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Nonlinear oscillation and control in the BZ chemical reaction.Li, Yongfeng 25 August 2008 (has links)
In this thesis, a reversible LotkaVolterra model was proposed to study the nonlinear oscillation of the BelousovZhabotinsky(BZ) reaction in a closed isothermal chemical system. The reaction zone can be divided into two zones, oscillation zone and transition zone, where the oscillation time and the transition time and the number of the complete oscillations are estimated. By applying the geometric singular perturbation method, it was proved that there exist an oscillation axis in the oscillation zone, a strongly stable twodimensional invariant manifold in transition zone, on which there is also a onedimensional stable invariant
manifold, which is the part of the central axis. There is no oscillation in the vicinity of the equilibrium, as indicated by Onsager's reciprocal symmetry relation. Furthermore, the damped oscillation is studied in terms of the actionactionangle variables. In the end, the model reference control technique is employed to control the oscillation amplitude in the
BZ reaction.

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Surface evolution and self assembly of epitaxial thin films nonlinear and anisotropic effects /Pang, Yaoyu. January 1900 (has links)
Thesis (Ph. D.)University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

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Topics on spatially highorder accurate methods and preconditioning for the NavierStokes equations with finiterate chemistryGodfrey, Andrew Grady 06 June 2008 (has links)
This dissertation discusses two aspects of computational fluid dynamics: high order spatial accuracy and convergencerate acceleration through system preconditioning. Concerning highorder accuracy, the computational qualities of various spatial methods for the finitevolume solution of the Euler equations are presented. The twodimensional essentially nonoscillatory (ENO), kexact, and dimensionally split ENO reconstruction operators are discussed and compared in terms of reconstruction and solution accuracy and computational cost. Standard variable extrapolation methods are included for completeness. Inherent steadystate convergence difficulties are demonstrated for adaptivestencil algorithms. Methods for reconstruction error analysis are presented and an exact solution to the heat equation is used as an example. Numerical experiments presented include the Ringleb flow for numerical accuracy and a shockreflection problem. A vortexshock interaction demonstrates the ability of the EN 0 scheme to excel in capturing unsteady highfrequency flow physics.
Concerning convergencerate acceleration, characteristicwave preconditioning is extended to include generalized finiterate chemistry with nonequilibrium thermodynamics Additionally, the proper preconditioning for the onedimensional NavierStokes equations is presented. Eigenvalue stiffness is resolved and convergencerate acceleration is demonstrated over the entire Machnumber range from the incompressible to the hypersonic. Specific benefits are realized at low and transonic flow speeds. The extended preconditioning matrix accounts for thermal and chemical nonequilibrium and its implementation is explained for both explicit and implicit time marching. The effects of highorder spatial accuracy and various flux splittings are investigated. Numerical analysis reveals the possible theoretical improvements from using preconditioning at all Mach numbers. Numerical results confirm the expectations from the analysis. The preconditioning matrix is applied with dual time stepping to obtain arbitrarily highorder accurate temporal solutions within an implicit formulation. Representative test cases include flows with previously troublesome embedded highconditionnumber regions. / Ph. D.

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Nonlinear reactive processes in constrained mediaBullara, Domenico 27 March 2015 (has links)
In this thesis we show how reactive processes can be affected by the presence of different types of spatial constraints, so much so that their nonlinear dynamics can be qualitatively altered or that new and unexpected behaviors can be produced. To understand how this interplay can occur in general terms, we theoretically investigate four very different examples of this situation. <p><p>The first system we study is a reversible trimolecular chemical reaction which is taking place in closed onedimensional lattices. We show that the low dimensionality may or may not prevent the reaction from reaching its equilibrium state, depending on the microscopic properties of the molecular reactive mechanism. <p><p>The second reactive process we consider is a network of biological interactions between pigment cells on the skin of zebrafish. We show that the combination of shortrange and longrange contactmediated feedbacks can promote a Turing instability which gives rise to stationary patterns in space with intrinsic wavelength, without the need of any kind of motion.<p><p>Then we investigate the behavior of a typical chemical oscillator (the Brusselator) when it is constrained in a finite space. We show that molecular crowding can in such cases promote new nonlinear dynamical behaviors, affect the usual ones or even destroy them. <p><p>Finally we look at the situation where the constraint is given by the presence of a solid porous matrix that can react with a perfect gas in an exothermic way. We show on one hand that the interplay between reaction, heat flux and mass transport can give rise to the propagation of adsorption waves, and on the other hand that the coupling between the chemical reaction and the changes in the structural properties of the matrix can produce sustained chemomechanical oscillations. <p><p>These results show that spatial constraints can affect the kinetics of reactions, and are able to produce otherwise absent nonlinear dynamical behaviors. As a consequence of this, the usual understanding of the nonlinear dynamics of reactive systems can be put into question or even disproved. In order to have a better understanding of these systems we must acknowledge that mechanical and structural feedbacks can be important components of many reactive systems, and that they can be the very source of complex and fascinating phenomena.<p> / Doctorat en Sciences / info:eurepo/semantics/nonPublished

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On the non equilibrium thermodynamics and dynamics of a deformable interface between two electromagnetically controllable fluidsVanhaelen, Quentin 10 November 2010 (has links)
This thesis is devoted to the study of a deformable material interface between two immiscible moving<p>media, both of them being magnetizable. The first part concerns the establishment of a complete set of dynamical equations allowing a complete description of the non equilibrium phenomena including a coupling between the internal angular momentum and the electromagnetic field. The effects of the relaxation processes are also discussed. We show that the deformation of the interface introduces a nonlinear term, proportional to the mean curvature, in<p>the surface dynamical equations of mass momentum and angular momentum. That term<p>intervenes also in the singular magnetic and electric fields inside the interface which lead to<p>the influence of currents and charge densities at the interface. In a second part, we give the expression<p>for the entropy production inside the interface as well as in the bulk phase. Using the general principles of non equilibrium thermodynamics, we compute the different thermodynamical fluxes. / Doctorat en Sciences / info:eurepo/semantics/nonPublished

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Applications of the HelmholtzHodge Decomposition to Networks and Random ProcessesStrang, Alexander 07 September 2020 (has links)
No description available.

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Termodinâmica estatística de nãoequilíbrio da condensação de FröhlichBoseEinstein de mágnons excitados / Nonequilibrium statistical thermodynamics of the FröhlichBoseEinstein condensation of hot magnonsVannucchi, Fabio Stucchi, 1981 31 October 2018 (has links)
Orientadores: Roberto Luzzi, Áurea Rosas Vasconcellos / Tese (doutorado)  Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 20181031T13:25:44Z (GMT). No. of bitstreams: 1
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Previous issue date: 2011 / Resumo: Este trabalho tem por objetivo desenvolver uma teoria sobre a termodinâmica de nãoequilíbrio de mágnons excitados por fonte externa e em contato com um banho térmico. A teoria é aplicada ao recém observado acúmulo de mágnons nos estados de mínima freqüência em experimentos com filmes finos magnetizados de granada de ferroítrio afastados do equilíbrio via fonte de radiação de microondas. Seguindo um formalismo de ensembles estatísticos de nãoequilíbrio, a partir do hamiltoniano do sistema magnético são obtidas as equações de evolução para as variáveis termodinâmicas. Entre estas equações, as que descrevem a evolução das populações médias de mágnons são estudadas em detalhe e atenção especial é dada às contribuições não lineares. Mostrase que, por um lado, o termo nãolinear proveniente da interação do sistema magnético com a rede cristalina transfere energia das populações dos modos de alta freqüência para os de baixa, gerando um acúmulo nos modos de mínima freqüência  o Efeito Fröhlich. Por outro lado, a interação mágnonmágnon origina uma contribuição à evolução das populações que tende a termalizar o sistema em termos de uma temperatura de nãoequilíbrio. É ainda utilizada uma ¿modelagem de dois fluidos¿, em que as equações cinéticas das populações de mágnons associadas a todos os modos são contraídas em apenas duas, que representa os modos de mínima freqüência e aqueles alimentados. Esta modelagem permite estudar quantitativamente a evolução temporal do sistema via integração numérica. Constatase que, para um determinado intervalo de taxas de alimentação, formase o condensado devido ao Efeito Fröhlich. Para valores mais altos da potência da fonte de alimentação, a contribuição devido à interação entre mágnons tornase dominante e a formação do condensado é inibida. Por fim, os diversos processos de relaxação do condensado para o equilíbrio são investigados em função do valor da fonte externa do sistema / Abstract: The purpose of this work is to develop a nonequilibrium thermodynamic theory on rnagnons excited by an external pumping source embedded in a thermal bath. This theory is applied to the recently observed experiments with magnetic thin films of yttrium iron garnet driven out of equilibrium through microwave radiation pumping. Resorting to a NonEquilibrium Statistical Ensemble Formalism, the evolution equations for the magnon populations are obtained and studied. The nonlinear contribution arising out of the spinlattice interaction transfers the energy in excess of equilibrium from the pumped frequency modes to the lower frequency ones, and, in a cascade down process, occurs a large grow in the magnon populations of the lowest in frequency modes  a phenomenon we call Frohlich Effect. In opposition to this contribution, there is anot her one, generated by the magnonmagnon interaction, that tends to lead the system to a state of internal nonequilibrium thermalization. We introduce a modeling consisting in a kind of ¿twofluid model", in which the kinetic equations for the magnon populations are contracted in only two, representing the modes lowest in frequency and the ones that are pumped by the external source. A quantitative study is performed through numerical integration of the two related evolution equations. The emergence of the condensate, due to the Frohlich Effect, is evidenced for a range of source power. For higher feeding taxes, the contribution originated by the magnonmagnon interaction becomes dominant and the emergence of the condensate is inhibited. Finally, the several relaxation processes in the condensate leading to equilibrium are analyzed in terms of the source power / Doutorado / Física Estatistica e Termodinamica / Doutor em Ciências

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Nonequilibrium Thermomechanics of Multifunctional Energetic Structural MaterialsNarayanan, Vindhya 28 November 2005 (has links)
Shock waves create a unique environment of high pressure, high temperature and high strainrates. It has been observed that chemical reactions that occur in this regime are exothermic and can lead to the synthesis of new materials that are not possible under other conditions. The exothermic reaction is used in the development of binary energetic materials. These materials are of significant interest to the energetic materials community because of its capability of releasing high heat content during a chemical reaction and the relative insensitivity of these types of energetic materials. Synthesis of these energetic materials, at nano grain sizes with structural reinforcements, provides an opportunity to develop a dual functional material with both strength and energetic characteristics.
Shockinduced chemical reactions pose challenges in experiment and instrumentation. This thesis is addressed to the theoretical development of constitutive models of shockinduced chemical reactions in energetic composites, formulated in the framework of nonequilibrium thermodynamics and mixture theories, in a continuum scale. Transition statebased chemical reaction models are introduced and incorporated with the conservation equations that can be used to calculate and simulate the shockinduced reaction process. The energy that should be supplied to reach the transition state has been theoretically modeled by considering both the pore collapse mechanism and the plastic flow with increasing yield stress behind the shock wave. A nonequilibrium thermodynamics framework and the associated evolution equations are introduced to account for time delays that are observed in the experiments of shockinduced or assisted chemical reactions. An appropriate representation of the particle size effects is introduced by modifying the initial energy state of the reactants. Numerical results are presented for shockinduced reactions of mixtures of Al, Fe2O3 and Ni, Al with epoxy as the binder.
The theoretical model, in the continuum scale, requires parameters that should be experimentally determined. The experimental characterization has many challenges in measurement and development of nano instrumentation. An alternate approach to determine these parameters is through abinitio calculations. Thus, this thesis has initiated abinitio molecular dynamics studies of shockinduced chemical reactions. Specifically, the case of thermal initiation of chemical reactions in aluminum and nickel is considered.

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Desenvolvimento de modelagens de não equilibrio para caracterização e aplicação em simulação de colunas de destilação complexas / Development of nonequilibrium models for characterization and application in simulation of complex distillation columnsReis, Miria Hespanhol Miranda 16 January 2006 (has links)
Orientador : Maria Regina Wolf Maciel / Tese (doutorado)  Universidade Estadual de Campinas, Faculdade de Engenharia Quimica / Made available in DSpace on 20180806T15:22:51Z (GMT). No. of bitstreams: 1
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Previous issue date: 2006 / Resumo: A destilação é, certamente, o processo mais aplicado na separação de misturas líquidas. Embora esta seja uma operação unitária conhecida de longa data, ainda, nos dias de hoje persistem algumas dificuldades na proposição de esquemas de destilação apropriados. Sendo assim, o objetivo deste trabalho de tese foi aplicar modelos mais realistas na caracterização de misturas e na simulação de processos de destilação, em regimes estacionários e dinâmicos. Para tanto, foram avaliados dois softawes, desenvolvidos no Laboratório de Desenvolvimentos de Processos de Separação, para simulações de colunas de destilação considerando os modelos de estágios de equilíbrio e de não equilíbrio. Os resultados obtidos mostraram que, geralmente, os perfis obtidos com as duas modelagens são diferentes, em ambos os regimes. A modelagem de estágios de não equilíbrio foi aplicada também para a caracterização de sistemas, utilizando mapas de curvas residuais. Avaliouse, ainda, a influência das correlações de eficiência de Barros & Wolf em mapas de curvas residuais. Os perfis obtidos com as correlações de eficiência de Barros & Wolf mostram grande concordância com os calculados pelo modelo de estágios de não equilíbrio. Com os mapas de curvas residuais calculados concluiuse que as trajetórias líquidas de composição não cruzam as fronteiras de destilação, sendo esta um questão de polêmica na atualidade, no entanto, nossos resultados mostram os perfis corretos. Além disso, desenvolveuse, neste trabalho de tese, um programa computacional para a caracterização de sistemas reativos. A vantagem do novo algoritmo proposto está, principalmente, no fato do programa não depender de estimativas inicias e ser de fácil convergência. O programa é, também, capaz de predizer todos os azeótropos presentes na mistura, quando existam um ou mais de um, ou ainda de afirmar que a mistura é zeotrópica. Os resultados obtidos são concordantes com valores experimentais ou calculados por outros métodos. Na linha do processo de destilação reativa, sendo este um processo inovador, foi proposta a separação da mistura fenol + água. A separação desta mistura é de grande interesse, por questões econômicas e ambientais. Preliminarmente, fezse um estudo na busca de uma reação apropriada para o consumo de fenol. O processo proposto atende completamente às questões ambientais, visto que gera somente correntes limpas e é, portanto, uma nova alternativa para o tratamento de correntes fenólicas. Por fim, desenvolveuse neste trabalho um conjunto completo para caracterização de sistemas e simulação de processos, envolvendo desde o modelo de estágios de equilíbrio até o modelo de estágios de não equilíbrio. Propôsse, ainda, um eficiente processo para o tratamento de águas fenólicas / Abstract: Distillation is, certainly, the most applied process in the separation of liquid mixtures. Although this is a very known unit operation, still nowadays some difficulties persist in the proposal of appropriate distillation schemes. Thus, the objective of this work was to apply more realistic models in the characterization of mixtures and in the simulation of distillation process in, both, steady state and dynamic regime. In this way, two softwares developed in the Laboratory of Separation Processes Development were evaluated. These softwares consider the equilibrium and the nonequilibrium stage models in steady state and dynamic regime. The results show that, generally, the profiles obtained with the two models are different, in both regimes. The nonequilibrium stage model was also applied for the systems characterization, in residue curve maps. It was evaluated, still, the influence of Barros & Wolf correlations for efficiencies on residue curve maps. The profiles obtained with the Barros & Wolf correlations show good agreement with the calculated with the nonequilibrium stage model. The calculated residue curve maps showed that residue curves do not cross distillation boundaries. Nowadays, this is a question of controversy, however our results show the correct behavior. Moreover, it was developed in this work a computational program for the characterization of reactive systems. The advantage of the new proposed algorithm is mainly because the program does not depend on initial estimates and it is of easy convergence. The program is, also, able to predict all the azeotropes present in the mixture, when one or more than one exist, or still to affirm that the mixture is zeotropic. The obtained results are in agreement with experimental values or values calculated by other methods. Regarding to reactive distillation, being an innovative process, it was proposed the separation of the mixture phenol + water. The separation of this mixture is of great interest, for economic and environmental issues. Preliminarily, it was carried out a study of an appropriate reaction for the phenol consumption. The considered process takes care of environmental questions, since it only generates current clean and it is, therefore, an alternative process for the phenolic wastewater treatment. Finally, in this work, it was developed a complete set for characterization of systems and simulation of processes, involving the equilibrium and the nonequilibrium stage modes, in steady state and dynamic regime. It was considered, still, an efficient process for the phenolic wastewater treatment / Doutorado / Desenvolvimento de Processos Químicos / Doutor em Engenharia Química

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Computational Methods for the Optimal Reconstruction of Material Properties in Complex Multiphysics SystemsBukshtynov, Vladislav 04 1900 (has links)
<p>In this work we propose and validate a computational method for reconstructing constitutive relations (material properties) in complex multiphysics phenomena based on incomplete and noisy measurements which is applicable to different problems arising in nonequilibrium thermodynamics and continuum mechanics. The parameter estimation problem is solved as PDE–constrained optimization using a gradient–based technique in the optimize–then–discretize framework. The reconstructed material properties taken as an example here are the transport coefficients characterizing diffusion processes such as the viscosity and the thermal conductivity, and we focus on problems in which these coefficients depend on the state variables in the system. The proposed method allows one to reconstruct a smooth constitutive relation defined over a broad range of the dependent variable. This research is motivated by questions arising in the computational analysis and optimization of advanced welding processes which involves modelling complex alloys in the liquid phase at high temperatures.</p> / Doctor of Philosophy (PhD)

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