Symmetry analysis of an integrable reaction-diffusion equation

In this paper, we investigate the invariance and integrability properties of an integrable two-component reaction-diffusion equation. We perform Painleve analysis for both the reaction-diffusion equation modelled by a coupled nonlinear partial differential equations and its general similarity reduced ordinary differential equation and confirm its integrability. Further, we perform Lie symmetry analysis for this model. Interestingly our investigations reveals a rich variety of particular solutions, which have not been reported in the literature, for this model. (C) 2000 Elsevier B.V. Ltd. All rights reserved.

A Decomposition and Noise Removal Method Combining Diffusion Equation and Wave Atoms for Textured Images

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

Particular solution for anomalous diffusion equation with source term

In literature the phenomenon of diffusion has been widely studied, however for nonextensive systems which are governed by a nonlinear stochastic dynamic, there are a few soluble models. The purpose of this study is to present the solution of the nonlinear Fokker-Planck equation for a model of potential with barrier considering a term of absorption. Systems of this nature can be observed in various chemical or biological processes and their solution enriches the studies of existing nonextensive systems.

Bright solitons in coupled defocusing NLS equation supported by coupling: Application to Bose-Einstein condensation

We demonstrate the formation of bright solitons in coupled self-defocusing nonlinear Schrodinger (NLS) equation supported by attractive coupling. As an application we use a time-dependent dynamical mean-field model to study the formation of stable bright solitons in two-component repulsive Bose-Einstein condensates (BECs) supported by interspecies attraction in a quasi one-dimensional geometry. When all interactions are repulsive, there cannot be bright solitons. However, bright solitons can be formed in two-component repulsive BECs for a sufficiently attractive interspecies interaction, which induces an attractive effective interaction among bosons of same type. (c) 2005 Elsevier B.V. All rights reserved.

Squeezed states, generalized Hermite polynomials and pseudo-diffusion equation

We show that the wavefunctions 〈pq; λ|n〈, of the harmonic oscillator in the squeezed state representation, have the generalized Hermite polynomials as their natural orthogonal polynomials. These wavefunctions lead to generalized Poisson Distribution Pn(pq;λ), which satisfy an interesting pseudo-diffusion equation: ∂Pnp,q;λ) ∂λ= 1 4 [ ∂2 ∂p2-( 1 λ2) ∂2 ∂q2]P2(p,q;λ), in which the squeeze parameter λ plays the role of time. Th entropies Sn(λ) have minima at the unsqueezed states (λ=1), which means that squeezing or stretching decreases the correlation between momentum p and position q. © 1992.

An Informatics Technical Note on Interaction of DNA - Graphene Chemical Sensor System as Reaction-Diffusion Wave-Based Computing System in Ionised Gaseous environments and their Applications Using Theoretical Studies and Scientific Computation Overview

The physics of plasmas encompasses basic problems from the universe and has assured us of promises in diverse applications to be implemented in a wider range of scientific and engineering domains, linked to most of the evolved and evolving fundamental problems. Substantial part of this domain could be described by R–D mechanisms involving two or more species (reaction–diffusion mechanisms). These could further account for the simultaneous non-linear effects of heating, diffusion and other related losses. We mention here that in laboratory scale experiments, a suitable combination of these processes is of vital importance and very much decisive to investigate and compute the net behaviour of plasmas under consideration. Plasmas are being used in the revolution of information processing, so we considered in this technical note a simple framework to discuss and pave the way for better formalisms and Informatics, dealing with diverse domains of science and technologies. The challenging and fascinating aspects of plasma physics is that it requires a great deal of insight in formulating the relevant design problems, which in turn require ingenuity and flexibility in choosing a particular set of mathematical (and/or experimental) tools to implement them.

Dynamics in dumbbell domains I. Continuity of the set of equilibria

We analyze the dynamics of a reaction-diffusion equation with homogeneous Neumann boundary conditions in a dumbbell domain. We provide an appropriate functional setting to treat this problem and, as a first step, we show in this paper the continuity of the set of equilibria and of its linear unstable manifolds. (c) 2006 Elsevier B.V. All rights reserved.

Dynamics in dumbbell domains III. Continuity of attractors

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

How population loss through habitat boundaries determines the dynamics of a predator-prey system

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

Coordinate and time-dependent diffusion dynamics in protein folding

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

NUMERICAL SIMULATION of CONVECTION-DIFFUSION PROBLEMS BY THE CONTROL-VOLUME-BASED FINITE-ELEMENT METHOD

This work presents a numerical study of the tri-dimensional convection-diffusion equation by the control-volume-based on finite-element method using quadratic hexahedral elements. Considering that the equation governing this problem in its main variable may represent several properties, including temperature, turbulent kinetic energy, viscous dissipation rate of the turbulent kinetic energy, specific dissipation rate of the turbulent kinetic energy, or even the concentration of a contaminant in a given medium, among others, the wide applicability of this problem is thus evidenced. Three cases of temperature distributions will be studied specifically in this work, in addition to one case of pollutant dispersion upon analysis of the concentration of a contaminant in a fixed flow point. Some comparisons will be carried out against works found in the open literature, while others will be done according to each phenomenon characteristics.

Edge detection and noise removal by use of a partial differential equation with automatic selection of parameters

This work deals with noise removal by the use of an edge preserving method whose parameters are automatically estimated, for any application, by simply providing information about the standard deviation noise level we wish to eliminate. The desired noiseless image u(x), in a Partial Differential Equation based model, can be viewed as the solution of an evolutionary differential equation u t(x) = F(u xx, u x, u, x, t) which means that the true solution will be reached when t ® ¥. In practical applications we should stop the time ''t'' at some moment during this evolutionary process. This work presents a sufficient condition, related to time t and to the standard deviation s of the noise we desire to remove, which gives a constant T such that u(x, T) is a good approximation of u(x). The approach here focused on edge preservation during the noise elimination process as its main characteristic. The balance between edge points and interior points is carried out by a function g which depends on the initial noisy image u(x, t0), the standard deviation of the noise we want to eliminate and a constant k. The k parameter estimation is also presented in this work therefore making, the proposed model automatic. The model's feasibility and the choice of the optimal time scale is evident through out the various experimental results.

Dynamics in dumbbell domains II. The limiting problem

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Stochastic Skellam model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Lap number properties for p-Laplacian problems investigated by Lyapunov methods

In this work we consider a one-dimensional quasilinear parabolic equation and we prove that the lap number of any solution cannot increase through orbits as the time passes if the initial data is a continuous function. We deal with the lap number functional as a Lyapunov function, and apply lap number properties to reach an understanding on the asymptotic behavior of a particular problem. (c) 2006 Published by Elsevier Ltd.