Testing the principle of equivalence by supernova neutrinos

We study the possible impact of the neutrino oscillation which could be induced by a tiny violation of equivalence principle (VEP) on the observation of neutrinos emitted from supernova driven by gravitational collapse. We show that using supernova neutrinos, one can probe very small values of VEP parameters, delta(tau) less than or similar to O(10(-31)) for massless or degenerated neutrinos and delta(tau) less than or similar to O(10(-16)) x (Deltam(2)/10(-5) eV(2)) for massive neutrinos. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Fluctuating dimension in a discrete model for quantum gravity based on the spectral principle

The spectral principle of Connes and Chamseddine is used as a starting point to define a discrete model for Euclidean quantum gravity. Instead of summing over ordinary geometries, we consider the sum over generalized geometries where topology, metric, and dimension can fluctuate. The model describes the geometry of spaces with a countable number n of points, and is related to the Gaussian unitary ensemble of Hermitian matrices. We show that this simple model has two phases. The expectation value , the average number of points in the Universe, is finite in one phase and diverges in the other. We compute the critical point as well as the critical exponent of . Moreover, the space-time dimension delta is a dynamical observable in our model, and plays the role of an order parameter. The computation of is discussed and an upper bound is found, < 2.

Quantitative estimates of time-averaging in terebratulid brachiopod shell accumulations from a modern tropical shelf

Quantitative estimates of time-averaging in marine shell accumulations available to date are limited primarily to aragonitic mollusk shells. We assessed time-averaging in Holocene assemblages of calcitic brachiopod shells by direct dating of individual specimens of the terebratulid brachiopod Bouchardia rosea. The data were collected from exceptional (brachiopod-rich) shell assemblages, occurring surficially on a tropical mixed carbonate-siliciclastic shelf (the Southeast Brazilian Bight, SW Atlantic), a setting that provides a good climatic and environmental analog for many Paleozoic brachiopod shell beds of North America and Europe. A total of 82 individual brachiopod shells, collected from four shallow (5-25 m) nearshore (<2.5 km from the shore) localities, were dated by using amino acid racemization (D-alloisoleucine/L-isoleucine value) calibrated with five AMS-radiocarbon dates (r(2) = 0.933). This is the first study to demonstrate that amino acid racemization methods can provide accurate and precise ages for individual shells of calcitic brachiopods.The dated shells vary in age from modern to 3000 years, with a standard deviation of 690 years. The age distribution is strongly right-skewed: the young shells dominate the dated specimens and older shells are increasingly less common. However, the four localities display significant differences in the range of time-averaging and the form of the age distribution. The dated shells vary notably in the quality of preservation, but there is no significant correlation between taphonomic condition and age, either for individual shells or at assemblage level.These results demonstrate that fossil brachiopods may show considerable time-averaging, but the scale and nature of that mixing may vary greatly among sites. Moreover, taphonomic condition is not a reliable indicator of pre-burial history of individual brachiopod shells or the scale of temporal mixing within the entire assemblage. The results obtained for brachiopods are strikingly similar to results previously documented for mollusks and suggest that differences in mineralogy and shell microstructure are unlikely to be the primary factors controlling the nature and scale of time-averaging. Environmental factors and local fluctuations in populations of shell-producing organisms are more likely to be the principal determinants of time-averaging in marine benthic shelly assemblages. The long-term survival of brachiopod shells is incongruent with the rapid shell destruction observed in taphonomic experiments. The results support the taphonomic model that shells remain protected below (but perhaps near) the surface through their early taphonomic history. They may be brought back up to the surface intermittently by bioturbation and physical reworking, but only for short periods of time. This model explains the striking similarities in time-averaging among different types of organisms and the lack of correlation between time-since-death and shell taphonomy.

Kinetics of the polarization reversal process in a non-constant applied electric field and the generalized superposition principle

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Fourier duality as a quantization principle

The Weyl-Wigner prescription for quantization on Euclidean phase spaces makes essential use of Fourier duality. The extension of this property to more general phase spaces requires the use of Kac algebras, which provide the necessary background for the implementation of Fourier duality on general locally compact groups. Kac algebras - and the duality they incorporate - are consequently examined as candidates for a general quantization framework extending the usual formalism. Using as a test case the simplest nontrivial phase space, the half-plane, it is shown how the structures present in the complete-plane case must be modified. Traces, for example, must be replaced by their noncommutative generalizations - weights - and the correspondence embodied in the Weyl-Wigner formalism is no longer complete. Provided the underlying algebraic structure is suitably adapted to each case, Fourier duality is shown to be indeed a very powerful guide to the quantization of general physical systems.

The δ expansion and the principle of minimal sensitivity

The δ-expansion is a nonperturbative approach for field theoretic models which combines the techniques of perturbation theory and the variational principle. Different ways of implementing the principle of minimal sensitivity to the δ-expansion produce in general different results for observables. For illustration we use the Nambu-Jona-Lasinio model for chiral symmetry restoration at finite density and compare results with those obtained with the Hartree-Fock approximation.

On non-ideal and non-linear portal frame dynamics analysis using Bogoliubov averaging method

We apply the Bogoliubov Averaging Method to the study of the vibrations of an elastic foundation, forced by a Non-ideal energy source. The considered model consists of a portal plane frame with quadratic nonlinearities, with internal resonance 1:2, supporting a direct current motor with limited power. The non-ideal excitation is in primary resonance in the order of one-half with the second mode frequency. The results of the averaging method, plotted in time evolution curve and phase diagrams are compared to those obtained by numerically integrating of the original differential equations. The presence of the saturation phenomenon is verified by analytical procedures.

Road segment delineation using active testing principle and an edge-based post-processing strategy

This paper presents a semi-automated method for extracting road segments from medium-resolution images based on active testing and edge analysis. The method is based on two sequential and independent stages. Firstly, an active testing method is used to extract an approximated road centreline which is based on a sequential and local exploitation of the image. Secondly, an iterative strategy based on edge analysis and the approximated centreline is used to measure precisely the road centreline. Based on the results obtained using medium-resolution test images, the method seems to be very promising. In general, the method proved to be very accurate whenever the roads are characterized by two well-defined anti-parallel edges and robust even in the presence of larger obstacles such as trees and shadows.

Schwinger's principle and gauge fixing in the free electromagnetic field

A manifestly covariant treatment of the free quantum eletromagnetic field, in a linear covariant gauge, is implemented employing Schwinger's variational principle and the B-field formalism. It is also discussed the Abelian Proca model as an example of a system without constraints. © Società Italiana di Fisica.

Is the equivalence principle doomed forever to Dante's Inferno on account of quantum mechanics?

It is commonly assumed that the equivalence principle can coexist without conflict with quantum mechanics. We shall argue here that, contrary to popular belief, this principle does not hold in quantum mechanics. We illustrate this point by computing the second-order correction for the scattering of a massive scalar boson by a weak gravitational field, treated as an external field. The resulting cross-section turns out to be mass-dependent. A way out of this dilemma would be, perhaps, to consider gravitation without the equivalence principle. At first sight, this seems to be a too much drastic attitude toward general relativity. Fortunately, the teleparallel version of general relativity - a description of the gravitational interaction by a force similar to the Lorentz force of electromagnetism and that, of course, dispenses with the equivalence principle - is equivalent to general relativity, thus providing a consistent theory for gravitation in the absence of the aforementioned principle. © World Scientific Publishing Company.

3-Dimensional hopf bifurcation via averaging theory

We consider the Lorenz system ẋ = σ(y - x), ẏ = rx - y - xz and ż = -bz + xy; and the Rössler system ẋ = -(y + z), ẏ = x + ay and ż = b - cz + xz. Here, we study the Hopf bifurcation which takes place at q± = (±√br - b,±√br - b, r - 1), in the Lorenz case, and at s± = (c+√c2-4ab/2, -c+√c2-4ab/2a, c±√c2-4ab/2a) in the Rössler case. As usual this Hopf bifurcation is in the sense that an one-parameter family in ε of limit cycles bifurcates from the singular point when ε = 0. Moreover, we can determine the kind of stability of these limit cycles. In fact, for both systems we can prove that all the bifurcated limit cycles in a neighborhood of the singular point are either a local attractor, or a local repeller, or they have two invariant manifolds, one stable and the other unstable, which locally are formed by two 2-dimensional cylinders. These results are proved using averaging theory. The method of studying the Hopf bifurcation using the averaging theory is relatively general and can be applied to other 3- or n-dimensional differential systems.

Conflict between the classical equivalence principle and quantum mechanics

As far as external gravitational fields described by Newton's theory are concerned, theory shows that there is an unavoidable conflict between the universality of free fall (Galileo's equivalence principle) and quantum mechanics - a result confirmed by experiment. Is this conflict due perhaps to the use of Newton's gravity, instead of general relativity, in the analysis of the external gravitational field? The response is negative. To show this we compute the low corrections to the cross-section for the scattering of different quantum particles by an external gravitational field, treated as an external field, in the framework of Einstein's linearized gravity. To first order the cross-sections are spin-dependent; if the calculations are pushed to the next order they become dependent upon energy as well. Therefore, the Galileo's equivalence and, consequently, the classical equivalence principle, is violated in both cases. We address these issues here.

A maximum principle for infinite time asymptotically stable impulsive dynamic control systems

We consider an infinite horizon optimal impulsive control problems for which a given cost function is minimized by choosing control strategies driving the state to a point in a given closed set C ∞. We present necessary conditions of optimality in the form of a maximum principle for which the boundary condition of the adjoint variable is such that non-degeneracy due to the fact that the time horizon is infinite is ensured. These conditions are given for conventional systems in a first instance and then for impulsive control problems. They are proved by considering a family of approximating auxiliary interval conventional (without impulses) optimal control problems defined on an increasing sequence of finite time intervals. As far as we know, results of this kind have not been derived previously. © 2010 IFAC.