Long-range effects in granular avalanching

We introduce a model for granular flow in a one-dimensional rice pile that incorporates rolling effects through a long-range rolling probability for the individual rice grains proportional to $r^{-\rho}$, $r$ being the distance traveled by a grain in a single topling event. The exponent $\rho$ controls the average rolling distance. We have shown that the crossover from power law to stretched exponential behaviors observed experimentally in the granular dynamics of rice piles can be well described as a long-range effect resulting from a change in the transport properties of individual grains. We showed that stretched exponential avalanche distributions can be associated with a long-range regime for $1<\rho<2$ where the average rolling distance grows as a power law with the system size, while power law distributions are associated with a short range regime for $\rho>2$, where the average rolling distance is independent of the system size.Comment: 5 pages, 3 figure

Dynamical Compactification, Standard Cosmology and the Accelerating Universe

A cosmological model based on Kaluza-Klein theory is studied. A metric, in which the scale factor of the compact space evolves as an inverse power of the radius of the observable universe, is constructed. The Freedmann-Robertson-Walker equations of standard four-dimensional cosmology are obtained precisely. The pressure in our universe is an effective pressure expressed in terms of the components of the higher dimensional energy-momentum tensor. In particular, this effective pressure could be negative and might therefore explain the acceleration of our present universe. A special feature of this model is that, for a suitable choice of the parameters of the metric, the higher dimensional gravitational coupling constant could be negative.Comment: 11 pages, uses revte

Plasma Wave Properties of the Schwarzschild Magnetosphere in a Veselago Medium

We re-formulate the 3+1 GRMHD equations for the Schwarzschild black hole in a Veselago medium. Linear perturbation in rotating (non-magnetized and magnetized) plasma is introduced and their Fourier analysis is considered. We discuss wave properties with the help of wave vector, refractive index and change in refractive index in the form of graphs. It is concluded that some waves move away from the event horizon in this unusual medium. We conclude that for the rotating non-magnetized plasma, our results confirm the presence of Veselago medium while the rotating magnetized plasma does not provide any evidence for this medium.Comment: 20 pages, 15 figures, accepted for publication in Astrophys. Space Sc

Dynamics of systems with isotropic competing interactions in an external field: a Langevin approach

We study the Langevin dynamics of a ferromagnetic Ginzburg-Landau Hamiltonian with a competing long-range repulsive term in the presence of an external magnetic field. The model is analytically solved within the self consistent Hartree approximation for two different initial conditions: disordered or zero field cooled (ZFC), and fully magnetized or field cooled (FC). To test the predictions of the approximation we develop a suitable numerical scheme to ensure the isotropic nature of the interactions. Both the analytical approach and the numerical simulations of two-dimensional finite systems confirm a simple aging scenario at zero temperature and zero field. At zero temperature a critical field $h_c$ is found below which the initial conditions are relevant for the long time dynamics of the system. For $h < h_c$ a logarithmic growth of modulated domains is found in the numerical simulations but this behavior is not captured by the analytical approach which predicts a $t^1/2$ growth law at $T = 0$

A Grand Canonical Ensemble Approach to the Thermodynamic Properties of the Nucleon in the Quark-Gluon Coupling Model

In this paper, we put forward a way to study the nucleon's thermodynamic properties such as its temperature, entropy and so on, without inputting any free parameters by human hand, even the nucleon's mass and radius. First we use the Lagrangian density of the quark gluon coupling fields to deduce the Dirac Equation of the quarks confined in the gluon fields. By boundary conditions we solve the wave functions and energy eigenvalues of the quarks, and thus get energy-momentum tensor, nucleon mass, and density of states. Then we utilize a hybrid grand canonical ensemble, to generate the temperature and chemical potentials of quarks, antiquarks of three flovars by the four conservation laws of the energy and the valence quark numbers, after which, all other thermodynamic properties are known. The only seemed free paremeter, the nucleon radius is finally determined by the grand potential minimal principle.Comment: 5 pages, LaTe

Nonequilibrium Evolution of Correlation Functions: A Canonical Approach

We study nonequilibrium evolution in a self-interacting quantum field theory invariant under space translation only by using a canonical approach based on the recently developed Liouville-von Neumann formalism. The method is first used to obtain the correlation functions both in and beyond the Hartree approximation, for the quantum mechanical analog of the $\phi^{4}$ model. The technique involves representing the Hamiltonian in a Fock basis of annihilation and creation operators. By separating it into a solvable Gaussian part involving quadratic terms and a perturbation of quartic terms, it is possible to find the improved vacuum state to any desired order. The correlation functions for the field theory are then investigated in the Hartree approximation and those beyond the Hartree approximation are obtained by finding the improved vacuum state corrected up to ${\cal O}(\lambda^2)$. These correlation functions take into account next-to-leading and next-to-next-to-leading order effects in the coupling constant. We also use the Heisenberg formalism to obtain the time evolution equations for the equal-time, connected correlation functions beyond the leading order. These equations are derived by including the connected 4-point functions in the hierarchy. The resulting coupled set of equations form a part of infinite hierarchy of coupled equations relating the various connected n-point functions. The connection with other approaches based on the path integral formalism is established and the physical implications of the set of equations are discussed with particular emphasis on thermalization.Comment: Revtex, 32 pages; substantial new material dealing with non-equilibrium evolution beyond Hartree approx. based on the LvN formalism, has been adde

Isothermal Plasma Wave Properties of the Schwarzschild de-Sitter Black Hole in a Veselago Medium

In this paper, we study wave properties of isothermal plasma for the Schwarzschild de-Sitter black hole in a Veselago medium. We use ADM 3+1 formalism to formulate general relativistic magnetohydrodynamical (GRMHD) equations for the Schwarzschild de-Sitter spacetime in Rindler coordinates. Further, Fourier analysis of the linearly perturbed GRMHD equations for the rotating (non-magnetized and magnetized) background is taken whose determinant leads to a dispersion relation. We investigate wave properties by using graphical representation of the wave vector, the refractive index, change in refractive index, phase and group velocities. Also, the modes of wave dispersion are explored. The results indicate the existence of the Veselago medium.Comment: 24 pages, 12 figures, accepted for publication in Astrophys. Space Sci. arXiv admin note: text overlap with arXiv:1101.0884 and arxiv:1007.285

Asymptotically Improved Convergence of Optimized Perturbation Theory in the Bose-Einstein Condensation Problem

We investigate the convergence properties of optimized perturbation theory, or linear $\delta$ expansion (LDE), within the context of finite temperature phase transitions. Our results prove the reliability of these methods, recently employed in the determination of the critical temperature T_c for a system of weakly interacting homogeneous dilute Bose gas. We carry out the explicit LDE optimized calculations and also the infrared analysis of the relevant quantities involved in the determination of $T_c$ in the large-N limit, when the relevant effective static action describing the system is extended to O(N) symmetry. Then, using an efficient resummation method, we show how the LDE can exactly reproduce the known large-N result for $T_c$ already at the first non-trivial order. Next, we consider the finite N=2 case where, using similar resummation techniques, we improve the analytical results for the nonperturbative terms involved in the expression for the critical temperature allowing comparison with recent Monte Carlo estimates of them. To illustrate the method we have considered a simple geometric series showing how the procedure as a whole works consistently in a general case.Comment: 38 pages, 3 eps figures, Revtex4. Final version in press Phys. Rev.