Finite element modelling of dissipative structures for nonequilibrium chemical reactions in fluid-saturated porous media

We use the finite element method to model and predict the dissipative structures of chemical species for a nonequilibrium chemical reaction system in a fluid-saturated porous medium. In particular, we explore the conditions under which dissipative structures of the species may exist in the Brusselator type of nonequilibrium chemical reaction. Since this is the first time the finite element method and related strategies have been used to study the chemical instability problems in a fluid-saturated porous medium, it is essential to validate the method and strategies before they are put into application. For this purpose, we have rigorously derived the analytical solutions for dissipative structures of chemical species in a benchmark problem, which geometrically is a square. Comparison of the numerical solutions with the analytical ones demonstrates that the proposed numerical method and strategy are robust enough to solve chemical instability problems in a fluid-saturated porous medium. Finally, the related numerical results from two application examples indicate that both the regime and the magnitude of pore-fluid flow have significant effects on the nature of the dissipative structures that developed for a nonequilibrium chemical reaction system in a fluid-saturated porous medium. The motivation for this study is that self-organization under conditions of pore-fluid flow in a porous medium is a potential mechanism of the orebody formation and mineralization in the upper crust of the Earth. (C) 2000 Elsevier Science S.A. All rights reserved.

Dissipative nonlinear structures in fiber optics

Optical fiber materials exhibit a nonlinear response to strong electric fields, such as those of optical signals confined within the small fiber core. Fiber nonlinearity is an essential component in the design of the next generation of advanced optical communication systems, but its use is often avoided by engineers because of its intractability. The application of nonlinear technologies in fiber optics offers new opportunities for the design of photonic systems and devices. In this chapter, we make an overview of recent progress in mathematical theory and practical applications of temporal dissipative solitons and self-similar nonlinear structures in optical fiber systems. The design of all-optical high-speed signal processing devices, based on nonlinear dissipative structures, is discussed.

Dissipative nonlinear structures in optical fiber systems I : dissipative dispersion managed solitons in mode-locked lasers

In this first talk on dissipative structures in fiber applications, we extend theory of dispersion-managed solitons to dissipative systems with a focus on mode-locked fibre lasers. Dissipative structures exist at high map strengths leading to the generation of stable, short pulses with high energy. Two types of intra-map pulse evolutions are observed depending on the net cavity dispersion. These are characterized by a reduced model and semi-analytical solutions are obtained.

Dissipative nonlinear structures in optical fiber systems II : self-similar parabolic pulses in active fibers

In this second talk on dissipative structures in fiber applications, we overview theoretical aspects of the generation, evolution and characterization of self-similar parabolic-shaped pulses in fiber amplifier media. In particular, we present a perturbation analysis that describes the structural changes induced by third-order fiber dispersion on the parabolic pulse solution of the nonlinear Schrödinger equation with gain. Promising applications of parabolic pulses in optical signal post-processing and regeneration in communication systems are also discussed.

Dissipative nonlinear structures in optical fiber systems III : dissipative solitons via nonlinear mapping

In the third and final talk on dissipative structures in fiber applications, we discuss mathematical techniques that can be used to characterize modern laser systems that consist of several discrete elements. In particular, we use a nonlinear mapping technique to evaluate high power laser systems where significant changes in the pulse evolution per cavity round trip is observed. We demonstrate that dissipative soliton solutions might be effectively described using this Poincaré mapping approach.

Dissipative nonlinear structures in optical fiber systems I:dissipative dispersion managed solitons in mode-locked lasers

In this first talk on dissipative structures in fiber applications, we extend theory of dispersion-managed solitons to dissipative systems with a focus on mode-locked fibre lasers. Dissipative structures exist at high map strengths leading to the generation of stable, short pulses with high energy. Two types of intra-map pulse evolutions are observed depending on the net cavity dispersion. These are characterized by a reduced model and semi-analytical solutions are obtained.

Dissipative nonlinear structures in optical fiber systems II:self-similar parabolic pulses in active fibers

In this second talk on dissipative structures in fiber applications, we overview theoretical aspects of the generation, evolution and characterization of self-similar parabolic-shaped pulses in fiber amplifier media. In particular, we present a perturbation analysis that describes the structural changes induced by third-order fiber dispersion on the parabolic pulse solution of the nonlinear Schrödinger equation with gain. Promising applications of parabolic pulses in optical signal post-processing and regeneration in communication systems are also discussed.

Dissipative nonlinear structures in optical fiber systems III:dissipative solitons via nonlinear mapping

In the third and final talk on dissipative structures in fiber applications, we discuss mathematical techniques that can be used to characterize modern laser systems that consist of several discrete elements. In particular, we use a nonlinear mapping technique to evaluate high power laser systems where significant changes in the pulse evolution per cavity round trip is observed. We demonstrate that dissipative soliton solutions might be effectively described using this Poincaré mapping approach.

Dissipative nonlinear structures in fiber optics

Optical fiber materials exhibit a nonlinear response to strong electric fields, such as those of optical signals confined within the small fiber core. Fiber nonlinearity is an essential component in the design of the next generation of advanced optical communication systems, but its use is often avoided by engineers because of its intractability. The application of nonlinear technologies in fiber optics offers new opportunities for the design of photonic systems and devices. In this chapter, we make an overview of recent progress in mathematical theory and practical applications of temporal dissipative solitons and self-similar nonlinear structures in optical fiber systems. The design of all-optical high-speed signal processing devices, based on nonlinear dissipative structures, is discussed.

Dissipative metabolic patterns respond during neutrophil transmembrane signaling

Self-organization is a common theme in biology. One mechanism of self-organization is the creation of chemical patterns by the diffusion of chemical reactants and their nonlinear interactions. We have recently observed sustained unidirectional traveling chemical redox [NAD(P)H − NAD(P)+] waves within living polarized neutrophils. The present study shows that an intracellular metabolic wave responds to formyl peptide receptor agonists, but not antagonists, by splitting into two waves traveling in opposite directions along a cell's long axis. Similar effects were noted with other neutrophil-activating substances. Moreover, when cells were exposed to an N-formyl-methionyl-leucyl-phenylalanine (FMLP) gradient whose source was perpendicular to the cell's long axis, cell metabolism was locally perturbed with reorientation of the pattern in a direction perpendicular to the initial cellular axis. Thus, extracellular activating signals and the signals' spatial cues are translated into distinct intracellular dissipative structures.

Dissipative dispersion-managed solitons in mode-locked lasers

We extend the theory of dispersion-managed solitons to dissipative systems with a focus on mode-locked fiber lasers. Dissipative structures exist at high map strengths, leading to the generation of stable, short pulses with high energy. Two types of intramap pulse evolution are observed depending on the net cavity dispersion. These are characterized by a reduced model, and semianalytical solutions are obtained.

Dissipative dispersion managed solitons in mode-locked fibre lasers

We extend theory of dispersion-managed solitons to dissipative systems with a focus on mode-locked fibre lasers. Dissipative structures exist at high map strengths, and different pulse evolutions are observed depending on the net cavity dispersion.

Dissipative dispersion managed solitons in mode-locked fibre lasers

We extend theory of dispersion-managed solitons to dissipative systems with a focus on mode-locked fibre lasers. Dissipative structures exist at high map strengths, and different pulse evolutions are observed depending on the net cavity dispersion.

Historicidade, entropia e não-linearidade : algumas aplicações possíveis na Ciência Econômica

The objective of this paper is to definite Historicity in Economic Sciences applying the principles of Entropy and methodological indeterminism. This implies the definition of two kinds of economic universes: one characterized by ergodicity and reversibility of Time and processes and the other by the opposite properties. The first part will deal with the construction of the subject of study and the nature of the proper analysis to these two universes. Taking such dichotomy into account, the second part will examine its implications as regards to the nature of equilibrium, the properties of stability and instability and the closure of the systems.

O paradigma sistêmico na Ciência Econômica : convergências entre Veblen, estruturas dissipativas e autopoiese

O debate entre os paradigmas da mecânica e o sistêmico tem causado importantes revoluções nos mais diversos campos de conhecimento, principalmente na física, química e biologia. Sendo assim, esta dissertação tem o objetivo de analisar como as teorias sistêmicas mais recentes desenvolvidas na química, a partir de Prigogine, e na biologia, conforme Maturana e Varela, podem contribuir para a abordagem institucionalista de Veblen. Para isso, apoiar-se-á na hipótese fornecida pela Teoria Geral dos Sistemas, de Bertalanffy (2006), no qual se refere que os princípios que regem um determinado sistema independem das particularidades de seus componentes mas do modo como estes se inter-relacionam. Assim, a convergência entre estas três teorias passa a ser válida uma vez que o tipo de sistema tratado em todas seja caracterizado por: 1) irreversibilidade da trajetória de suas mudanças, 2) com oposição à ideia de equilíbrio e 3) a introdução de uma abordagem evolucionária e com tempo histórico. Este trabalho se inicia a partir da introdução ao debate entre os paradigmas da mecânica e sistêmico surgido no ramo da física. Na sequência apresenta os referenciais teóricos do institucionalismo de Veblen e da teoria das estruturas dissipativas e autopoiese. Em seguida é feito a análise de convergência entre os arcabouços teóricos vistos, e verificado como as abordagens de Prigogine juntamente com a de Maturana e Varela podem contribuir para o estudo das instituições. Por fim é mostrado como a abordagem desenvolvida neste trabalho pode auxiliar no tratamento de questões relacionadas à economia, com ênfase dada especificamente no que tange a economia monetária.