequent, making systems with a low degree of organization competitive; iii) for [(S)\dot]_F/3 < [(S)\dot] < [(S)\dot]_F/2\dot{S}_{F}/3 < \dot{S} < \dot{S}_{F}/2 the systems display global evolutive transitions between periods of calm (few aggressions and high degree of organization) and periods of belligerence (frequent aggressions and low degree of organization); iv) for $ \dot{S} > \dot{S}_{F}/2$ \dot{S} > \dot{S}_{F}/2 the periods of aggression becomes progressively rarer and shorter. Finally, when [(S)\dot]\dot{S} approaches [(S)\dot]_F\dot{S}_{F} the selection pressure on the cooperativity and the aggression between systems disappears. This kind of model can be useful to analyse the interplay of the cooperation/competition processes that can be found in some social, economic, ecological and biochemical systems; as an illustration we refer to the competition between drug-selling gangs.     

Production of strange secondaries in high-energy Σ<Superscript>−</Superscript><Emphasis Type="Italic">A</Emphasis> collisions

The WA89 Collaboration experimental data on production of Λ, Σ⁻, Σ⁺, Ξ⁻, Ω⁻ baryons, $ \bar \Lambda $ \bar \Lambda and $ \bar \Xi ^ + $ \bar \Xi ^ + antibaryons in Σ⁻ collisions with C and Cu targets at 345 GeV/c ($ \sqrt {s_{\Sigma N} } $ \sqrt {s_{\Sigma N} } ≈ 25.5 GeV) in the frame of the Quark-Gluon String Model is described. The comparison of the theoretical results with the experimental data is discussed. Finally, some relations among the values of the model parameters obtained with the help of quark combinatorics are presented.     

The value of the cosmological constant

We make the cosmological constant, Λ, into a field and restrict the variations of the action with respect to it by causality. This creates an additional Einstein constraint equation. It restricts the solutions of the standard Einstein equations and is the requirement that the cosmological wave function possess a classical limit. When applied to the Friedmann metric it requires that the cosmological constant measured today, t _U , be L ~ t_U^-2 ~ 10^-122{\Lambda \sim t_{U}^{-2} \sim 10^{-122}} , as observed. This is the classical value of Λ that dominates the wave function of the universe. Our new field equation determines Λ in terms of other astronomically measurable quantities. Specifically, it predicts that the spatial curvature parameter of the universe is W_k0 o -k/a₀²H²=-0.0055{\Omega _{\mathrm{k0}} \equiv -k/a_{0}^{2}H^{2}=-0.0055} , which will be tested by Planck Satellite data. Our theory also creates a new picture of self-consistent quantum cosmological history.     

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.     

A new approach to Ermakov systems and applications in quantum physics

Milne–Pinney equation [(x)\ddot]=-w²(t)x+ k/x³\ddot x=-\omega^2(t)x+ k/{x^3} is usually studied together with the time-dependent harmonic oscillator [(y)\ddot]+w²(t) y=0\ddot y+\omega^2(t) y=0 and the system is called Ermakov system, and actually Pinney showed in a short paper that the general solution of the first equation can be written as a superposition of two solutions of the associated harmonic oscillator. A recent generalization of the concept of Lie systems for second order differential equations and the usual techniques of Lie systems will be used to study the Ermakov system. Several applications of Ermakov systems in Quantum Mechanics as the relation between Schroedinger and Milne equations or the use of Lewis–Riesenfeld invariant will be analysed from this geometric viewpoint.     

Theoretical study of the dynamics for the H + Li H ( v = 0, j = 0) $\to$ H2 + Li reaction and its isotopic variants

Quasi-classical trajectory (QCT) method is carried out to calculate the dynamics of the H + LiH (v = 0, j = 0) ?\to H₂ + Li reaction and its isotopic variants based on the potential energy surface of the lowest ²A￠^2A' electronic state reported by Prudente et al. [Chem. Phys. Lett. 474, 18 (2009)]. The reaction cross-section, product rotational alignment parameter áP₂\langle P_2 ([(j￠)\vec]\vec{j'} ·\cdot [(k)\vec])?\vec{k})\rangle and one generalized polarization-dependent differential cross-section (2π/σ)(ds₀₀d\sigma_{00}/d w_t\omega_t) are calculated. We found that different collision energies and mass factors show driving influence on the process of the reactions and product molecules H₂ (HD, D₂) polarization distribution, and the trend of the isotopic effects in the high collision energy range is different to that in the low collision energy range. The calculations are also interpreted in relation to the features of the underlying potential energy surface. A comparison between the title reactions and a barrier-less reaction F + HBr ?\to FH + Br has been discussed in detail.     

Representation of Quantum States as Points in a Probability Simplex Associated to a SIC-POVM

The quantum state of a d-dimensional system can be represented by a probability distribution over the d ² outcomes of a Symmetric Informationally Complete Positive Operator Valued Measure (SIC-POVM), and then this probability distribution can be represented by a vector of \mathbb R^d2-1\mathbb {R}^{d^{2}-1} in a (d ²−1)-dimensional simplex, we will call this set of vectors Q\mathcal{Q}. Other way of represent a d-dimensional system is by the corresponding Bloch vector also in \mathbb R^d2-1\mathbb {R}^{d^{2}-1}, we will call this set of vectors B\mathcal{B}. In this paper it is proved that with the adequate scaling B=Q\mathcal{B}=\mathcal{Q}. Also we indicate some features of the shape of Q\mathcal{Q}.     

Plasticity and dynamical heterogeneity in driven glassy materials

Many amorphous glassy materials exhibit complex spatio-temporal mechanical response and rheology, characterized by an intermittent stress strain response and a fluctuating velocity profile. Under quasistatic and athermal deformation protocols this heterogeneous plastic flow was shown to be composed of plastic events of various sizes, ranging from local quadrupolar plastic rearrangements to system spanning shear bands. In this paper, through numerical study of a 2D Lennard-Jones amorphous solid, we generalize the study of the heterogeneous dynamics of glassy materials to the finite shear rate ( [(g)\dot] \dot{{\gamma}} 1 \neq 0 and temperature case (T 1 \neq 0 . In practice, we choose an effectively athermal limit (T ∼ 0 and focus on the influence of shear rate on the rheology of the glass. In line with previous works we find that the model Lennard-Jones glass follows the rheological behavior of a yield stress fluid with a Herschel-Bulkley response of the form, s \sigma = s_Y \sigma_{{Y}}^{} + c ₁ [(g)\dot]^b \dot{{\gamma}}^{{\beta}}_{} . The global mechanical response obtained through the use of Molecular Dynamics is shown to converge in the limit [(g)\dot] \dot{{\gamma}} ? \rightarrow 0 to the quasistatic limit obtained with an energy minimization protocol. The detailed analysis of the plastic deformation at different shear rates shows that the glass follows different flow regimes. At sufficiently low shear rates the mechanical response reaches a shear-rate-independent regime that exhibits all the characteristics of the quasistatic response (finite-size effects, cascades of plastic rearrangements, yield stress, ...). At intermediate shear rates the rheological properties are determined by the externally applied shear rate and the response deviates from the quasistatic limit. Finally at higher shear the system reaches a shear-rate-independent homogeneous regime. The existence of these three regimes is also confirmed by the detailed analysis of the atomic motion. The computation of the four-point correlation function shows that the transition from the shear-rate-dominated to the quasistatic regime is accompanied by the growth of a dynamical cooperativity length scale x \xi that is shown to diverge with shear rate as x \xi μ \propto [(g)\dot]^-n \dot{{\gamma}}^{{-\nu}}_{} , with n \nu ∼ 0.2 -0.3. This scaling is compared with the prediction of a simple model that assumes the diffusive propagation of plastic events.     

Directed flow of identified particles from Au+Au collisions at RHIC

We present the measurement of directed flow (v ₁) for the identified particles, namely, Λ, $ \bar \Lambda $ \bar \Lambda and K _s ⁰, as a function of rapidity and centrality in Au+Au collisions at $ \sqrt {s_{NN} } $ \sqrt {s_{NN} } = 200 GeV and 62.4 GeV. The measurement is based on the run IV data obtained by the STAR experiment at RHIC. In order to enhance event plane resolution, we use tracks reconstructed from the Forward Time Projection Chambers (FTPCs), together with the sideward deflection of spectator neutrons measured by the STAR’s Shower Maximum Detector at Zero Degree Calorimeters (ZDC-SMDs). We find that for 200 GeV, proton and antiproton v ₁ is less than 1%, the K _s ⁰ Λ, $ \bar \Lambda $ \bar \Lambda v ₁ is less than 2%; for 62 GeV, proton v ₁ is less than 1% and antiproton is less than 2%, v ₁ for K _s ⁰, Λ, $ \bar \Lambda $ \bar \Lambda is less than 2% in Au+Au collisions at 200 GeV.     

Propagation of electromagnetic waves generated by moving sources in dispersive media

The propagation of electromagnetic waves issued by modulated moving sources of the form j( t,x ) = a( t )e ^{- iw₀ t} [(x)\dot]₀ ( t )d( x - x₀ ( t ) )j\left( {t,x} \right) = a\left( t \right)e^{ - i\omega _0 t} \dot x_0 \left( t \right)\delta \left( {x - x_0 \left( t \right)} \right) is considered, where j(t, x) stands for the current density vector, x = (x ₁, x ₂, x ₃) ∈ ℝ³ for the space variables, t ∈ ℝ for time, t → x ₀(t) ∈ ℝ³ for the vector function defining the motion of the source, ω ₀ for the eigenfrequency of the source, a(t) for a narrow-band amplitude, and δ for the standard δ function. Suppose that the media under consideration are dispersive. This means that the electric and magnetic permittivity ɛ(ω), μ(ω) depends on the frequency ω. We obtain a representation of electromagnetic fields in the form of time-frequency oscillating integrals whose phase contains a large parameter λ > 0 characterizing the slowness of the change of the amplitude a(t) and the velocity [(x)\dot]₀ ( t )\dot x_0 \left( t \right) and a large distance between positions of the source and the receiver. Applying the two-dimensional stationary phase method to the integrals, we obtain explicit formulas for the electromagnetic field and for the Doppler effects. As an application of our approach, we consider the propagation of electromagnetic waves produced by moving source in a cold nonmagnetized plasma and the Cherenkov radiation in dispersive media.