Extended Birkhoff's Theorem in the f(T) Gravity

The f(T) theory, a generally modified teleparallel gravity, has been proposed as an alternative gravity model to account for the dark energy phenomena. Following our previous work [Xin-he Meng and Ying-bin Wang, EPJC(2011), arXiv:1107.0629v1], we prove that the Birkhoff's theorem holds in a more general context, specifically with the off diagonal tetrad case, in this communication letter. Then, we discuss respectively the results of the external vacuum and internal gravitational field in the f(T) gravity framework, as well as the extended meaning of this theorem. We also investigate the validity of the Birkhoff's theorem in the frame of f(T) gravity via conformal transformation by regarding the Brans-Dicke-like scalar as effective matter, and study the equivalence between both Einstein frame and Jordan frame.Comment: 7 pages, 1 figure, submitted to EPJ-C. arXiv admin note: substantial text overlap with arXiv:1107.062

Cherenkov radiation emitted by ultrafast laser pulses and the generation of coherent polaritons

We report on the generation of coherent phonon polaritons in ZnTe, GaP and LiTaO$_{3}$ using ultrafast optical pulses. These polaritons are coupled modes consisting of mostly far-infrared radiation and a small phonon component, which are excited through nonlinear optical processes involving the Raman and the second-order susceptibilities (difference frequency generation). We probe their associated hybrid vibrational-electric field, in the THz range, by electro-optic sampling methods. The measured field patterns agree very well with calculations for the field due to a distribution of dipoles that follows the shape and moves with the group velocity of the optical pulses. For a tightly focused pulse, the pattern is identical to that of classical Cherenkov radiation by a moving dipole. Results for other shapes and, in particular, for the planar and transient-grating geometries, are accounted for by a convolution of the Cherenkov field due to a point dipole with the function describing the slowly-varying intensity of the pulse. Hence, polariton fields resulting from pulses of arbitrary shape can be described quantitatively in terms of expressions for the Cherenkov radiation emitted by an extended source. Using the Cherenkov approach, we recover the phase-matching conditions that lead to the selection of specific polariton wavevectors in the planar and transient grating geometry as well as the Cherenkov angle itself. The formalism can be easily extended to media exhibiting dispersion in the THz range. Calculations and experimental data for point-like and planar sources reveal significant differences between the so-called superluminal and subluminal cases where the group velocity of the optical pulses is, respectively, above and below the highest phase velocity in the infrared.Comment: 13 pages, 11 figure

A resonant-term-based model including a nascent disk, precession, and oblateness: application to GJ 876

Investigations of two resonant planets orbiting a star or two resonant satellites orbiting a planet often rely on a few resonant and secular terms in order to obtain a representative quantitative description of the system's dynamical evolution. We present a semianalytic model which traces the orbital evolution of any two resonant bodies in a first- through fourth-order eccentricity or inclination-based resonance dominated by the resonant and secular arguments of the user's choosing. By considering the variation of libration width with different orbital parameters, we identify regions of phase space which give rise to different resonant ''depths,'' and propose methods to model libration profiles. We apply the model to the GJ 876 extrasolar planetary system, quantify the relative importance of the relevant resonant and secular contributions, and thereby assess the goodness of the common approximation of representing the system by just the presumably dominant terms. We highlight the danger in using ''order'' as the metric for accuracy in the orbital solution by revealing the unnatural libration centers produced by the second-order, but not first-order, solution, and by demonstrating that the true orbital solution lies somewhere ''in-between'' the third- and fourth-order solutions. We also present formulas used to incorporate perturbations from central-body oblateness and precession, and a protoplanetary or protosatellite thin disk with gaps, into a resonant system. We quantify these contributions to the GJ 876 system, and thereby highlight the conditions which must exist for multi-planet exosystems to be significantly influenced by such factors. We find that massive enough disks may convert resonant libration into circulation; such disk-induced signatures may provide constraints for future studies of exoplanet systems.Comment: 39 pages of body text, 21 figures, 5 tables, 1 appendix, accepted for publication in Celestial Mechanics and Dynamical Astronom

Typical structural properties of state spaces

Abstract. Explicit model checking algorithms explore the full state space of a system. We have gathered a large collection of state spaces and performed an extensive study of their structural properties. The results show that state spaces have several typical properties and that they differ significantly from both random graphs and regular graphs. We point out how to exploit these typical properties in practical model checking algorithms.

MATURIDADE EM GESTÃO AMBIENTAL: REVISITANDO AS MELHORES PRÁTICAS

Este estudo tem por objetivo avaliar os fundamentos da gestão ambiental em empresas localizadas em Goiás que utilizam as chamadas melhores práticas nesta área. Este estado teve um forte crescimento econômico nas últimas quatro décadas, mas as preocupações na área ambiental não necessariamente acompanharam este desenvolvimento. A avaliação tomou como base modelos de maturidade já utilizados pela literatura, que classificam a competência organizacional em gestão ambiental por meio de estágios que evoluem desde a inexperiência até o pleno domínio sobre o assunto. O trabalho de campo incluiu uma investigação sobre as atividades de três organizações em setores de grande relevância no estado: mineração, alimentos e bebidas e setor sucroalcooleiro. Foram realizados estudos de caso múltiplos tendo como principais evidências entrevistas, documentos e publicações sobre o assunto. Algumas empresas não se mostraram predispostas a abrir suas informações referentes à gestão ambiental, o que é compreensível uma vez que o tema envolve questões delicadas como a relação entre a organização e seu meio ambiente. Aquelas que se mostraram abertas para discutir o assunto indicaram estarem bem resolvidas em relação à questão. Foi o caso das três empresas objeto dos estudos de caso múltiplos. Os resultados mostraram que as empresas com alto grau de maturidade em gestão ambiental atuam de forma planejada, com estrutura organizacional dedicada e utilizam como referência padrões internacionais rigorosos sobre o tema.