Zeros of Jacobi functions of second kind

The number of zeros in (- 1, 1) of the Jacobi function of second kind Q(n)((alpha, beta)) (x), alpha, beta > - 1, i.e. The second solution of the differential equation(1 - x(2))y (x) + (beta - alpha - (alpha + beta + 2)x)y' (x) + n(n + alpha + beta + 1)y(x) = 0,is determined for every n is an element of N and for all values of the parameters alpha > - 1 and beta > - 1. It turns out that this number depends essentially on alpha and beta as well as on the specific normalization of the function Q(n)((alpha, beta)) (x). Interlacing properties of the zeros are also obtained. As a consequence of the main result, we determine the number of zeros of Laguerre's and Hermite's functions of second kind. (c) 2005 Elsevier B.V. All rights reserved.

Superstrings in 2D backgrounds with R-R flux and new extremal black holes

The hybrid formalism is used to quantize the superstring compactified to two-dimensional target-space in a manifestly spacetime supersymmetric manner. A quantizable sigma model action is then constructed for the type II superstring in curved two-dimensional supergravity backgrounds which can include Ramond-Ramond flux. Such curved backgrounds include Calabi-Yau fourfold compactifications with Ramond-Ramond flux, and new extremal black hole solutions in two-dimensional dilaton supergravity theory. These black hole solutions are a natural generalization of the CGHS model and might be possible to describe using a supergroup version of the SL(2, R)/U(1) WZW model. We also study some dynamical aspects of the new black holes, such as formation and evaporation. (C) 2001 Published by Elsevier B.V. B.V.

Conformal Klein-Gordon equations and quasinormal modes

Using conformal coordinates associated with conformal relativity-associated with de Sitter spacetime homeomorphic projection into Minkowski spacetime-we obtain a conformal Klein-Gordon partial differential equation, which is intimately related to the production of quasi-normal modes (QNMs) oscillations, in the context of electromagnetic and/or gravitational perturbations around, e.g., black holes. While QNMs arise as the solution of a wave-like equation with a Poschl-Teller potential, here we deduce and analytically solve a conformal 'radial' d'Alembert-like equation, from which we derive QNMs formal solutions, in a proposed alternative to more completely describe QNMs. As a by-product we show that this 'radial' equation can be identified with a Schrodinger-like equation in which the potential is exactly the second Poschl-Teller potential, and it can shed some new light on the investigations concerning QNMs.

Correlation times in stochastic equations with delayed feedback and multiplicative noise

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Black hole partition function using the hybrid formalism of superstrings

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

On some classes of exactly-solvable Klein-Gordon equations

In this work we discuss some exactly solvable Klein-Gordon equations. We basically discuss the existence of classes of potentials with different nonrelativistic limits, but which shares the intermediate effective Schroedinger differential equation. We comment about the possible use of relativistic exact solutions as approximations for nonrelativistic inexact potentials. (c) 2005 Elsevier B.V. All rights reserved.

Sliding Vector Fields via Slow-Fast Systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Analytical optimization of spread and change of exponential decay of generalized Wannier functions in one dimension

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dissipative three-wave structures in stimulated backscattering. I. A subluminous solitary attractor

We present a solitary solution of the three-wave nonlinear partial differential equation (PDE) model - governing resonant space-time stimulated Brillouin or Raman backscattering - in the presence of a cw pump and dissipative material and Stokes waves. The study is motivated by pulse formation in optical fiber experiments. As a result of the instability any initial bounded Stokes signal is amplified and evolves to a subluminous backscattered Stokes pulse whose shape and velocity are uniquely determined by the damping coefficients and the cw-pump level. This asymptotically stable solitary three-wave structure is an attractor for any initial conditions in a compact support, in contrast to the known superluminous dissipative soliton solution which calls for an unbounded support. The linear asymptotic theory based on the Kolmogorov-Petrovskii-Piskunov assertion allows us to determine analytically the wave-front slope and the subluminous velocity, which are in remarkable agreement with the numerical computation of the nonlinear PDE model when the dynamics attains the asymptotic steady regime. © 1997 The American Physical Society.

Object oriented modeling of piston engines

This work reports a conception phase of a piston engine global model. The model objective is forecast the motor performance (power, torque and specific consumption as a function of rotation and environmental conditions). Global model or Zero-dimensional is based on flux balance through each engine component. The resulting differential equations represents a compressive unsteady flow, in which, all dimensional variables are areas or volumes. A review is presented first. The ordinary differential equation system is presented and a Runge-Kutta method is proposed to solve it numerically. The model includes the momentum conservation equation to link the gas dynamics with the engine moving parts rigid body mechanics. As an oriented to objects model the documentation follows the UML standard. A discussion about the class diagrams is presented, relating the classes with physical model related. The OOP approach allows evolution from simple models to most complex ones without total code rewrite. Copyright © 2001 Society of Automotive Engineers, Inc.

Stable two-dimensional dispersion-managed soliton

The existence of a dispersion-managed soliton in two-dimensional nonlinear Schrodinger equation with periodically varying dispersion has been explored. The averaged equations for the soliton width and chirp are obtained which successfully describe the long time evolution of the soliton. The slow dynamics of the soliton around the fixed points for the width and chirp are investigated and the corresponding frequencies are calculated. Analytical predictions are confirmed by direct partial differential equation (PDE) and ordinary differential equation (ODE) simulations. Application to a Bose-Einstein condensate in optical lattice is discussed. The existence of a dispersion-managed matter-wave soliton in such system is shown.

Analytical/numerical hybrid solution for one-dimensional ablation problem

Ablation is a thermal protection process with several applications in engineering, mainly in the field of airspace industry. The use of conventional materials must be quite restricted, because they would suffer catastrophic flaws due to thermal degradation of their structures. However, the same materials can be quite suitable once being protected by well-known ablative materials. The process that involves the ablative phenomena is complex, could involve the whole or partial loss of material that is sacrificed for absorption of energy. The analysis of the ablative process in a blunt body with revolution geometry will be made on the stagnation point area that can be simplified as a one-dimensional plane plate problem, hi this work the Generalized Integral Transform Technique (GITT) is employed for the solution of the non-linear system of coupled partial differential equations that model the phenomena. The solution of the problem is obtained by transforming the non-linear partial differential equation system to a system of coupled first order ordinary differential equations and then solving it by using well-established numerical routines. The results of interest such as the temperature field, the depth and the rate of removal of the ablative material are presented and compared with those ones available in the open literature.

The Canny detector with edge region focusing using an anisotropic diffusion process

This paper proposes a methodology for edge detection in digital images using the Canny detector, but associated with a priori edge structure focusing by a nonlinear anisotropic diffusion via the partial differential equation (PDE). This strategy aims at minimizing the effect of the well-known duality of the Canny detector, under which is not possible to simultaneously enhance the insensitivity to image noise and the localization precision of detected edges. The process of anisotropic diffusion via thePDE is used to a priori focus the edge structure due to its notable characteristic in selectively smoothing the image, leaving the homogeneous regions strongly smoothed and mainly preserving the physical edges, i.e., those that are actually related to objects presented in the image. The solution for the mentioned duality consists in applying the Canny detector to a fine gaussian scale but only along the edge regions focused by the process of anisotropic diffusion via the PDE. The results have shown that the method is appropriate for applications involving automatic feature extraction, since it allowed the high-precision localization of thinned edges, which are usually related to objects present in the image. © Nauka/Interperiodica 2006.

Detecção de bordas em imagens digitais através de um processo de difusão anisotrópica não linear

The edges detection model by a non-linear anisotropic diffusion, consists in a mathematical model of smoothing based in Partial Differential Equation (PDE), alternative to the conventional low-pass filters. The smoothing model consists in a selective process, where homogeneous areas of the image are smoothed intensely in agreement with the temporal evolution applied to the model. The level of smoothing is related with the amount of undesired information contained in the image, i.e., the model is directly related with the optimal level of smoothing, eliminating the undesired information and keeping selectively the interest features for Cartography area. The model is primordial for cartographic applications, its function is to realize the image preprocessing without losing edges and other important details on the image, mainly airports tracks and paved roads. Experiments carried out with digital images showed that the methodology allows to obtain the features, e.g. airports tracks, with efficiency.

Limit cycles for singular perturbation problems via inverse integrating factor

In this paper singularly perturbed vector fields Xε defined in ℝ2 are discussed. The main results use the solutions of the linear partial differential equation XεV = div(Xε)V to give conditions for the existence of limit cycles converging to a singular orbit with respect to the Hausdorff distance. © SPM.