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He, Taiping. "Reaction-Diffusion Systems with Discontinuous Reaction Functions." NCSU, 2005. http://www.lib.ncsu.edu/theses/available/etd-03192005-101102/.
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This dissertation studies coupled reaction diffusion systems with discontinuous reaction functions. It includes three parts: The first part is concerned with the existence of solutions for a coupled system of two parabolic equations and the second part is devoted to the monotone iterative methods for monotone and mixed quasimonotone functions. Various monotone iterative schemes are presented and each of these schemes leads to an existence-comparison theorem and the monotone convergence of the maximal and minimal sequences. In the third part, the monotone iterative schemes are applied to compute numerical solutions of the system. These numerical solutions are based on the finite element method which gives a finite approximation of the coupled system. Numerical results for some scalar parabolic bounday problems and a coupled system of parabolic equations are also given.
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Yangari, Sosa Miguel Ángel. "Fractional reaction-diffusion problems." Tesis, Universidad de Chile, 2014. http://www.repositorio.uchile.cl/handle/2250/115538.
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Doctor en Ciencias de la Ingeniería, Mención Modelación MatemáticaThis thesis deals with two different problems: in the first one, we study the large-time behavior of solutions of one-dimensional fractional Fisher-KPP reaction diffusion equations, when the initial condition is asymptotically front-like and it decays at infinity more slowly than a power x^b, where b < 2\alpha and \alpha\in (0,1) is the order of the fractional Laplacian (Chapter 2); in the second problem, we study the time asymptotic propagation of solutions to the fractional reaction diffusion cooperative systems (Chapter 3). For the first problem, we prove that the level sets of the solutions move exponentially fast as time goes to infinity. Moreover, a quantitative estimate of motion of the level sets is obtained in terms of the decay of the initial condition. In the second problem, we prove that the propagation speed is exponential in time, and we find a precise exponent depending on the smallest index of the fractional laplacians and of the nonlinearity, also we note that it does not depend on the space direction.
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Yangari, Sosa Miguel Angel. "Fractional reaction-diffusion problems." Toulouse 3, 2014. http://thesesups.ups-tlse.fr/2270/.
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Cette thèse porte sur deux problèmes différents : dans le premier, nous étudions le comportement en temps long des solutions des équations de réaction diffusion 1d-fractionnaire de type Fisher-KPP lorsque la condition initiale est asymptotiquement de type front et décroît à l'infini plus lentement que, où et est l'indice du laplacien fractionnaire (Chapitre 2). Dans le second problème, nous étudions la propagation asymptotique en temps des solutions de systèmes coopératifs de réaction-diffusion (Chapitre 3). Dans le premier problème, nous démontrons que les ensembles de niveau des solutions se déplacent exponentiellement vite en temps quand t tend vers l'infini. De plus, une estimation quantitative du mouvement de ces ensembles est obtenue en fonction de la décroissance à l'infini de la condition initiale. Dans le second problème, nous montrons que la vitesse de propagation est exponentielle en temps et nous trouvons un exposant précis qui dépend du plus petit ordre des laplaciens fractionnaires considérés et de la non-linéarité. Nous notons aussi que cet indice ne dépend pas de la direction spatiale de propagationThis thesis deals with two different problems: in the first one, we study the large-time behavior of solutions of one-dimensional fractional Fisher-KPP reaction diffusion equations, when the initial condition is asymptotically front-like and it decays at infinity more slowly than a power , where and is the order of the fractional Laplacian (Chapter 2); in the second problem, we study the time asymptotic propagation of solutions to the fractional reaction diffusion cooperative systems (Chapter 3). For the first problem, we prove that the level sets of the solutions move exponentially fast as time goes to infinity. Moreover, a quantitative estimate of motion of the level sets is obtained in terms of the decay of the initial condition. In the second problem, we prove that the propagation speed is exponential in time, and we find a precise exponent depending on the smallest index of the fractional laplacians and of the nonlinearity, also we note that it does not depend on the space direction
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Coulon, Anne-Charline. "Propagation in reaction-diffusion equations with fractional diffusion." Doctoral thesis, Universitat Politècnica de Catalunya, 2014. http://hdl.handle.net/10803/277576.
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This thesis focuses on the long time behaviour of solutions to Fisher-KPP reaction-diffusion equations involving fractional diffusion. This type of equation arises, for example, in spatial propagation or spreading of biological species (rats, insects,...). In population dynamics,
the quantity under study stands for the density of the population.
It is well-known that, under some specific assumptions, the solution tends to a stable state of the evolution problem, as time goes to infinity. In other words, the population invades the medium, which corresponds to the survival of the species, and we want to understand at which speed this invasion takes place. To answer this question, we set up a new method to study the speed of propagation when fractional diffusion is at stake and apply it on three different problems.
Part I of the thesis is devoted to an analysis of the asymptotic location of the level sets of the solution to two different problems : Fisher-KPP models in periodic media and cooperative systems, both including fractional diffusion. On the first model, we prove that, under some assumptions on the periodic medium, the solution spreads exponentially fast in time and we find the precise exponent that appears in this exponential speed of propagation. We also carry out numerical simulations to investigate the dependence of the speed of propagation on the initial condition. On the second model, we prove that the speed of propagation is once again exponential in time, with an exponent depending on the smallest index of the fractional Laplacians at stake and on the reaction term.
Part II of the thesis deals with a two dimensional environment, where reproduction of Fisher-KPP type and usual diffusion occur, except on a line of the plane, on which fractional diffusion takes place. The plane is referred to as 'the field' and the line to 'the road', as a reference to the biological situations we have in mind. Indeed, it has long been known that fast diffusion on roads can have a driving effect on the spread of epidemics. We prove that the speed of propagation is exponential in time on the road, whereas it depends linearly on time in the field. Contrary to the precise asymptotics obtained in Part I, for this model, we are not able to give a sharp location of the level sets on the road and in the field. The expansion shape of the level sets in the field is investigated through numerical simulations.Esta tesis se centra en el comportamiento en tiempos grandes de las soluciones de la ecuación de Fisher- KPP de reacción-difusión con difusión fraccionaria. Este tipo de ecuación surge, por ejemplo, en la propagación espacial o en la propagación de especies biológicas (ratas, insectos,...). En la dinámica de poblaciones, la cantidad que se estudia representa la densidad de la población. Es conocido que, bajo algunas hipótesis específicas, la solución tiende a un estado estable del problema de evolución, cuando el tiempo tiende a infinito. En otras palabras, la población invade el medio, lo que corresponde a la supervivencia de la especie, y nosotros queremos entender con qué velocidad se lleva a cabo esta invasión. Para responder a esta pregunta, hemos creado un nuevo método para estudiar la velocidad de propagación cuando se consideran difusiones fraccionarias, además hemos aplicado este método en tres problemas diferentes. La Parte I de la tesis está dedicada al análisis de la ubicación asintótica de los conjuntos de nivel de la solución de dos problemas diferentes: modelos de Fisher- KPP en medios periódicos y sistemas cooperativos, ambos consideran difusión fraccionaria. En el primer modelo, se prueba que, bajo ciertas hipótesis sobre el medio periódico, la solución se propaga exponencialmente rápido en el tiempo, además encontramos el exponente exacto que aparece en esta velocidad de propagación exponencial. También llevamos a cabo simulaciones numéricas para investigar la dependencia de la velocidad de propagación con la condición inicial. En el segundo modelo, se prueba que la velocidad de propagación es nuevamente exponencial en el tiempo, con un exponente que depende del índice más pequeño de los Laplacianos fraccionarios y también del término de reacción. La Parte II de la tesis ocurre en un entorno de dos dimensiones, donde se reproduce un tipo ecuación de Fisher- KPP con difusión estándar, excepto en una línea del plano, en el que la difusión fraccionada aparece. El plano será llamado "campo" y la línea "camino", como una referencia a las situaciones biológicas que tenemos en mente. De hecho, desde hace tiempo se sabe que la difusión rápida en los caminos puede causar un efecto en la propagación de epidemias. Probamos que la velocidad de propagación es exponencial en el tiempo en el camino, mientras que depende linealmente del tiempo en el campo. Contrariamente a los precisos exponentes obtenidos en la Parte I, para este modelo, no fuimos capaces de dar una localización exacta de los conjuntos de nivel en la carretera y en el campo. La forma de propagación de los conjuntos de nivel en el campo se investiga a través de simulaciones numéricas
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Benson, Debbie Lisa. "Reaction diffusion models with spatially inhomogeneous diffusion coefficients." Thesis, University of Oxford, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239337.
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Fei, Ning Fei. "Studies in reaction-diffusion equations." Thesis, Heriot-Watt University, 2003. http://hdl.handle.net/10399/310.
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Grant, Koryn. "Symmetries and reaction-diffusion equations." Thesis, University of Kent, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.264601.
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Frömberg, Daniela. "Reaction Kinetics under Anomalous Diffusion." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2011. http://dx.doi.org/10.18452/16374.
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Die vorliegende Arbeit befasst sich mit der Verallgemeinerung von Reaktions-Diffusions-Systemen auf Subdiffusion. Die subdiffusive Dynamik auf mesoskopischer Skala wurde mittels Continuous-Time Random Walks mit breiten Wartezeitverteilungen modelliert. Die Reaktion findet auf mikroskopischer Skala, d.h. während der Wartezeiten, statt und unterliegt dem Massenwirkungsgesetz. Die resultierenden Integro-Differentialgleichungen weisen im Integralkern des Transportterms eine Abhängigkeit von der Reaktion auf. Im Falle der Degradation A->0 wurde ein allgemeiner Ausdruck für die Lösungen beliebiger Dirichlet-Randwertprobleme hergeleitet. Die Annahme, dass die Reaktion dem Massenwirkungsgesetz unterliegt, ist eine entscheidende Voraussetzung für die Existenz stationärer Profile unter Subdiffusion. Eine nichtlineare Reaktion stellt die irreversible autokatalytische Reaktion A+B->2A unter Subdiffusion dar. Es wurde ein Analogon zur Fisher-Kolmogorov-Petrovskii-Piscounov-Gleichung (FKPP) aufgestellt und die resultierenden propagierenden Fronten untersucht. Numerische Simulationen legten die Existenz zweier Regimes nahe, die sowohl mittels eines Crossover-Argumentes als auch durch analytische Berechnungen untersucht wurden. Das erste Regime ist charakterisiert durch eine Front, deren Breite und Geschwindigkeit sich mit der Zeit verringert. Das zweite, fluktuationsdominierte Regime liegt nicht im Geltungsbereich der kontinuierlichen Gleichung und weist eine stärkere Abnahme der Frontgeschwindigkeit sowie eine atomar scharf definierte Front auf. Ein anderes Szenario, bei dem eine Spezies A in ein mit immobilen B-Partikeln besetztes Medium hineindiffundiert und gemäß dem Schema A+B->(inert) reagiert, wurde ebenfalls betrachtet. Diese Anordnung wurde näherungsweise als ein Randwertproblem mit einem beweglichen Rand (Stefan-Problem) formuliert. Die analytisch gewonnenen Ergebnisse bzgl. der Position des beweglichen Randes wurden durch numerische Simulationen untermauert.The present work studies the generalization of reaction-diffusion schemes to subdiffusion. The subdiffusive dynamics was modelled by means of continuous-time random walks on a mesoscopic scale with a heavy-tailed waiting time pdf lacking the first moment. The reaction was assumed to take place on a microscopic scale, i.e. during the waiting times, obeying the mass action law. The resultant equations are of integro-differential form, and the reaction explicitly affects the transport term. The long ranged memory of the subdiffusion kernel is modified by a factor accounting for the reaction of particles during the waiting times. The degradation A->0 was considered and a general expression for the solution to arbitrary Dirichlet Boundary Value Problems was derived. For stationary solutions to exist in reaction-subdiffusion, the assumption of reactions according to classical rate kinetics is essential. As an example for a nonlinear reaction-subdiffusion system, the irreversible autocatalytic reaction A+B->2A under subdiffusion is considered. A subdiffusive analogue of the classical Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) equation was derived and the resultant propagating fronts were studied. Two different regimes were detected in numerical simulations, and were discussed using both crossover arguments and analytic calculations. The first regime is characterized by a decaying front velocity and width. The fluctuation dominated regime is not within the scope of the continuous description. The velocity of the front decays faster in time than in the continuous regime, and the front is atomically sharp. Another setup where reactants A penetrate a medium initially filled with immobile reactants B and react according to the scheme A+B->(inert) was also considered. This problem was approximately described in terms of a moving boundary problem (Stefan-problem). The theoretical predictions concerning the moving boundary were corroborated by numerical simulations.
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Coulon, Chalmin Anne-Charline. "Fast propagation in reaction-diffusion equations with fractional diffusion." Toulouse 3, 2014. http://thesesups.ups-tlse.fr/2427/.
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Cette thèse est consacrée à l'étude du comportement en temps long, et plus précisément de phénomènes de propagation rapide, des équations de réaction-diffusion de type Kisher-KPP avec diffusion fractionnaire. Ces équations modélisent, par exemple, la propagation d'espèces biologiques. Sous certaines hypothèses, la population envahit le milieu et nous voulons comprendre à quelle vitesse cette invasion a lieu. Pour répondre à cette question, nous avons mis en place une nouvelle méthode et nous l'appliquons à différents modèles. Dans une première partie, nous étudions deux problèmes d'évolution comprenant une diffusion fractionnaire : un modèle de type Fisher-KPP en milieu périodique et un système coopératif. Dans les deux cas, nous montrons, sous certaines conditions, que la vitesse de propagation est exponentielle en temps, et nous donnons une expression précise de l'exposant de propagation. Nous menons des simulations numériques pour étudier la dépendance de cette vitesse de propagation en la donnée initiale. Dans une seconde partie, nous traitons un environnement bidimensionnel, dans lequel le terme de reproduction est de type Fisher-KPP et le terme diffusif est donné par un laplacien standard, excepté sur une ligne du plan où une diffusion fractionnaire intervient. Le plan est nommé "le champ" et la ligne "la route", en référence aux situations biologiques que nous voulons modéliser. Nous prouvons que la vitesse de propagation est exponentielle en temps sur la route, alors qu'elle dépend linéairement du temps dans le champ. La forme des lignes de niveau dans le champ est étudiée au travers de simulations numériquesThis thesis focuses on the long time behaviour, and more precisely on fast propagation, in Fisher-KPP reaction diffusion equations involving fractional diffusion. This type of equation arises, for example, in spreading of biological species. Under some specific assumptions, the population invades the medium and we want to understand at which speed this invasion takes place when fractional diffusion is at stake. To answer this question, we set up a new method and apply it on different models. In a first part, we study two different problems, both including fractional diffusion : Fisher-KPP models in periodic media and cooperative systems. In both cases, we prove, under additional assumptions, that the solution spreads exponentially fast in time and we find the precise exponent of propagation. We also carry out numerical simulations to investigate the dependence of the speed of propagation on the initial condition. In a second part, we deal with a two dimensional environment, where reproduction of Fisher-KPP type and usual diffusion occur, except on a line of the plane, on which fractional diffusion takes place. The plane is referred to as "the field" and the line to "the road", as a reference to the biological situations we have in mind. We prove that the speed of propagation is exponential in time on the road, whereas it depends linearly on time in the field. The expansion shape of the level sets in the field is investigated through numerical simulations
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Coville, Jerome. "Equations de reaction diffusion non-locale." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2003. http://tel.archives-ouvertes.fr/tel-00004313.
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Cette thèse est consacrée à l'étude des équations de réaction diffusion non-locale du type $u_(t)-(\int_(\R)J(x-y)[u(y)-u(x)]dy)=f(u)$. Ces équations non-linéaires apparaissent naturellement en physique et en biologie. On s'intéresse plus particulièrement aux propriétés (existence, unicité, monotonie) des solutions du type front progressif. Trois classes de non-linéarités $f$ (bistable, ignition, monostable) sont étudiées. L'existence dans les cas bistable et ignition est obtenue via une technique d'homotopie. Le cas monostable nécessite une autre approche. L'existence est obtenue via une approximation des équations sur des semi-intervales infinis $(-r,+\infty)$. L'unicité et la monotonie des solutions sont quand elles obtenues par méthode de glissement. Le comportement asymptotique ainsi que des formules pour les vitesses sont aussi établis.
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Bishop, Donald Paul. "Diffusion-based microalloying via reaction sintering." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq39320.pdf.
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Hemming, Christopher John. "Resonantly forced inhomogeneous reaction-diffusion systems." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape3/PQDD_0022/MQ50344.pdf.
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Lunney, Michael E. "Numerical dynamics of reaction-diffusion equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ61659.pdf.
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Bradshaw-Hajek, Bronwyn. "Reaction-diffusion equations for population genetics." Access electronically, 2004. http://www.library.uow.edu.au/adt-NWU/public/adt-NWU20041221.160902/index.html.
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Hellander, Stefan. "Stochastic Simulation of Reaction-Diffusion Processes." Doctoral thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-198522.
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Numerical simulation methods have become an important tool in the study of chemical reaction networks in living cells. Many systems can, with high accuracy, be modeled by deterministic ordinary differential equations, but other systems require a more detailed level of modeling. Stochastic models at either the mesoscopic level or the microscopic level can be used for cases when molecules are present in low copy numbers. In this thesis we develop efficient and flexible algorithms for simulating systems at the microscopic level. We propose an improvement to the Green's function reaction dynamics algorithm, an efficient microscale method. Furthermore, we describe how to simulate interactions with complex internal structures such as membranes and dynamic fibers. The mesoscopic level is related to the microscopic level through the reaction rates at the respective scale. We derive that relation in both two dimensions and three dimensions and show that the mesoscopic model breaks down if the discretization of space becomes too fine. For a simple model problem we can show exactly when this breakdown occurs. We show how to couple the microscopic scale with the mesoscopic scale in a hybrid method. Using the fact that some systems only display microscale behaviour in parts of the system, we can gain computational time by restricting the fine-grained microscopic simulations to only a part of the system. Finally, we have developed a mesoscopic method that couples simulations in three dimensions with simulations on general embedded lines. The accuracy of the method has been verified by comparing the results with purely microscopic simulations as well as with theoretical predictions.eSSENCE
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Tang, François-David. "Reaction-diffusion fronts in heterogeneous combustion." Thesis, McGill University, 2011. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=104561.
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Heterogeneous flames are modeled in a simplified system where the fuel particles are discrete heat sources embedded in an inert, heat conducting medium. Two asymptotic regimes of flame propagation are found and exhibit differences in both the propagation limits and the front speeds. When the flame thickness is much larger than the characteristic particle spacing, the media containing the sources can be approximated as homogeneous in the reaction zone. In this case, the propagation of the front is defined as being in the continuum regime. In contrast, when the front thickness is on the same scale as that of the heterogeneities, the front propagates in the discrete regime and a solution based on a continuum is no longer valid. Discrete effects arise from the localization of the reaction around the sources. The first contribution of this thesis investigates the effects of discreteness using numerical simulations. These effects result in a limit in the absence of heat losses, a strong dependence of the front speed on the dimensionality of the system and a weak dependence of the front speed on the reaction time of sources. In a system of regularly spaced particles, the limit can be found analytically in one-, two-, and three-dimensional systems and the front exhibits complex dynamics of bifurcations near this limit. Propagation beyond this limit is only possible through concentration fluctuations in a system with randomly distributed particles. Furthermore, the limit can only be defined as a probabilistic quantity reflecting different possible propagation outcomes depending on the presence, or absence, of propagation paths in discrete random systems. Heterogeneous reaction-diffusion fronts were also studied experimentally in the context of laminar flames propagating in suspensions of iron particulates. Experiments were performed in a reduced-gravity environment on board a parabolic flight aircraft to minimize particle settling and buoyancy-induced convective flows that cause flame disruptions. The experiment consisted of producing a suspension of iron particulates inside a glass tube and initiating a propagating flame at the open-end of the tube. Quenching plate assemblies forming rectangular channels with variable widths were installed inside the tube. Pass and quench events across the channel were used to find the quenching distance. Flame propagation was recorded by a high-speed digital camera and spectral measurements were used to determine the temperature of the condensed-phase emitters in the flame. The objectives of these experiments were threefold. First, experimental measurements of the flame speed and the quenching distance were used to validate a previously developed one-dimensional dust flame model. Second, the particle combustion mode was investigated by varying the transport properties of the gas mixture by changing the balancing gas between helium and argon. It was found that the ratio between the flame speeds measured in helium and argon mixtures for 3 micron-sized particles was smaller compared to the ratios obtained for larger powders. The lower value of the ratio obtained for 3 micron-sized particles was attributed to a combustion controlled by kinetic rates. Flames propagating in mixtures containing particles larger than 7 microns exhibited a larger ratio of the flame speeds in helium and argon, which was associated to the diffusion mode of particle combustion. Lastly, evidence of a transition from a continuum to a discrete propagation regime was observed in experiments by changing the inert component of the gas mixtures from helium to xenon. The flame speeds measured in helium-balanced mixtures exhibited a stronger dependence on the oxygen concentration than flames propagating in xenon mixtures. A stronger dependence of the flame speed on the oxygen concentration is consistent with the continuum regime, whereas a weaker dependence on the oxygen concentration is evidence of the discrete propagation regime.Dans un système de sources réactives hétérogène, une flamme peut se déplacer dans l'un des deux régimes de propagation. Lorsque l'épaisseur de la flamme est plus grande que la distance entre les sources, le système se comporte tel un qu'espace continue. A l'autre extrême, lorsque la flamme est très fine en comparaison avec l'espacement entre les sources réactives, une flamme hétérogène ne peut plus être d'écrite de manière continue dû à l'importance accrue attribuée aux effets locaux prenant place à l'échelle des sources. Ces effets locaux sont caractérisés par une dépendance importante des paramètres de propagation sur la distribution spatiale des sources. Cette thèse étudie les effets liés au régime de propagation où les interactions locales entre les sources dominent le comportement de la flamme. Les effets associées à la localisation des sources mènent à une limite de propagation en l'absence de perte de chaleur, une dépendance de la vitesse de propagation sur la dimension du système, ainsi qu'une dépendance entre le temps de réaction des sources sur la vitesse de propagation de la flamme. Dans un système dans lequel les sources sont disposées dans un arrangement spatial formant une structure cubique, la limite de propagation est déterminée au moyen d'une solution analytique dans un espace unidimensionnel. Cette limite the propagation est identique dans un espace deux et trois dimensionnel. La propagation de la flamme au-delà de cette limite nécessite une distribution aléatoire des particules. Due au fait que la flamme se propage dans un milieu contenant des sources placées de manière aléatoire, la limite de propagation doit être exprimée sous la forme d'une probabilité. Afin d'étudier les fronts de type réaction-diffusion de manière expérimentale, la propagation de flammes laminaires dans un mélange contenant des particules de fer a été étudiée dans un environnement de gravité réduite obtenu au moyen de vols paraboliques permettant d'éliminer les effets dus à la sédimentation des particules. Des mélanges uniformes de poudres de fer ont été formés à l'intérieur de tubes de verre dans lesquels des flammes laminaires ont été observées se propageant de l'extrémité ouverte vers l'extrémité fermée du tube. Des assemblages de plaques métalliques placées en parallèles ont été installés à l'intérieur de tubes afin de mesurer l'espacement minimale entre deux plaques parallèles permettant la propagation d'une flamme. La vitesse de la flamme a été mesurée à l'aide d'une caméra haute vitesse et des mesures spectrales ont permis de déterminer la température de combustion des particules durant la combustion. Il y a trois objectifs à ces expériences. Premièrement, ces expériences ont permis de valider un modèle théorique unidimensionnel d'une flamme hétérogène. Dans un second temps, le mode de réaction des particules a été déterminée en comparant les vitesses de flamme entre des mélanges compos\'es d'argon et d'hélium. Une diminution marquée du quotient entre les vitesses mesurées dans un mélange contant de l'argon et d'hélium indique que la combustion de fines particules d'un diamètre de 3 microns est limitée par les coefficients de réaction entre le fer et l'oxygène et que la combustion de particules plus grandes est principalement limitée par la diffusion d'oxygène vers la surface des particules. Finalement, ces expériences ont permis de démontrer la différence entre les deux régimes de propagation de la flamme (i.e, local contre continu). Dans un mélange gazeux contenant du xénon, la flamme présente une dépendance réduite sur la concentration d'oxygène, un effet typique d'un régime de propagation principalement locale, limitée par la diffusion de chaleur. Lorsque le xénon est remplacé par de l'hélium, la flamme démontre une dépendance marquée à la concentration d'oxygène, en accord avec la prédiction associée avec le régime continu.
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Stapley, Andrew G. F. "Diffusion & reaction in wheat chains." Thesis, University of Cambridge, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.390002.
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Crampin, Edmund John. "Reaction-diffusion patterns on growing domains." Thesis, University of Oxford, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.325756.
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Smith, Stephen. "Stochastic reaction-diffusion models in biology." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/33142.
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Every cell contains several millions of diffusing and reacting biological molecules. The interactions between these molecules ultimately manifest themselves in all aspects of life, from the smallest bacterium to the largest whale. One of the greatest open scientific challenges is to understand how the microscopic chemistry determines the macroscopic biology. Key to this challenge is the development of mathematical and computational models of biochemistry with molecule-level detail, but which are sufficiently coarse to enable the study of large systems at the cell or organism scale. Two such models are in common usage: the reaction-diffusion master equation, and Brownian dynamics. These models are utterly different in both their history and in their approaches to chemical reactions and diffusion, but they both seek to address the same reaction-diffusion question. Here we make an in-depth study into the physical validity of these models under various biological conditions, determining when they can reliably be used. Taking each model in turn, we propose modifications to the models to better model the realities of the cellular environment, and to enable more efficient computational implementations. We use the models to make predictions about how and why cells behave the way they do, from mechanisms of self-organisation to noise reduction. We conclude that both models are extremely powerful tools for clarifying the details of the mysterious relationship between chemistry and biology.
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Pfeifer, Peter, and Chen Hou. "Diffusion-Reaction in space-filling networks." Universitätsbibliothek Leipzig, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-184563.
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Nagaiah, Chamakuri. "Adaptive numerical simulation of reaction-diffusion systems." [S.l.] : [s.n.], 2007. http://deposit.ddb.de/cgi-bin/dokserv?idn=985277882.
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Claus, Isabelle. "Microscopic chaos, fractals, and reaction-diffusion processes." Doctoral thesis, Universite Libre de Bruxelles, 2002. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/211441.
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Sun, Xiaodi. "Metastable dynamics of convection-diffusion-reaction equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0002/NQ34630.pdf.
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Rondoni, Lamberto. "A stochastic treatment of reaction and diffusion." Diss., This resource online, 1991. http://scholar.lib.vt.edu/theses/available/etd-07282008-134042/.
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Santos, Jaime Eduardo Moutinho. "Non-equilibrium dynamics of reaction-diffusion processes." Thesis, University of Oxford, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.361994.
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Furtado, Kalli. "Mesoscopic simulations of reaction-diffusion-advection problems." Thesis, University of Oxford, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.442953.
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Davidson, Fordyce A. "Bifurcation in systems of reaction-diffusion equations." Thesis, Heriot-Watt University, 1993. http://hdl.handle.net/10399/1444.
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Freitas, Pedro S. C. de. "Some problems in nonlocal reaction-diffusion equations." Thesis, Heriot-Watt University, 1994. http://hdl.handle.net/10399/1401.
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Howard, Martin. "Non-equilibrium dynamics of reaction-diffusion systems." Thesis, University of Oxford, 1996. http://ora.ox.ac.uk/objects/uuid:4485a178-6262-4487-b40f-7c7ec790d687.
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Fluctuations are known to radically alter the behaviour of reaction-diffusion systems. Below a certain upper critical dimension dc , this effect results in the breakdown of traditional approaches, such as mean field rate equations. In this thesis we tackle this fluctuation problem by employing systematic field theoretic/renormalisation group methods, which enable perturbative calculations to be made below dc. We first consider a steady state reaction front formed in the two species irreversible reaction A + B → Ø. In one dimension we demonstrate that there are two components to the front - one an intrinsic width, and one caused by the ability of the centre of the front to wander. We make theoretical predictions for the shapes of these components, which are found to be in good agreement with our one dimensional simulations. In higher dimensions, where the intrinsic component dominates, we also make calculations for its asymptotic profile. Furthermore, fluctuation effects lead to a prediction of asymptotic power law tails in the intrinsic front in all dimensions. This effect causes high enough order spatial moments of a time dependent reaction front to exhibit multiscaling. The second system we consider is a time dependent multispecies reaction-diffusion system with three competing reactions A+A → Ø, B + B → Ø, and A + B → Ø, starting with homogeneous initial conditions. Using our field theoretic formalism we calculate the asymptotic density decay rates for the two species for d ≤ dc. These calculations are compared with other approximate methods, such as the Smoluchowski approach, and also with previous simulations and exact results.
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Turpin, Kevin. "Patterns and fronts in reaction-diffusion systems." Thesis, University of Nottingham, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.287233.
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Aldurayhim, Abdullah Mohammed. "Propagating waves in reaction cross-diffusion systems." Thesis, University of Exeter, 2017. http://hdl.handle.net/10871/31129.
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This research focuses on the reaction diffusion systems where the matrix of diffusion co- efficients is not diagonal. We call these systems reaction cross-diffusion systems. These systems possess interesting solutions that do not appear in the reaction self-diffusion systems that have a diagonal diffusion matrix. Compared to research conducted on re- action self-diffusion systems, the reaction cross-diffusion systems have received little attentions. The aim of this research is to extend existing literature on these systems. In this thesis we considered two-components reaction cross-diffusion systems. We find an ana- lytical solution of reaction diffusion system with replacing FitzHugh-Nagumo kinetics by quartic polynomial. Finding the analytical solution is extends analytical results pre- sented in [9]. This analytical solution is presented in a wave front profile. We study the possibility of imitating Fisher-KPP and ZFK-Nagumo front waves by our analytical solution which we have introduced. The existence of a quartic polynomial yields four different cases with respect to the positions of the roots of the quartic polynomial and the resting states of the wave front. We solve the problem numerically and compare the numerical solution to the analytical solution for those four cases. Finally, we extend the analysis of the different wave regimes in reaction cross- diffusion system with FitzHugh-Nagumo kinetics by varying parameters in the system using numerical continuation. We compute the speed of propagating waves in this sys- tem and show the corresponding eigenvalues of equilibrium which gives an indication about the profile of the propagating waves. We find a stable propagating wave that is not obtained by direct numerical simulation in [55]. We investigate the stability of prop- agating waves by using direct numerical simulation.
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Kammogne, Kamgaing Rodrigue. "Domain decomposition methods for reaction-diffusion systems." Thesis, University of Birmingham, 2014. http://etheses.bham.ac.uk//id/eprint/4599/.
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Domain Decomposition (DD) methods have been successfully used to solve elliptic problems, as they deal with them in a more elegant and efficient way than other existing numerical methods. This is achieved through the division of the domain into subdomains, followed by the solving of smaller problems within these subdomains which leads to the solution. Furthermore DD-techniques can incorporate in their implementation not only the physics of the different phenomena associated with the modeling, but also the enhancement of parallel computing. They can be divided into two major categories: with and without overlapping. The most important factor in both cases is the ability to solve the interface problem referred to as the Steklov-Poincaré problem. There are two existing approaches to solving the interface problem. The first approach consists of approximating the interface problem by solving a sequence of subproblems within the subdomains, while the second approach aims to tackle the interface problem directly. The solution method presented in this thesis falls into the latter category. This thesis presents a non-overlapping domain decomposition (DD) method for solving reaction-diffusion systems. This approach addresses the problem directly on the interface which allows for the presentation and analysis of a new type of interface preconditioner for the arising Schur complement problem. This thesis will demonstrate that the new interface preconditioner leads to a solution technique independent of the mesh parameter. More precisely, the technique, when used effectively, exploits the fact that the Steklov-Poincaré operators arising from a non-overlapping DD-algorithm are coercive and continuous, with respect to Sobolev norms of index 1/2, in order to derive a convergence analysis for a DD-preconditioned GMRES algorithm. This technique is the first of its kind that presents a class of substructuring methods for solving reaction diffusion systems and analyzes their behaviour using fractional Sobolev norms.
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Agliari, Elena, Raffaella Burioni, Davide Cassi, and Franco M. Neri. "Autocatalytic reaction-diffusion processes in restricted geometries." Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-192966.
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Mahmutovic, Anel. "Reaction-Diffusion kinetics of Protein DNA Interactions." Doctoral thesis, Uppsala universitet, Beräknings- och systembiologi, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-263527.
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Transcription factors need to rapidly find one specific binding site among millions of nonspecific sites on the chromosomal DNA. In this thesis I use various aspects of reaction-diffusion theory to investigate the interaction between proteins and DNA and to explain the searching, finding and binding to specific operator sites. Using molecular dynamics methods we calculate the free energy profile for the model protein LacI as it leaves a nonspecific stretch of DNA and as it slides along DNA. Based on the free energy profiles we estimate the microscopic dissociation rate constant, kdmicro ~1.45×104s-1, and the 1D diffusion coefficient, D1 ~ 0.05-0.29 μm2s-1 (2-40μs to slide 1 basepair (bp)). At a non-atomistic level of detail we estimate the number of microscopic rebindings before a macroscopic dissociation occurs which leads to the macroscopic residence time, τDmacro ~ 48±12ms resulting in a in vitro sliding length estimate of 135-345bp. When we fit the DNA interaction parameters for in vivo conditions to recent single molecule in vivo experiments we conclude that neither hopping nor intersegment transfer contribute to the target search for the LacI dimer, that it appears to bind the specific Osym operator site as soon as it slides into it, and that the sliding length is around 40bp in the cell. The estimated in vivo D1 ~ 0.025 μm2s-1 is higher than expected from estimates of D1 based on viscosity and the atomistic simulations. Surprisingly, we were also forced to conclude that the nonspecific association for the LacI dimer appeared reaction limited which is in conflict with the free energy profile. This inconsistency is resolved by allowing for steric effects. Using reaction-diffusion theory and simulations we show that an apparent reaction limited association can be diffusion limited if geometry and steric effects are taken into account. Furthermore, the simulations show that a protein binds ~2 times faster to a DNA molecule with a helical reactive patch than to a stripe patch running along the length of the DNA. This facilitated binding has a direct impact on the search time especially in the presence of other DNA binding proteins.
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Agliari, Elena, Raffaella Burioni, Davide Cassi, and Franco M. Neri. "Autocatalytic reaction-diffusion processes in restricted geometries." Diffusion fundamentals 7 (2007) 1, S. 1-8, 2007. https://ul.qucosa.de/id/qucosa%3A14157.
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Van, Wijland Frédéric. "Marches aleatoires et problemes de reaction-diffusion." Paris 11, 1998. http://www.theses.fr/1998PA112008.
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Cette these comprend deux parties. La premiere est consacree a l'etude de quelques proprietes de la marche aleatoire simple, la seconde traite des reactions limitees par diffusion avec transition de phase dans l'etat stationnaire. Dans la partie traitant de la marche aleatoire simple, l'objet central de l'etude est le support de la marche, c'est-a-dire l'ensemble des sites visites. Nous considerons en detail les proprietes topologiques du support d'une marche bidimensionnelle. Combien y a-t-il d'ilots de sites non visites enfermes dans le support apres un grand nombre de pas ? quelle est la longueur de la courbe formant l'interface entre les regions visitees et les regions non visitees ? nous montrons alors que le nombre de sites visites, le nombre d'ilots et la longueur de la frontiere, fluctuent proportionnellement a une unique variable aleatoire. En dimension 3, nous montrons que la propriete d'universalite des fluctuations vaut toujours pour les variables analogues, mais qu'elle est mise en defaut des que d > 3. Nous concluons par les proprietes d'auto-correlation temporelle de ces variables. Nous etudions dans la seconde partie une reaction modelisant la propagation d'une epidemie mettant en jeu deux especes. Son etat stationnaire presente une transition de phase continue alors que l'on varie la densite totale de particules de part et d'autre d'une valeur seuil. Cette transition est caracterisee par des lois d'echelle que nous determinons en exploitant une version dynamique du groupe de renormalisation a la wilson. Nous considerons le probleme obtenu en remplacant le mouvement purement diffusif des particules par des vols de levy. Nous cherchons a etendre nos methodes d'etude aux reactions se deroulant en presence d'un desordre gele.
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Yu, Weiming. "Identification of Coefficients in Reaction-Diffusion Equations." University of Cincinnati / OhioLINK, 2004. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1076186036.
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Al-Ofl, Abdalaziz Saleem. "Analysis of complex nonlinear reaction-diffusion equations." Thesis, Durham University, 2008. http://etheses.dur.ac.uk/2422/.
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A mathematical analysis has been carried out for some nonlinear reaction- diffusion equations on open bounded convex domains Ω C R(^d)(d < 3) with Robin boundary conditions- Existence, uniqueness and continuous dependence on initial data of weak and strong solutions are proved. A numerical analysis has also been undertaken for these nonlinear reaction- diffusion equations on the above domains. A fully practical piecewise linear finite element approximation is proposed for which existence and uniqueness of the numerical solution are proved. Semi-discrete and fully discrete error estimates are given. A practical algorithm for computing the numerical solution is given and its convergence is proved. Finally, some numerical simulations in one-dimensional space are exhibited.
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Hagberg, Aric Arild. "Fronts and patterns in reaction-diffusion equations." Diss., The University of Arizona, 1994. http://hdl.handle.net/10150/186901.
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This is a study of fronts and patterns formed in reaction-diffusion systems. A doubly-diffusive version of the two component FitzHugh-Nagumo equations with bistable reaction dynamics is investigated as an abstract model for the study of pattern phenomenologies found in many different physical systems. Front solutions connecting the two stable uniform states are found to be key building blocks for understanding extended patterns such as stationary domains and traveling pulses in one dimension, and labyrinthine structures, splitting spots, and spiral wave turbulence in two dimensions. The number and type of front solutions is controlled by a bifurcation that we derive both analytically and numerically. At this bifurcation, called the nonequilibrium Ising-Bloch (NIB) bifurcation, a single stationary Ising front loses stability to a pair of counterpropagating Bloch fronts. In two dimensions, we derive a boundary where extended fronts become unstable to transverse perturbations. In addition, near the NIB bifurcation, we discover a multivalued relation between the front speed and general perturbations such as curvature or an external convective field. This multivalued form allows perturbations to induce transitions that reverse the direction of front propagation. When occurring locally along an extended front, these transitions nucleate spiral-vortex pairs. The NIB bifurcation and transverse instability boundaries divide parameter space into regions of different pattern behaviors. Before the bifurcation, the system may form transient patterns or stationary domains consisting of pairs of Ising fronts. Above the transverse instability boundary, two-dimensional planar fronts destabilize, grow, and finger to form a space-filling labyrinthine, or lamellar, pattern. Beyond the bifurcation the multiplicity of Bloch front solutions allows for the formation of persistent traveling pulses and spiral waves. Near the NIB bifurcation there is an intermediate region where new unexpected patterns are found. One-dimensional stationary domains become unstable to oscillating or breathing domains. In two dimensions, the transverse instability and local front transitions are the mechanisms behind spot splitting and the development of spiral wave turbulence. Similar patterns have been observed recently in the ferrocyanide-iodate-sulfite reaction.
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Poole, Anthony John. "Reaction-diffusion structures in nonlinear chemical kinetics." Thesis, University of Leeds, 1998. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.712528.
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Burke, Meghan A. "Suicide substrates : an analysis of the enzyme reaction and reaction-diffusion equations." Thesis, University of Oxford, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.305420.
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Filho, Sergio Muniz Oliva. "Reaction-diffusion systems on domains with thin channels." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/28837.
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Rolland, Guillaume. "Global existence and fast-reaction limit in reaction-diffusion systems with cross effects." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2012. http://tel.archives-ouvertes.fr/tel-00785757.
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This thesis is devoted to the study of parabolic systems of partial differential equations arising in mass action kinetics chemistry, population dynamics and electromigration theory. We are interested in the existence of global solutions, uniqueness of weak solutions, and in the fast-reaction limit in a reaction-diffusion system. In the first chapter, we study two cross-diffusion systems. We are first interested in a population dynamics model, where cross effects in the interactions between the different species are modeled by non-local operators. We prove the well-posedness of the corresponding system for any space dimension. We are then interested in a cross-diffusion system which arises as the fast-reaction limit system in a classical system for the chemical reaction C1+C2=C3. We prove the convergence when k goes to infinity of the solution of the system with finite reaction speed k to a global solution of the limit system. The second chapter contains new global existence results for some reaction-diffusion systems. For networks of elementary chemical reactions of the type Ci+Cj=Ck and under Mass Action Kinetics assumption, we prove the existence and uniqueness of global strong solutions, for space dimensions N<6 in the semi-linear case, and N<4 in the quasi-linear case. We also prove the existence of global weak solutions for a class of parabolic quasi-linear systems with at most quadratic non-linearities and with initial data that are only assumed to be nonnegative and integrable. In the last chapter, we generalize a global well-posedness result for reaction-diffusion systems whose nonlinearities have a "triangular" structure, for which we now take into account advection terms and time and space dependent diffusion coefficients. The latter result is then used in a Leray-Schauder fixed point argument to prove the existence of global solutions in a diffusion-electromigration system.
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Büger, Matthias. "Systems of reaction-diffusion equations and their attractors." Giessen : Selbstverlag des Mathematischen Instituts, 2005. http://catalog.hathitrust.org/api/volumes/oclc/62216537.html.
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Stich, Michael. "Target patterns and pacemakers in reaction-diffusion systems." [S.l.] : [s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=967163943.
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Provatas, Nikolas. "Kinetic roughening and bifurcations in reaction-diffusion systems." Thesis, McGill University, 1994. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=28886.
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We study the dynamics of two reaction-diffusion phenomena driven by chemical activation and thermal dissipation and evolving, respectively, on a randomly distributed or continuous medium. The first system describes the process of slow combustion of a randomly distributed reactant. It is studied by a phase-field model built up from first principles and describes the evolution of thermal and reactant concentration fields. Our combustion model incorporates thermal diffusion, activation and dissipation. We examine it in a manner which makes a connection between the propagation of combustion fronts, their kinetic roughening and the percolation transition. In so doing, we examine slow combustion in the context phase transitions. The second system describes propagation of reaction fronts arising in transformations obeying the Arrhenius law of chemical reactions. It too is modelled by a set of phase-field equations describing the dynamics of both thermal and concentration fields. A typical example of this transformation is the crystallization of an amorphous material. In addition to the features of our combustion model, this model also incorporated a realistic treatment of mass diffusion. Front propagation of our model is shown to undergo period doubling bifurcations as one varies the background temperature at which the system is maintained. The signature of these bifurcations is the same as those of the logistics map. We study how the bifurcation structure changes as a function mass diffusion, focusing on changes of the background temperature for which period doubling first emerges. This temperature is the most easily obtained experimentally.
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Xu, Lu. "Large deviations technique on stochastic reaction-diffusion equations." Thesis, University of Warwick, 2008. http://wrap.warwick.ac.uk/2736/.
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There are two different problems studied in this thesis. The first one is a travelling wave problem. We will improve the result proved in [4] to derive the ergodic property of the travelling wave behind the wavefront. The second problem is a large deviation problem concerning solutions to certain kind stochastic partial differential equations. We will first briefly introduce some basics about SPDE in chapter 2. In chapter 3, we will prove a large deviation principle for super-Brownian motion when it is considered as a solution to an SPDE, using the LDP for super-Brownian motion when it is considered as a measure-valued branching process as solution to a martingale problem. In chapter 4, we will prove another LDP result for solutions of a stochastic reaction-diffusion equation with degenerate noise term. Finally in chapter 5, we will explore some applications of those LDP results proved previously.
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Huang, Ke. "Diffusion and reaction in selected uranium alloy system." Doctoral diss., University of Central Florida, 2012. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/5311.
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U-Mo metallic fuels with Al alloys as the matrix/cladding are being developed as low enriched uranium fuels under the Reduced Enrichment for Research and Test Reactor (RERTR) program. Significant interactions have been observed to occur between the U-Mo fuel and the Al alloy during fuel processing and irradiation. U-Zr metallic fuels with stainless steel claddings have been developed for the generation IV sodium fast reactor (SFR). The fuel cladding chemical interaction (FCCI) induced by the interdiffusion of components was also observed. These interactions induce deleterious effects on the fuel system, such as thinning of the cladding layer, formation of phases with undesirable properties, and thermal cracking due to thermal expansion mismatches and changes in molar volume. The interaction between the fuel and the cladding involves multi-component interdiffusion. To determine the ternary interdiffusion coefficients using a single diffusion couple, a new method based on regression via the matrix transformation approach is proposed in this study. This new method is clear in physical meaning and simple in mathematical calculation. The reliability and accuracy of this method have been evaluated through application to three case studies: a basic asymptotic concentration profile, a concentration profile with extrema and a smoothed concentration profile with noise. Generally, this new method works well in all three cases. In order to investigate the interdiffusion behavior in U-Mo alloys, U vs. Mo diffusion couples were assembled and annealed in the temperature range of 650 to 1000°C. The interdiffusion microstructures and concentration profiles were examined via scanning electron microscopy (SEM) and electron probe microanalysis (EPMA), respectively. Interdiffusion coefficients and activation energies were calculated as functions of temperature and Mo composition. The intrinsic diffusion coefficients of U and Mo at the marker composition were also determined. The activity of U and the thermodynamic factor of the U-Mo alloy have been calculated using the ideal solution, the regular solution, and the subregular solution models based on the molar excess Gibbs free energy of the U-Mo alloy. The calculated intrinsic diffusivities of U and Mo along with the thermodynamic factor of the U-Mo alloy were employed to estimate the atomic mobilities and the vacancy wind effects of U and Mo according to Manning's description. To explore potential diffusion barrier materials for reducing the fuel cladding chemical interaction between the U-Mo fuel and the Al alloy matrix/cladding, the interdiffusion behavior between U-Mo alloys and Mo, Zr, Nb and Mg were systematically studied. U-10wt.%Mo vs. Mo, Zr and Nb diffusion couples were annealed in the temperature range from 600 to 1000°C. A diffusion couple between U-7wt.%Mo and Mg was annealed at 550°C for 96 hours. SEM and transmission electron microscopy (TEM) were applied to characterize the microstructure of the interdiffusion zone. X-ray energy dispersive spectroscopy (XEDS) and EPMA were utilized to examine the concentration redistribution and the phase constituents. For the U-Mo vs. Mo diffusion couples, the interdiffusion coefficients at high Mo concentrations ranging from 22 to 32 at.%Mo were determined for the first time. In the U-Mo vs. Zr diffusion couples, the Mo2Zr phase was found at the interface. The diffusion paths were estimated and investigated according to the Mo-U-Zr ternary phase diagram. Thermal cracks and pure U precipitates were found within the diffusion zone in the U-Mo vs. Nb system. The growth rate of the interdiffusion zone was found to be lower by about 103 times for Zr, 105 times for Mo and 106 times for Nb compared to those observed in the U-10wt.%Mo vs. Al or Al-Si systems. For the diffusion couple of U-Mo vs. Mg, the U-Mo was bonded very well to the Mg and there was negligible diffusion observed even after 96 hours annealing at 550°C. For a more fundamental understanding of the complex diffusion behavior between U-Zr fuels and their stainless steel claddings, U vs. Fe, Fe-15wt.%Cr and Fe-15wt.%Cr-15wt.%Ni diffusion couples were examined to investigate the interdiffusion behaviors between U and Fe and the effects of the alloying elements Cr and Ni. The diffusion couples were annealed in the temperature range from 580 to 700°C for various times. Two intermetallic phases, U6Fe and UFe2, developed in all of the diffusion couples with the U6Fe layer growing faster than the UFe2 layer. For the diffusion couples of U vs. Fe, extrinsic growth constants, intrinsic growth constants, integrated interdiffusion coefficients and activation energies in each phase were calculated. The results suggest that U6Fe impeded the growth of UFe2, and the boundary condition change caused by the allotropic transformation of U played a role in the growth of the U6Fe and UFe2 layers. The reasons why U6Fe grew much faster than UFe2 are also discussed. The additions of Cr and Ni into Fe affected the growth rates of U6Fe and UFe2. The solubility of Cr and Ni in U6Fe and UFe2 were determined, and it was found that Cr diffused into U more slowly than Fe or Ni.Ph.D.
Doctorate
Materials Science Engineering
Engineering and Computer Science
Materials Science and Engineering
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Wu, Yixiang. "Long Time Behavior for Reaction-Diffusion Population Models." Thesis, University of Louisiana at Lafayette, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10002390.
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In this work, we study the long time behavior of reaction-diffusion models arising from mathematical biology. First, we study a reaction-diffusion population model with time delay. We establish a comparison principle for coupled upper/lower solutions, prove the existence/uniqueness result for the model, and show the global asymptotic behavior of the model by constructing successive improved upper/lower solutions. Next, we consider a reaction-diffusion equation with continuous delay and spatial variable coefficients. We prove the global attractivity of the positive steady state by showing that the omega limit set is a singleton. Finally, we study an SIS reaction-diffusion model with spatial heterogeneous disease transmission and recovery rates. We define a basic reproduction number and obtain some existence and non-existence results of the endemic equilibrium of the model. We then study the global attractivity of the steady state for two special cases.
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Menon, Shakti Narayana. "Bifurcation problems in chaotically stirred reaction-diffusion systems." Thesis, The University of Sydney, 2008. http://hdl.handle.net/2123/3685.
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A detailed theoretical and numerical investigation of the behaviour of reactive systems under the influence of chaotic stirring is presented. These systems exhibit stationary solutions arising from the balance between chaotic advection and diffusion. Excessive stirring of such systems results in the termination of the reaction via a saddle-node bifurcation. The solution behaviour of these systems is analytically described using a recently developed nonperturbative, non-asymptotic variational method. This method involves fitting appropriate parameterised test functions to the solution, and also allows us to describe the bifurcations of these systems. This method is tested against numerical results obtained using a reduced one-dimensional reaction-advection-diffusion model. Four one- and two-component reactive systems with multiple homogeneous steady-states are analysed, namely autocatalytic, bistable, excitable and combustion systems. In addition to the generic stirring-induced saddle-node bifurcation, a rich and complex bifurcation scenario is observed in the excitable system. This includes a previously unreported region of bistability characterised by a hysteresis loop, a supercritical Hopf bifurcation and a saddle-node bifurcation arising from propagation failure. Results obtained with the nonperturbative method provide a good description of the bifurcations and solution behaviour in the various regimes of these chaotically stirred reaction-diffusion systems.