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.

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.

A regularized nonlinear diffusion approach for texture image denoising

In this paper a new partial differential equation based method is presented with a view to denoising images having textures. The proposed model combines a nonlinear anisotropic diffusion filter with recent harmonic analysis techniques. A wave atom shrinkage allied to detection by gradient technique is used to guide the diffusion process so as to smooth and maintain essential image characteristics. Two forcing terms are used to maintain and improve edges, boundaries and oscillatory features of an image having irregular details and texture. Experimental results show the performance of our model for texture preserving denoising when compared to recent methods in literature. © 2009 IEEE.

Utilização de equações diferenciais parciais no tratamento de imagens orbitais

Pós-graduação em Ciências Cartográficas - FCT

Simulação numérica de escoamentos gás-sólido em leito fluidizado borbulhante utilizando a teoria cinética dos escoamentos granulares

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Restauração de imagens digitais com texturas utilizando técnicas de decomposição e equações diferenciais parciais

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

Estudo de métodos numéricos para eliminação de ruídos em imagens digitais

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Modelos matemáticos para o retoque digital de imagens

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estudos de técnicas de reinicialização em métodos level-set e suas aplicações em escoamentos bifásicos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

An inverse method to estimate the moving heat source in machining process

The present work propounds an inverse method to estimate the heat sources in the transient two-dimensional heat conduction problem in a rectangular domain with convective bounders. The non homogeneous partial differential equation (PDE) is solved using the Integral Transform Method. The test function for the heat generation term is obtained by the chip geometry and thermomechanical cutting. Then the heat generation term is estimated by the conjugated gradient method (CGM) with adjoint problem for parameter estimation. The experimental trials were organized to perform six different conditions to provide heat sources of different intensities. This method was compared with others in the literature and advantages are discussed. (C) 2012 Elsevier Ltd. All rights reserved.

Temporal constraints in large optical flow estimation

[EN] The aim of this work is to propose a model for computing the optical flow in a sequence of images. We introduce a new temporal regularizer that is suitable for large displacements. We propose to decouple the spatial and temporal regularizations to avoid an incongruous formulation. For the spatial regularization we use the Nagel-Enkelmann operator and a newly designed temporal regularization. Our model is based on an energy functional that yields a partial differential equation (PDE). This PDE is embedded into a multipyramidal strategy to recover large displacements. A gradient descent technique is applied at each scale to reach the minimum.