Numerical simulation of Quasi-Normal Modes in time-dependent background

We study the massless scalar wave propagation in the time-dependent Schwarzschild black hole background. We find that the Kruskal coordinate is an appropriate framework to investigate the time-dependent spacetime. A time-dependent scattering potential is derived by considering dynamical black hole with parameters changing with time. It is shown that in the quasinormal ringing both the decay time-scale and oscillation are modified in the time-dependent background.Comment: 10 pages, 8 figures; reference adde

Counting the changes of random Δ20 sets

We study the number of changes of the initial segment Zs ↾n for computable approximations of a Martin-Löf random Δ02Δ20 set Z. We establish connections between this number of changes and various notions of computability theoretic lowness, as well as the fundamental thesis that, among random sets, randomness is antithetical to computational power. We introduce a new randomness notion, called balanced randomness, which implies that for each computable approximation and each constant c, there are infinitely many n such that Zs ↾n changes more than c2n times. We establish various connections with ω-c.e. tracing and omega;-c.e. jump domination, a new lowness property. We also examine some relationships to randomness theoretic notions of highness, and give applications to the study of (weak) Demuth cuppability.Fil: Figueira, Santiago. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Hirschfeldt, Denis R.. University of Chicago; Estados UnidosFil: Miller, Joseph S.. University of Wisconsin; Estados UnidosFil: Ng, Keng Meng. Nanyang Technological University; SingapurFil: Nies, André. The University Of Auckland; Nueva Zeland

Variational inference formulation for a model-free simulation of a dynamical system with unknown parameters by a recurrent neural network

We propose a recurrent neural network for a "model-free" simulation of a dynamical system with unknown parameters without prior knowledge. The deep learning model aims to jointly learn the nonlinear time marching operator and the effects of the unknown parameters from a time series dataset. We assume that the time series data set consists of an ensemble of trajectories for a range of the parameters. The learning task is formulated as a statistical inference problem by considering the unknown parameters as random variables. A latent variable is introduced to model the effects of the unknown parameters, and a variational inference method is employed to simultaneously train probabilistic models for the time marching operator and an approximate posterior distribution for the latent variable. Unlike the classical variational inference, where a factorized distribution is used to approximate the posterior, we employ a feedforward neural network supplemented by an encoder recurrent neural network to develop a more flexible probabilistic model. The approximate posterior distribution makes an inference on a trajectory to identify the effects of the unknown parameters. The time marching operator is approximated by a recurrent neural network, which takes a latent state sampled from the approximate posterior distribution as one of the input variables, to compute the time evolution of the probability distribution conditioned on the latent variable. In the numerical experiments, it is shown that the proposed variational inference model makes a more accurate simulation compared to the standard recurrent neural networks. It is found that the proposed deep learning model is capable of correctly identifying the dimensions of the random parameters and learning a representation of complex time series data

Numerical simulation of the massive scalar field evolution in the Reissner-Nordstr\"{o}m black hole background

We studied the massive scalar wave propagation in the background of Reissner-Nordstr\"{o}m black hole by using numerical simulations. We learned that the value $Mm$ plays an important role in determining the properties of the relaxation of the perturbation. For $Mm << 1$ the relaxation process depends only on the field parameter and does not depend on the spacetime parameters. For $Mm >> 1$, the dependence of the relaxation on the black hole parameters appears. The bigger mass of the black hole, the faster the perturbation decays. The difference of the relaxation process caused by the black hole charge $Q$ has also been exhibited.Comment: Accepted for publication in Phys. Rev.

Geometry of the extreme Kerr black holes

Geometrical properties of the extreme Kerr black holes in the topological sectors of nonextreme and extreme configurations are studied. We find that the Euler characteristic plays an essential role to distinguish these two kinds of extreme black holes. The relationship between the geometrical properties and the intrinsic thermodynamics are investigated.Comment: Latex version, 10 page

Quasinormal Modes in three-dimensional time-dependent Anti-de Sitter spacetime

The massless scalar wave propagation in the time-dependent BTZ black hole background has been studied. It is shown that in the quasi-normal ringing both the decay and oscillation time-scales are modified in the time-dependent background.Comment: 8 pages and 7 figure

Recent development in spinel cobaltites for supercapacitor application

Precious metal oxides exhibit impressive characteristics that caught worldwide attention due to their promising capacitive performance, excellent electrochemical stability and low resistance, and these metal oxides have been extensively employed in supercapacitor application. This type of supercapacitors is known as redox supercapacitors or pseudocapacitors which applied faradaic process in storing energy in their systems. Thus, new materials with impressive electrochemical performance are highly demanded. In this aspect, cobaltite system with spinel structure has been the subject of intense research due to its established applications in electrochemistry. Besides, carbonaceous materials like activated carbons, carbon nanotubes, graphites, graphenes and fullerenes utilize electric double-layer capacitance whereby energy is stored by charge separation at an electrode/electrolyte interface. With greater development conducted on metal oxides and carbonaceous materials for supercapacitor application, introduction of hybrid and composite electrodes comprise of these two types of materials have been well received

On Central Charges and Hamiltonians for 0-brane dynamics

We consider general properties of central charges of zero branes and associated duality invariants, in view of their double role, on the bulk and on the world volume (quantum-mechanical) theory. A detailed study of the BPS condition for the mass spectrum arising from toroidal compactifications is given for 1/2, 1/4 and 1/8 BPS states in any dimensions. As a byproduct, we retreive the U-duality invariant conditions on the charge (zero mode) spectrum and the orbit classification of BPS states preserving different fractions of supersymmetry. The BPS condition for 0-branes in theories with 16 supersymmetries in any dimension is also discussed.Comment: 23 pages, latex fil

Dirac Cosmology and the Acceleration of the Contemporary Universe

A model is suggested to unify the Einstein GR and Dirac Cosmology. There is one adjusted parameter $b_2$ in our model. After adjusting the parameter $b_2$ in the model by using the supernova data, we have calculated the gravitational constant $\bar G$ and the physical quantities of $a(t)$, $q(t)$ and $\rho_r(t)/ \rho_b(t)$ by using the present day quantities as the initial conditions and found that the equation of state parameter $w_{\theta}$ equals to -0.83, the ratio of the density of the addition creation $\Omega_{\Lambda}=0.8$ and the ratio of the density of the matter including multiplication creation, radiation and normal matter $\Omega_m =0.2$ at present. The results are self-consistent and in good agreement with present knowledge in cosmology. These results suggest that the addition creation and multiplication creation in Dirac cosmology play the role of the dark energy and dark matter.Comment: 13 pages, 8 figure

UK export performance research - review and implications

Previous research on export performance has been criticized for being a mosaic of autonomous endeavours and for a lack of theoretical development. Building upon extant models of export performance, and a review and analysis of research on export performance in the UK for the period 1990-2005, an integrated model of export performance is developed and theoretical explanations of export performance are put forward. It is suggested that a multi-theory approach to explaining export performance is viable. Management and policy implications for the UK emerging from the review and synthesis of the literature and the integrated model are discussed