Generic Bifurcations of Planar Filippov Systems via Geometric Singular Perturbations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A geometric interpretation for transmission real losses minimization through the optimal power flow and its influence on voltage collapse

This work presents an approach for geometric solution of an optimal power flow (OPF) problem for a two bus system (a slack and a PV busses). Additionally, the geometric relationship between the losses minimization and the increase of the reactive margin and, therefore, the maximum loading point, is shown. The algebraic equations for the calculation of the Lagrange multipliers and for the minimum losses value are obtained. These equations are used to validate the results obtained using an OPF program. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Improved geometric parameterisation techniques for continuation power flow

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Geographic variation in cranial shape in the Pumpkin Toadlet (Brachycephalus ephippium): A geometric analysis

The description of patterns of variation in any character system within well-defined species is fundamental for understanding lineage diversification and the identification of geographic units that represent opportunities for sustained evolutionary divergence. In this paper, we analyze intraspecific variation in cranial shape in the Pumpkin Toadlet, Brachycephalus ephippium-a miniaturized species composed of isolated populations on the slopes of the mountain ranges of southeastern Brazil. Shape variables were derived using geometric-statistical methods that describe shape change as localized deformations in a spatial framework defined by anatomical landmarks in the cranium of B. ephippium. By statistically weighting differences between landmarks that are not close together (changes at larger geometric scale), cranial variation among geographic samples of B. ephippium appears continuous with no obvious gaps. This pattern of variation is caused by a confounding effect between within-sample allometry and among-sample shape differences. In contrast, by statistically weighting differences between landmarks that are at close spacing (changes at smaller geometric scale), differences in shape within- and among-sample variation are not confounded, and a marked geographic differentiation among population samples of B. ephippium emerges. The observed pattern of geographic differentiation in cranial shape apparently cannot be explained as isolation-by-distance. This study provides the first evidence that the detection of morphological variation or lack thereof, that is, morphological conservatism, may be conditional on the scale of measurement of variation in shape within the methodological formalism of geometric morphometrics.

Quantization rules for bound states in quantum wells

An algebraic reformulation of the Bohr-Sommerfeld (BS) quantization rule is suggested and applied to the study of bound states in one-dimensional quantum wells. The energies obtained with the present quantization rule are compared to those obtained with the usual BS and WKB quantization rules and with the exact solution of the Schrodinger equation. We find that, in diverse cases of physical interest in molecular physics, the present quantization rule not only yields a good approximation to the exact solution of the Schrodinger equation, but yields more precise energies than those obtained with the usual BS and/or WKB quantization rules. Among the examples considered numerically are the Poeschl-Teller potential and several anharmonic oscillator potentials. which simulate molecular vibrational spectra and the problem of an isolated quantum well structure subject to an external electric field.

Quantization of the electromagnetic field outside static black holes and its application to low-energy phenomena

We discuss the Gupta-Bleuler quantization of the free electromagnetic field outside static black holes in the Boulware vacuum. We use a gauge which reduces to the Feynman gauge in Minkowski spacetime. We also discuss its relation with gauges used previously. Then we apply the low-energy sector of this held theory to investigate some low-energy phenomena. First, we discuss the response rate of a static charge outside the Schwarzschild black hole in four dimensions. Next, motivated by string physics, we compute the absorption cross sections of low-energy plane waves for the Schwarzschild and extreme Reissner-Nordstrom black holes in arbitrary dimensions higher than three.

Quantization of the superstring in Ramond-Ramond backgrounds

Sigma model actions are constructed for the type II superstring compactified to four-and six-dimensional curved backgrounds which can contain non-vanishing Ramond-Ramond fields. These actions are N = 2 worldsheet superconformally invariant and can be covariantly quantized preserving manifest spacetime supersymmetry. They are constructed using a hybrid Version of superstring variables which combines features of the Ramond-Neveu-Schwarz and Green-Schwarz formalisms. For the AdS(2) x S-2 and AdS(3) x S-3 backgrounds, these actions differ from the classical Green-Schwarz actions by a crucial kinetic term for the fermions. Parts of this work have been done in collaborations with M Bershadsky, T Hauer, W Siegel, C Vafa, E Witten, S Zhukov and B Zwiebach.

Reply to comment on 'Quantization rules for bound states in quantum wells'

In this reply to the comment on 'Quantization rules for bound states in quantum wells' we point out some interesting differences between the supersymmetric Wentzel-Kramers-Brillouin (WKB) quantization rule and a matrix generalization of usual WKB (mWKB) and Bohr-Sommerfeld (mBS) quantization rules suggested by us. There are certain advantages in each of the supersymmetric WKB (SWKB), mWKB and mBS quantization rules. Depending on the quantum well, one of these could be more useful than the other and it is premature to claim unconditional superiority of SWKB over mWKB and mBS quantization rules.

Electric charge quantization and the muon anomalous magnetic moment

We investigate some proposals to solve the electric charge quantization puzzle that simultaneously explain the recent measured deviation on the muon anomalous magnetic moment. For this we assess extensions of the electro-weak standard model spanning modifications on the scalar sector only. It is interesting to verify that one can have modest extensions which easily account for the solution for both problems.

First quantized approaches to neutrino oscillations and second quantization

Neutrino oscillations are treated from the point of view of relativistic first quantized theories and compared to second quantized treatments. Within first quantized theories, general oscillation probabilities can be found for Dirac fermions and charged spin 0 bosons. A clear modification in the oscillation formulas can be obtained and its origin is elucidated and confirmed to be inevitable from completeness and causality requirements. The left-handed nature of created and detected neutrinos can also be implemented in the first quantized Dirac theory in the presence of mixing; the probability loss due to the changing of initially left-handed neutrinos to the undetected right-handed neutrinos can be obtained in analytic form. Concerning second quantized approaches, it is shown in a calculation using virtual neutrino propagation that both neutrinos and antineutrinos may also contribute as intermediate particles. The sign of the contributing neutrino energy may have to be chosen explicitly without being automatic in the formalism. At last, a simple second quantized description of the flavor oscillation phenomenon is devised. In this description there is no interference terms between positive and negative components, but it still gives simple normalized oscillation probabilities. A new effect appearing in this context is an inevitable but tiny violation of the initial flavor of neutrinos. The probability loss due to the conversion of left-handed neutrinos to right-handed neutrinos is also presented.

Covariant quantization of the superstring

After reviewing the Green-Schwarz superstring using the approach of Siegel, the superstring is covariantly quantized by constructing a BRST operator from the fermionic constraints and a bosonic pure spinor ghost variable. Physical massless vertex operators are constructed and, for the first time, N-point tree amplitudes are computed in a manifestly ten-dimensional super-Poincare covariant manner. Quantization can be generalized to curved supergravity backgrounds and the vertex operator for fluctuations around AdS(5) x S-5 is explicitly constructed.

Increase of temperature of an ideal nondegenerate quantum gas in a suddenly expanding box due to energy quantization

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Stochastic quantization of real-time thermal field theory

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Path integral quantization of generalized quantum electrodynamics

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Quantization of the Proca field in the Rindler wedge and the interaction of uniformly accelerated currents with massive vector bosons from the Unruh thermal bath

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)