Dissertations / Theses on the topic 'Reaction-diffusion'
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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/.
Full textYangari, Sosa Miguel Ángel. "Fractional reaction-diffusion problems." Tesis, Universidad de Chile, 2014. http://www.repositorio.uchile.cl/handle/2250/115538.
Full textThis 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.
Yangari, Sosa Miguel Angel. "Fractional reaction-diffusion problems." Toulouse 3, 2014. http://thesesups.ups-tlse.fr/2270/.
Full textThis 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
Coulon, Anne-Charline. "Propagation in reaction-diffusion equations with fractional diffusion." Doctoral thesis, Universitat Politècnica de Catalunya, 2014. http://hdl.handle.net/10803/277576.
Full textEsta 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
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.
Full textFei, Ning Fei. "Studies in reaction-diffusion equations." Thesis, Heriot-Watt University, 2003. http://hdl.handle.net/10399/310.
Full textGrant, Koryn. "Symmetries and reaction-diffusion equations." Thesis, University of Kent, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.264601.
Full textFrömberg, Daniela. "Reaction Kinetics under Anomalous Diffusion." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2011. http://dx.doi.org/10.18452/16374.
Full textThe 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.
Coulon, Chalmin Anne-Charline. "Fast propagation in reaction-diffusion equations with fractional diffusion." Toulouse 3, 2014. http://thesesups.ups-tlse.fr/2427/.
Full textThis 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
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.
Full textBishop, 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.
Full textHemming, 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.
Full textLunney, 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.
Full textBradshaw-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.
Full textHellander, 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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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.
Full textDans 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.
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.
Full textCrampin, Edmund John. "Reaction-diffusion patterns on growing domains." Thesis, University of Oxford, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.325756.
Full textSmith, Stephen. "Stochastic reaction-diffusion models in biology." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/33142.
Full textPfeifer, Peter, and Chen Hou. "Diffusion-Reaction in space-filling networks." Universitätsbibliothek Leipzig, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-184563.
Full textNagaiah, Chamakuri. "Adaptive numerical simulation of reaction-diffusion systems." [S.l.] : [s.n.], 2007. http://deposit.ddb.de/cgi-bin/dokserv?idn=985277882.
Full textClaus, 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.
Full textSun, 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.
Full textRondoni, Lamberto. "A stochastic treatment of reaction and diffusion." Diss., This resource online, 1991. http://scholar.lib.vt.edu/theses/available/etd-07282008-134042/.
Full textSantos, 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.
Full textFurtado, Kalli. "Mesoscopic simulations of reaction-diffusion-advection problems." Thesis, University of Oxford, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.442953.
Full textDavidson, Fordyce A. "Bifurcation in systems of reaction-diffusion equations." Thesis, Heriot-Watt University, 1993. http://hdl.handle.net/10399/1444.
Full textFreitas, Pedro S. C. de. "Some problems in nonlocal reaction-diffusion equations." Thesis, Heriot-Watt University, 1994. http://hdl.handle.net/10399/1401.
Full textHoward, 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.
Full textTurpin, Kevin. "Patterns and fronts in reaction-diffusion systems." Thesis, University of Nottingham, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.287233.
Full textAldurayhim, Abdullah Mohammed. "Propagating waves in reaction cross-diffusion systems." Thesis, University of Exeter, 2017. http://hdl.handle.net/10871/31129.
Full textKammogne, Kamgaing Rodrigue. "Domain decomposition methods for reaction-diffusion systems." Thesis, University of Birmingham, 2014. http://etheses.bham.ac.uk//id/eprint/4599/.
Full textAgliari, 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.
Full textMahmutovic, 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.
Full textAgliari, 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.
Full textVan, Wijland Frédéric. "Marches aleatoires et problemes de reaction-diffusion." Paris 11, 1998. http://www.theses.fr/1998PA112008.
Full textYu, Weiming. "Identification of Coefficients in Reaction-Diffusion Equations." University of Cincinnati / OhioLINK, 2004. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1076186036.
Full textAl-Ofl, Abdalaziz Saleem. "Analysis of complex nonlinear reaction-diffusion equations." Thesis, Durham University, 2008. http://etheses.dur.ac.uk/2422/.
Full textHagberg, Aric Arild. "Fronts and patterns in reaction-diffusion equations." Diss., The University of Arizona, 1994. http://hdl.handle.net/10150/186901.
Full textPoole, 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.
Full textBurke, 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.
Full textFilho, Sergio Muniz Oliva. "Reaction-diffusion systems on domains with thin channels." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/28837.
Full textRolland, 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.
Full textBüger, Matthias. "Systems of reaction-diffusion equations and their attractors." Giessen : Selbstverlag des Mathematischen Instituts, 2005. http://catalog.hathitrust.org/api/volumes/oclc/62216537.html.
Full textStich, Michael. "Target patterns and pacemakers in reaction-diffusion systems." [S.l.] : [s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=967163943.
Full textProvatas, 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.
Full textXu, Lu. "Large deviations technique on stochastic reaction-diffusion equations." Thesis, University of Warwick, 2008. http://wrap.warwick.ac.uk/2736/.
Full textHuang, 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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Doctorate
Materials Science Engineering
Engineering and Computer Science
Materials Science and Engineering
Wu, Yixiang. "Long Time Behavior for Reaction-Diffusion Population Models." Thesis, University of Louisiana at Lafayette, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10002390.
Full textIn 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.
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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