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1
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.<br>eSSENCE
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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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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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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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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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Abdulbake, Janan. "A renormalisation approach to reaction-diffusion processes on fractals." Thesis, Glasgow Caledonian University, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.289517.
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Chaudhry, Qasim Ali. "Computational Modeling of Reaction and Diffusion Processes in Mammalian Cell." Doctoral thesis, KTH, Numerisk analys, NA, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-93466.
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PAHs are the reactive toxic chemical compounds which are present as environmental pollutants. These reactive compounds not only diffuse through the membranes of the cell but also partition into the membranes. They react with the DNA of the cell giving rise to toxicity and may cause cancer. To understand the cellular behavior of these foreign compounds, a mathematical model including the reaction-diffusion system and partitioning phenomenon has been developed. In order to reduce the complex structure of the cytoplasm due to the presence of many thin membranes, and to make the model less computationally expensive and numerically treatable, homogenization techniques have been used. The resulting complex system of PDEs generated from the model is implemented in Comsol Multiphysics. The numerical results obtained from the model show a nice agreement with the in vitro cell experimental results. Then the model was reduced to a system of ODEs, a compartment model (CM). The quantitative analysis of the results of the CM shows that it cannot fully capture the features of metabolic system considered in general. Thus the PDE model affords a more realistic representation. In order to see the influence of cell geometry in drug diffusion, the non-spherical axi-symmetric cell geometry is considered, where we showed that the cellular geometry plays an important role in diffusion through the membranes. For further reduction of complexity of the model, another simplified model was developed. In the simplified model, we used PDEs for the extracellular domain, cytoplasm and nucleus, whereas the plasma and nuclear membranes were taken away, and replaced by the membrane flux, using Fick's Law. We further extended the framework of our previously developed model by benchmarking against the results from four different cell lines. Global optimization techniques are used for the parameters describing the diffusion and reaction to fit the measured data. Numerical results were in good agreement with the in vitro results. For the further development of the model, the process of surface bound reactions were added, thus developing a new cell model. The effective equations were derived using iterative homogenization for this model. The numerical results of some of the species were qualitatively verified against the in vitro results found in literature.<br>QC 20120419
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Gérard, Thomas. "Theoretical study of spatiotemporal dynamics resulting from reaction-diffusion-convection processes." Doctoral thesis, Universite Libre de Bruxelles, 2011. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209861.
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Dans les réacteurs industriels ou dans la nature, l'écoulement de fluides peut être couplé à des réactions chimiques. Dans de nombreux cas, il en résulte l'apparition de structures complexes dont les propriétés dépendent entre autres de la géométrie du système.<p><p>Dans ce contexte, le but de notre thèse a été d'étudier de manière théorique et sur des modèles réaction-diffusion-convection simples les propriétés de dynamiques spatio-temporelles résultant du couplage chimie-hydrodynamique. <p>Nous nous sommes focalisés sur les instabilités hydrodynamiques de digitation visqueuse et de densité qui apparaissent respectivement lorsqu'un fluide dense est placé au-dessus d'un fluide moins dense dans le champ de gravité et lorsqu'un fluide visqueux est déplacé par un fluide moins visqueux dans un milieu poreux.<p><p>En particulier, nous avons étudié les problèmes suivants:<p>- L'influence d'une réaction chimique de type A + B → C sur la digitation visqueuse. Nous avons montré que les structures formées lors de cette instabilité varient selon que le réactif A est injecté dans le réactif B ou vice-versa si ces réactifs n'ont pas un coefficient de diffusion ou une concentration initiale identiques.<p>- Le rôle de pertes de chaleur par les parois du réacteur dans le cadre de la digitation de densité de fronts autocatalytiques exothermiques. Nous avons caractérisé les conditions de stabilité de fronts en fonction des pertes de chaleur et expliqué l'apparition de zones anormalement chaudes lors de cette instabilité.<p>- L'influence de l'inhomogénéité du milieu sur la digitation de densité de solutions réactives ou non. Nous avons montré que les variations spatiales de perméabilité d'un milieu poreux peuvent figer ou faire osciller la structure de digitation dans certaines conditions.<p>- L'influence d'un champ électrique transverse sur l'instabilité diffusive et la digitation de densité de fronts autocatalytiques. Il a été montré que cette interaction peut donner lieu à des nouvelles structures et changer les propriétés du front.<p><p>En conclusion, nous avons montré que le couplage entre réactions chimiques et mouvements hydrodynamiques est capable de générer de nouvelles structures spatio-temporelles dont les propriétés dépendent entre autres des conditions imposées au système.<p>/<p>In industrial reactors or in nature, fluid flows can be coupled to chemical reactions. In many cases, the result is the emergence of complex structures whose properties depend among others on the geometry of the system.<p>In this context, the purpose of our thesis was to study theoretically using simple models of reaction-diffusion-convection, the properties of dynamics resulting from the coupling between chemistry and hydrodynamics.<p><p>We focused on the hydrodynamic instabilities of viscous and density fingering that occur respectively when a dense fluid is placed above a less dense one in the gravity field and when a viscous fluid is displaced by a less viscous fluid in a porous medium.<p><p>In particular, we studied the following issues:<p>- The influence of a chemical reaction type A + B → C on viscous fingering. We have shown that the fingering patterns observed during this instability depends on whether the reactant A is injected into the reactant B or vice versa if they do not have identical diffusion coefficients or initial concentrations.<p>- The role of heat losses through the reactor walls on the density fingering of exothermic autocatalytic fronts. We have characterized the conditions of stability of fronts depending on heat losses and explained the appearance of unusually hot areas during this instability.<p>- The influence of the inhomogeneity of the medium on the density fingering of reactive solutions or not. We have shown that spatial variations of permeability of a porous medium may freeze or generate oscillating fingering pattern under certain conditions.<p>- The influence of a transverse electric field on the Rayleigh-Taylor and diffusive instabilities of autocatalytic fronts. It was shown that this interaction may lead to new structures and may change the properties of the front.<p><p>In conclusion, we showed that the coupling between chemical reactions and hydrodynamic motions can generate new space-time structures whose properties depend among others, on the conditions imposed on the system.<br>Doctorat en Sciences<br>info:eu-repo/semantics/nonPublished
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Larsson, Stig. "On reaction-diffusion equation and their approximation by finite element methods /." Göteborg : Chalmers tekniska högskola, Dept. of Mathematics, 1985. http://bibpurl.oclc.org/web/32831.
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Wang, Siyang. "Simulation of stochastic reaction-diffusion processes on lower dimensional manifolds with application in molecular biology." Thesis, Uppsala universitet, Institutionen för informationsteknologi, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-181613.
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In this thesis, we simulate stochastically the reaction-diffusion processes in a living cell. The simulation is done in three dimension (3D) by MATLAB. The one dimensional (1D) polymers are embedded in the 3D space. The reaction and diffusion events occur both in the space and on the polymers. There is also a possibility for the molecule to jump between the 3D space and 1D polymers. Two simulation levels are used: mesoscopic and microscopic. An accurate and efficient algorithm is developed for the mesoscopic simulation. The corresponding microscopic Smoluchowski equation is solved numerically by a finite difference method in a specific coordinate system adapted to its boundary conditions. The comparison between the result of the mesoscopic simulation and the solution of the microscopic Smoluchowski equation is provided. Good agreement is observed in the experiments.
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Eigel, Martin. "An adaptive meshfree method for reaction-diffusion processes on complex domains applications in cell biology." Thesis, University of Warwick, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.502535.
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A mesh-free numerical method for solving partial differential equations (PDE) on geometrically complex domains is presented. The approach is based on the general Partition of Unity Method (PUM), a framework developed by Babuska and Melenk in [8, 122]. In order to underline the universality of our method, we summarise the current state-of-the-art of the PUM in a comprehensive, self-contained way. Additionally, as an interesting research direction, fundamental and recent a posteriori error estimation techniques are discussed and transferred to the PUM. These are employed to steer an adaptive refinement process with the aim to reduce the overall error in an efficient way, Le. with the least additional computational complexity. Particular attention is paid to the targeted application area: the life sciences and, more specifically, transport processes in cell biology. Biological environments exhibit several features which make them quite different to classical fields of application. We discuss some of these properties and propose a novel approach to define and examine complex transport mechanisms based on 'elementary modules' describing typical phenomena. This systematic approach culminates in the definition of a biological transport toolbox whose building blocks can be plugged together to form more complex systems. One of the paramount challenges one has to tackle in biological simulations is the spatial discretisation of c'omplex geometries. Hence, we develop a general method to automatically handle complicated shapes which may be organised hierarchically, thus allowing for the simulation of processes spanning several nested domains. Additionally, processes may also take place on the interfaces, reminiscent of biological binding and transport phenomena on membranes. The numerical technique employed in this case is a mixed mesh-based and mesh-free discretisation. '!\vo interesting and important biological systems are discussed in order to relate the presented ideas to real-world applications. First, we summarise some properties of the nucleus of the eukaryote cell, a compartment where nearly the entire genetic information of a cell is contained. Second, the thylakoid, an organelle of the chloroplast of the plant cell, is depicted. Typical transport processes encountered in these model systems are then examined to demonstrate the developed methodology. The powerful combination of a systematic and modular modelling approach and 'in silica' experiments based on a versatile numerical method represents, we hope, an important contribution to the interdisciplinary research required to attack the multitude of challenges the study of biological systems poses.
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Ayodele, Segun Gideon [Verfasser]. "Lattice Boltzmann Modeling of Advection-Diffusion-Reaction Equations in Non-equilibrium Transport Processes / Segun Gideon Ayodele." Aachen : Shaker, 2013. http://d-nb.info/1050344170/34.
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Hellander, Andreas. "Multiscale Stochastic Simulation of Reaction-Transport Processes : Applications in Molecular Systems Biology." Doctoral thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-152098.
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Quantitative descriptions of reaction kinetics formulated at the stochastic mesoscopic level are frequently used to study various aspects of regulation and control in models of cellular control systems. For this type of systems, numerical simulation offers a variety of challenges caused by the high dimensionality of the problem and the multiscale properties often displayed by the biochemical model. In this thesis I have studied several aspects of stochastic simulation of both well-stirred and spatially heterogenous systems. In the well-stirred case, a hybrid method is proposed that reduces the dimension and stiffness of a model. We also demonstrate how both a high performance implementation and a variance reduction technique based on quasi-Monte Carlo can reduce the computational cost to estimate the probability density of the system. In the spatially dependent case, the use of unstructured, tetrahedral meshes to sample realizations of the stochastic process is proposed. Using such meshes, we then extend the reaction-diffusion framework to incorporate active transport of cellular cargo in a seamless manner. Finally, two multilevel methods for spatial stochastic simulation are considered. One of them is a space-time adaptive method combining exact stochastic, approximate stochastic and macroscopic modeling levels to reduce the simualation cost. The other method blends together mesoscale and microscale simulation methods to locally increase modeling resolution.<br>eSSENCE
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Driver, David Philip. "An optimisation-based approach to FKPP-type equations." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/277769.
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In this thesis, we study a class of reaction-diffusion equations of the form $\frac{\partial u}{\partial t} = \mathcal{L}u + \phi u - \tfrac{1}{k} u^{k+1}$ where $\mathcal{L}$ is the stochastic generator of a Markov process, $\phi$ is a function of the space variables and $k\in \mathbb{R}\backslash\{0\}$. An important example, in the case when $k > 0$, is equations of the FKPP-type. We also give an example from the theory of utility maximisation problems when such equations arise and in this case $k < 0$. We introduce a new representation, for the solution of the equation, as the optimal value of an optimal control problem. We also give a second representation which can be seen as a dual problem to the first optimisation problem. We note that this is a new type of dual problem and we compare it to the standard Lagrangian dual formulation. By choosing controls in the optimisation problems we obtain upper and lower bounds on the solution to the PDE. We use these bounds to study the speed of the wave front of the PDE in the case when $\mathcal{L}$ is the generator of a suitable Lévy process.
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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 Matemática<br>This 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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Bock, Josué. "Contribution à l'élaboration d'un modèle d'évolution physico-chimique de la neige." Thesis, Grenoble, 2012. http://www.theses.fr/2012GRENU037/document.
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Il est aujourd'hui avéré que la composition chimique de l'atmosphère des régions enneigées – et notamment des régions polaires – est sensiblement affectée par les échanges d'espèces chimiques réactives entre l'air et la neige. En effet, le manteau neigeux constitue un véritable réacteur photochimique multiphasique, mais les mécanismes physico-chimiques à l'œuvre en son sein sont encore mal connus. Une compréhension détaillée des processus s'y déroulant est indispensable pour modéliser correctement la composition et la réactivité de l'atmosphère au-dessus des régions enneigées. De plus, la reconstitution de l'évolution post-dépôt des composés chimiques stables de la neige est également un préalable indispensable pour permettre l'interprétation paléoclimatique de leurs profils de concentration enregistrés dans les carottes de glace.Le nitrate (NO3-) présent dans la neige joue un rôle fondamental, car sa photolyse induit notamment l'émission d'oxydes d'azote (NOx = NO + NO2) par le manteau neigeux, qui modifient la capacité oxydante de l'atmosphère via la production d'ozone. L'objet de cette thèse a donc été d'étudier par modélisations les processus physico-chimiques intervenants dans l'évolution de la concentration du nitrate dans la neige.Une première approche, prolongeant des études préexistantes, a visé à identifier un mécanisme réactionnel pour la photochimie du nitrate dans la neige, en postulant notamment l'existence d'une couche quasi-liquide à la surface des grains de neige. Néanmoins, les propriétés exactes de l'interface air – glace sont, à l'heure actuelle, encore mal caractérisées, et il est apparu que cette démarche présentait de trop larges incertitudes pour être poursuivie.Une discussion approfondie a alors été menée afin d'évaluer les tentatives actuelles de modélisation de la chimie de la neige, et dans le but de proposer une nouvelle approche plus réaliste au regard du niveau de connaissance actuel.Ainsi, dans une seconde partie, l'ensemble des processus d'échange physico-chimiques du nitrate entre l'air et la neige ont été étudiés puis modélisés : adsorption à la surface, diffusion en phase solide et co-condensation. Parmi les résultats obtenus, il est apparu que les paramétrisations actuelles de la couverture surfacique en nitrate étaient incapables de reproduire les concentrations mesurées, dans le cas de la neige de surface à Dome C, et révèlent d'importantes surestimations. A contratio, la prise en compte conjointe de la diffusion en phase solide ainsi que d'un processus de co-condensation permet de bien reproduire qualitativement les séries temporelles de plus d'un an, couvrant donc à la fois l'été et l'hiver austral, qui présentent chacun des caractéristiques distinctes en terme de concentration mesurées.Cette étude révèle ainsi l'importance de ces processus physico-chimiques d'échange dans la modélisation de la chimie de la neige, et pose les bases des mécanismes à prendre en compte dans le cadre de développements futurs<br>It is increasingly recognized that the atmosphere composition of snow covered regions – especially polar regions – is noticeably affected by air-snow interactions. Indeed, the snowpack is a multiphase reactor, but physico-chemical processes which take place inside are still poorly understood. A detailled understanding of snow-atmosphere interactions is essential for understanding and modeling properly the composition and reactivity of the atmosphere above snow covered regions. Reconstructions of past trends in atmospheric composition using ice cores also require to understand snowpack processes that affected the composition of interstitial air and burried snow after its deposition.Nitrate (NO3-) present in the snowpack plays an important role as it photochemically produces nitrogen oxides (NOx=NO+NO2), which affect the oxidative capacity of the atmosphere through ozone production.This thesis thus aimed at studying physico-chemical processes which take place inside the snowpack and modify nitrate concentration.In a first part, a reaction mechanism to reproduce nitrate photochemistry in snow were developed, based on previous studies. The main hypothesis was that chemical reactions take place in a quasi-liquid layer located on the surface of snow cristals. However, the properties of this ice-air interface are poorly known, and it appeared that this approach had too many uncertainties to be continued.Then, a thorough discussion were carried out to assess current attempts in snow chemistry modeling, and to propose another approach which could prevail given current knowledge on this topic.In a second part, physico-chemical exchange processes between air and snow were studied and modeled. This concerned adsorption, solid phase diffusion and co-condensation. Among the results that arise, it appeared that current parameterizations of nitrate surface coverage are unable to reproduce measured concentrations, in the studied case of Dome C surface snow, and further reveal sizeable overestimations. On the contrary, simultaneous modeling of solid phase diffusion and co-condensation allows a qualitatively good reproduction of measurements, which cover more than a year, thus including both austral summer and winter with their specific features.This study reveals the importance of exchange processes for snow chemistry modeling, and give basis for future work on this topic
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Moreira, Juliana. "Eletrogeração de peróxido de hidrogênio (H2O2) em eletrodos de difusão gasosa (EDG) modificados com quinonas (metil-p-benzoquinona, antraquinona-2-ácido carboxílico e ácido antraflávico) e azocomposto (Sudan Red 7B)." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/75/75135/tde-14032019-100953/.
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Os processos oxidativos avançados (POA) são uma alternativa para complementar os processos clássicos de tratamento de efluentes que podem não ser eficientes para remoção de alguns tipos de poluentes como, por exemplo, os poluentes emergentes. Os POA se baseiam na geração de espécies altamente reativas (radicais hidroxila), a partir de peróxido de hidrogênio (H2O2), que oxidam os poluentes. O H2O2 pode ser eletrogerado in situ pela reação de redução de oxigênio (RRO) no meio reacional. O uso de eletrodos de difusão gasosa (EDG) altamente porosos proporciona o suprimento de oxigênio na interface eletrodo/solução podendo aumentar a velocidade da RRO. O uso de modificadores como quinonas e azocompostos imobilizados à matriz de carbono dos EDG podem aumentar a geração de H2O2. Portanto, os modificadores orgânicos Sudan Red 7B (SR7B), metil-p-benzoquinona (MPB), ácido antraflávico (AA) e antraquinona-2-ácido carboxílico (A2CA) foram adicionados em diferentes teores ao carbono Printex L6 (CP) e microcamadas porosas destes materiais foram estudados por voltametria cíclica e de varredura linear em eletrodo de disco-anel rotatório (RRDE). Os materiais contendo 0,5% de SR7B e 5,0% de MPB levaram a aumento na eficiência de geração de H2O2 para 86,2 e 85,5%, respectivamente, em relação ao CP puro que levou a 82,8%. EDG de CP modificados com 0,5% de SR7B foram construídos com telas metálicas em sua faces externas e a aplicação de densidades de corrente de 75, 100 e 150 mA cm-2 levou a uma maior eletrogeração de H2O2. Em densidades de corrente de 75 mA cm-2, o EDG modificado gerou 1020,1 mg L-1 de H2O2 com consumo energético de 118,0 kWh kg-1 de H2O2, constante cinética aparente de 37,3 mg L-1 min-1 e eficiência de corrente de 17,9%, enquanto o EDG de CP puro gerou menor concentração de H2O2; 717, 3 mg L-1, com maior consumo energético; 168,5 kWh kg-1, menor constante cinética aparente; 21,4 mg L-1 min-1, e menor eficiência de corrente; 12,6%. Portanto, o EDG modificado poderia ser empregado em sistemas que precisem de altas gerações de H2O2.<br>The advanced oxidation processes (AOP) are an alternative to the classical processes of treatment of effluents that may not be effective for the removal of some types of pollutants such as emerging pollutants. The AOP are based on the highly reactive species (hydroxyl radicals) from hydrogen peroxide (H2O2), which oxidize pollutants. H2O2 can be electrogenerated in situ by the oxygen reduction reaction (ORR) in the reaction medium. The use of highly porous gas diffusion electrodes (GDE) provides the supply of oxygen at the electrode/solution interface, which can increase the RRO speed. The use of modifiers such as quinones and azocompounds immobilized on the carbon matrix of GDE may increase H2O2 generation. Therefore, the organic modifiers Sudan Red 7B (SR7B), methyl-p-benzoquinone (MPB), anthraflavic acid (AA) and anthraquinone-2-carboxylic acid (A2CA) were added in different contents to carbon Printex L6 (CP) and microporous layers of these materials were studied by cyclic voltammetry and linear sweep voltammetry on a rotating ring- disc electrode (RRDE). Materials with 0.5% of SR7B and 5.0% of MPB increased the current efficiency for electrogeneration of H2O2 to 86.2 and 85.5%, respectively, in relation to pure CP that leaded to 82.8%. GDE of CP modified with 0.5% of SR7B were constructed with metallic screens on their outer faces and an application of current densities of 75, 100 and 150 mA cm-2 led to a greater electrogeneration of H2O2. At current densities of 75 mA cm-2, the modified GDE generated 1020.1 mg L-1 of H2O2 with energy consumption of 118.0 kWh kg-1 of H2O2, apparent kinetic constant of 37.3 mg L-1 min-1 and current efficiency of 17.9%, while GDE of pure CP generated lower H2O2 concentration; 717, 3 mg L-1, with higher energy consumption; 168.5 kWh kg-1, lower apparent kinetic constant; 21.4 mg L-1 min-1, and lower current efficiency; 12.6%. Therefore, the modified GDE could be applied in systems that require high generations of H2O2.
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Shabala, Alexander. "Mathematical modelling of oncolytic virotherapy." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:cca2c9bc-cbd4-4651-9b59-8a4dea7245d1.
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This thesis is concerned with mathematical modelling of oncolytic virotherapy: the use of genetically modified viruses to selectively spread, replicate and destroy cancerous cells in solid tumours. Traditional spatially-dependent modelling approaches have previously assumed that virus spread is due to viral diffusion in solid tumours, and also neglect the time delay introduced by the lytic cycle for viral replication within host cells. A deterministic, age-structured reaction-diffusion model is developed for the spatially-dependent interactions of uninfected cells, infected cells and virus particles, with the spread of virus particles facilitated by infected cell motility and delay. Evidence of travelling wave behaviour is shown, and an asymptotic approximation for the wave speed is derived as a function of key parameters. Next, the same physical assumptions as in the continuum model are used to develop an equivalent discrete, probabilistic model for that is valid in the limit of low particle concentrations. This mesoscopic, compartment-based model is then validated against known test cases, and it is shown that the localised nature of infected cell bursts leads to inconsistencies between the discrete and continuum models. The qualitative behaviour of this stochastic model is then analysed for a range of key experimentally-controllable parameters. Two-dimensional simulations of in vivo and in vitro therapies are then analysed to determine the effects of virus burst size, length of lytic cycle, infected cell motility, and initial viral distribution on the wave speed, consistency of results and overall success of therapy. Finally, the experimental difficulty of measuring the effective motility of cells is addressed by considering effective medium approximations of diffusion through heterogeneous tumours. Considering an idealised tumour consisting of periodic obstacles in free space, a two-scale homogenisation technique is used to show the effects of obstacle shape on the effective diffusivity. A novel method for calculating the effective continuum behaviour of random walks on lattices is then developed for the limiting case where microscopic interactions are discrete.
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Mélykúti, Bence. "Theoretical advances in the modelling and interrogation of biochemical reaction systems : alternative formulations of the chemical Langevin equation and optimal experiment design for model discrimination." Thesis, University of Oxford, 2010. http://ora.ox.ac.uk/objects/uuid:d368c04c-b611-41b2-8866-cde16b283b0d.
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This thesis is concerned with methodologies for the accurate quantitative modelling of molecular biological systems. The first part is devoted to the chemical Langevin equation (CLE), a stochastic differential equation driven by a multidimensional Wiener process. The CLE is an approximation to the standard discrete Markov jump process model of chemical reaction kinetics. It is valid in the regime where molecular populations are abundant enough to assume their concentrations change continuously, but stochastic fluctuations still play a major role. We observe that the CLE is not a single equation, but a family of equations with shared finite-dimensional distributions. On the theoretical side, we prove that as many Wiener processes are sufficient to formulate the CLE as there are independent variables in the equation, which is just the rank of the stoichiometric matrix. On the practical side, we show that in the case where there are m_1 pairs of reversible reactions and m_2 irreversible reactions, there is another, simple formulation of the CLE with only m_1+m_2 Wiener processes, whereas the standard approach uses 2m_1+m_2. Considerable computational savings are achieved with this latter formulation. A flaw of the CLE model is identified: trajectories may leave the nonnegative orthant with positive probability. The second part addresses the challenge when alternative, structurally different ordinary differential equation models of similar complexity fit the available experimental data equally well. We review optimal experiment design methods for choosing the initial state and structural changes on the biological system to maximally discriminate between the outputs of rival models in terms of L_2-distance. We determine the optimal stimulus (input) profile for externally excitable systems. The numerical implementation relies on sum of squares decompositions and is demonstrated on two rival models of signal processing in starving Dictyostelium amoebae. Such experiments accelerate the perfection of our understanding of biochemical mechanisms.
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DELOUBRIERE, OLIVIER. "Problemes stochastiques associes a l'equation de langevin : persistance et processus de reaction-diffusion." Paris 6, 2001. http://www.theses.fr/2001PA066070.
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Cette these comprend deux parties independantes. Dans la premiere nous etudions la probabilite de persistance de differents processus aleatoires - probabilite qu'ils restent au-dessus d'un seuil fixe pendant un certain intervalle de temps - qui definit un nouvel exposant de la dynamique hors d'equilibre. Une theorie de perturbation au premier ordre a recemment ete elaboree pour calculer les exposants de persistance des processus gaussiens non markoviens. Nous elaborons ici la theorie au second ordre et l'appliquons au calcul de l'exposant de persistance de l'equation de la diffusion. Nous etudions ensuite une large classe de processus markoviens et non gaussiens. Les proprietes de persistance de la classe entiere, lorsque le seuil est fixe a la valeur moyenne du processus, sont universelles. Enfin dans la limite de grand seuil une methode originale nous permet d'etablir le comportement asymptotique de l'exposant de persistance en fonction du seuil et nous le comparons aux resultats donnes par des simulations. Dans la seconde partie nous abordons l'etude des equations de langevin avec bruit imaginaire qui definissent la dynamique sous-jacente de la theorie des champs associee aux processus de reaction-diffusion. Nous montrons, par exemple, comment la conservation de la parite du nombre de particules dans certains processus, se traduit dans ce formalisme. Ensuite nous etudions un modele extremement simplifie de la percolation dirigee ou la competition entre creation et annihilation de particules conduit a l'existence d'un etat stationnaire uniforme. Lorsque l'on varie l'un des parametres de controle - comme le taux de creation de particules - l'etat stationnaire exhibe une transition de phases continue ou le role des fluctuations peut etre analyse par le groupe de renormalisation. Nous montrons alors que la contrainte microscopique d'exclusion entre particules change les comportements critiques universels de ce modele en dimension un.
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Velleret, Aurélien. "Mesures quasi-stationnaires et applications à la modélisation de l'évolution biologique." Thesis, Aix-Marseille, 2020. http://www.theses.fr/2020AIXM0226.
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Je décris le comportement en temps long de plusieurs processus qui illustrent les mécanismes de sélection naturelle. Il arrive que ces effets de sélection s’interprètent comme un conditionnement qui biaise la dynamique d’un processus aléatoire "neutre". Ce processus évolue sur un espace potentiellement très général, notamment continu et non borné. On peut ainsi caractériser aussi bien la dynamique du profil complet de la population que celle du profil d’un individu choisi uniformément dans la population. On voit naturellement apparaître dans ces modèles des transitions brutales de ces lois qui rendent l’analyse plus délicate que pour les modèles sans conditionnement. La première partie de ce travail consiste à mettre en place des conditions permettant d’obtenir des résultats analogues à la stationnarité lorsqu’on prend en compte un tel conditionnement. La seconde porte sur l’application de ces critères à différents modèles de population sous sélection et sur leur interprétation. Les exemples d'applications concernent le modèle de l'optimum mobile pour l'adaptation à un changement environnemental, un modèle de sélection de groupes et celui du cliquet de Müller sur le maintien d'une sous-population préservée des mutations délétères<br>I describe the long term behavior of several processes that model the mechanisms of natural selection. In the cases under consideration, one can interpret those selective effects as a conditioning which introduces a bias on the dynamics of some « neutral » stochastic process. This process evolves in a potentially very general space, notably continuous and unbounded. By these means, one can characterize the dynamics of the whole profile of individuals in the population of study as well as the profile of an individual uniformly chosen in the population. One can naturally see in these descriptions some brutal transitions of the distribution laws as time evolves, which makes the analysis much trickier than for the models without conditioning. The first part of this thesis consists in setting the conditions under which one can prove results analogous to the notion of stationarity while taking the conditioning into account. The second part is dedicated to the application of these criteria for a diversity of models of populations under selection and their interpretation. Examples of application include the mobile optimum model for adaptation to environmental change, a group selection model and Müller's ratchet model that describes how the sub-population unaffected by deleterious mutations can maintain itself
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Galanti, Marta. "Processus de diffusion et réaction dans des milieux complexes et encombrés." Thesis, Orléans, 2016. http://www.theses.fr/2016ORLE2004/document.
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L'objectif général de cette thèse est d'analyser les processus de diffusion et les processus de réaction-diffusion dans plusieurs types de conditions non-idéales, et d'identifier dans quelle mesure ces conditions non idéales influencent la mobilité des particules et les réactions entre les molécules. Dans la première partie de la thèse, nous nous concentrons sur les effets de l'encombrement macromoléculaire sur la mobilité, ainsi élaborant une description des processus de diffusion dans des milieux densément peuplés. Tous les processus sont analysés à partir de la description microscopique du mouvement des agents individuels sous forme de marche aléatoire, tenant compte de l'espace occupé par les particules voisines. La deuxième partie de la thèse vise à caractériser le rôle de la géométrie de l'environnement et de la réactivité des corps qui y sont contenus sur la réaction entre des molécules sélectionnées. La théorie classique de Smoluchowski, formulée pour les réactions contrôlées par la diffusion dans un milieu dilué, est ainsi adaptée à des domaines arbitrairement décorés par des obstacles, dont certains réactifs, et l'équation stationnaire de diffusion est résolue avec des techniques d’analyse harmonique. Finalement, le calcul explicit de la constante de réaction et la dérivation des formules approximées sont utilisés pour étudier des applications biologiques et nano-technologiques<br>The overall purpose of this thesis is to analyze diffusion processes and diffusion-reaction processes in different types of non-ideal conditions, and to identify to which extent these non-ideal conditions influence the mobility of particles and the rate of the reactions occurring between molecules. In the first part of the thesis we concentrate on the effects of macromolecular crowding on the mobility of the agents, providing therefore a description of various diffusion processes in densely populated media. All the processes are analyzed by modeling the dynamics of the single agents as microscopic stochastic processes that keep track of the macromolecular crowding. The second part of the thesis aims at characterizing the role of the environment’s geometry (obstacles, compartmentalization) and distributed reactivity (competitive reactants, traps) on the reaction between selected molecules. The Smoluchowski theory for diffusion influenced reactions is thus adapted to domains arbitrarily decorated with obstacles and reactive boundaries, and the stationary diffusion equation is explicitly solved through harmonic-based techniques. The explicit calculation of the reaction rate constant and the derivation of simple approximated formulas are used for investigating nano-technological applications and naturally occurring reactions
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Janák, Marcel. "Diagnostika polovodičů a monitorování chemických reakcí metodou SIMS." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2021. http://www.nusl.cz/ntk/nusl-443241.
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Hmotnostná spektrometria sekundárnych iónov s analýzou doby letu (TOF-SIMS) patrí vďaka vysokej citlivosti na prvkové zloženie medzi významné metódy analýzy pevných povrchov. Táto práca demonštruje možnosti TOF-SIMS v troch odlišných oblastiach výskumu. Prvá časť práce sa zaoberá lokalizáciou defektov vysokonapäťových polovodičových súčiastok, ktorá je nevyhnutná k ich ďalšiemu skúmaniu metódou TOF-SIMS. Bola navrhnutá experimentálna zostava s riadiacim softvérom umožňujúca automatizované meranie záverného prúdu v rôznych miestach polovodičový súčiastok. Druhá časť práce sa zaoberá kvantifikáciou koncentrácie Mg dopantov v rôznych hĺbkach vzoriek AlGaN. Kvantifikácia je založená na metóde RSF a umožňuje charakterizáciu AlGaN heteroštruktúr určených na výrobu tranzistorov s vysokou elektrónovou mobilitou (HEMT) alebo na výrobu rôznych optoelektronických zariadení. Sada 12 AlGaN kalibračných vzoriek dopovaných Mg, určených na kvantifikáciu hĺbkových profilov, bola pripravená metódou iónovej implantácie. Posledná časť práce demonštruje možnosti metódy TOF-SIMS vo výskume heterogénnej katalýzy. Hlavným objektom nášho výskumu je dynamika oxidácie CO na oxid uhličitý na polykryštalickom povrchu platiny za tlakov vysokého vákua. V tejto práci prezentujem prvé TOF-SIMS pozorovanie časopriestorových vzorov v reálnom čase, ktoré vznikajú v dôsledku rôzneho pokrytia povrchu Pt reaktantmi. Výsledky TOF-SIMS experimentu boli porovnané s výsledkami podobného experiment v rastrovacom elektrónovom mikroskope (SEM).
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Bellot, Benoit. "Améliorer les connaissances sur les processus écologiques régissant les dynamiques de populations d'auxiliaires de culture : modélisation couplant paysages et populations pour l'aide à l'échantillonnage biologique dans l'espace et le temps." Thesis, Rennes 1, 2018. http://www.theses.fr/2018REN1B008/document.
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Une alternative prometteuse à la lutte chimique pour la régulation des ravageurs de culture consiste à favoriser les populations de leurs prédateurs en jouant sur la structure du paysage agricole. L'identification de structures spatio-temporelles favorables aux ennemis naturels peut se faire par l'exploration de scénarios paysagers via une modélisation couplée de paysages et de dynamiques de population. Dans cette approche, les dynamiques de populations sont simulées sur des paysages virtuels aux propriétés structurales contrôlées, et l'observation des motifs de populations associés permet l'identification de structures favorables. La modélisation des dynamiques de populations repose cependant sur une connaissance fine des processus écologiques et de leur variabilité entre les différentes unités du paysage. L'état actuel des connaissances sur les mécanismes écologiques régissant les dynamiques des ennemis naturels de la famille des carabidés demeure l'obstacle majeur à la recherche in silico de scénarios paysagers favorables. La littérature sur les liens entre motifs de population de carabes et variables paysagères permet de formuler un ensemble d'hypothèses en compétition sur ces mécanismes. Réduire le nombre de ces hypothèses en analysant les convergences entre les motifs de population qui leur sont associés, et étudier la stabilité de ces convergences le long d'un gradient paysager apparaît comme une première étape nécessaire vers l'amélioration de la connaissance sur les processus écologiques. Dans une première partie, nous proposons une heuristique méthodologique basée sur la simulation de modèles de réaction-diffusion porteurs de ces hypothèses en compétition. L'étude des motifs de population a permis d'effectuer une typologie des modèles en fonction de leur réponse à une variable paysagère, via un algorithme de classification, réduisant ainsi le nombre d’hypothèses en compétition. La sélection de l'hypothèse la plus plausible parmi cet ensemble irréductible doit s'effectuer sur la base d'une observation des motifs de population sur le terrain. Cela implique que ces derniers soient caractérisés à des résolutions spatiales et temporelles suffisantes pour sélectionner une unique hypothèse parmi celles en compétition. Dans la deuxième partie, nous proposons une heuristique méthodologique permettant de déterminer a priori des stratégies d'échantillonnage maximisant la robustesse de la sélection d'hypothèses écologiques. Dans un premier temps, la simulation de modèles de réaction-diffusion représentatifs des hypothèses écologiques en compétition permet de générer des données biologiques virtuelles en tout point de l'espace et du temps. Ces données biologiques sont ensuite échantillonnées suivant des protocoles différant dans l'effort total d'échantillonnage, le nombre de dates, le nombre de points par unité d'espace et le nombre de réplicats de paysages. Les motifs des populations sont caractérisés à partir de ces échantillons. Le potentiel des stratégies d'échantillonnage est évalué via un algorithme de classification qui classe les modèles biologiques selon les motifs de population associés. L'analyse des performances de classification, i.e. la capacité de l'algorithme à discriminer les processus écologiques, permet de sélectionner un protocole d'échantillonnage optimal. Nous montrons également que la manière de distribuer l'effort d'échantillonnage entre ses composantes spatiales et temporelles est un levier majeur sur l'inférence des processus écologiques. La réduction du nombre d'hypothèses en compétition et l'aide à l'échantillonnage pour la sélection de modèles répondent à un besoin fort dans le processus d'acquisition de connaissances écologiques pour l'exploration in silico de scénarios paysagers favorisant des services écosystémiques. Nous discutons dans une dernière partie des implications de nos travaux et de leurs perspectives d'amélioration<br>A promising alternative to the chemical control of pests consists in favoring their natural enemies populations by managing the agricultural landscape structure. Identifying favorable spatio-temporal structures can be performed through the exploration of landscape scenarios using coupled models of landscapes and population dynamics. In this approach, population dynamics are simulated on virtual landscapes with controlled properties, and the observation of population patterns allows for the identification of favorable structures. Population modeling however relies on a good knowledge about the ecological processes and their variability within the landscape elements. Current state of knowledge about the ecological mechanisms underlying natural enemies’ of the carabid family population dynamics remains a major obstacle to in silico investigation of favorable landscape scenarios. Literature about the relationship between carabid population and landscape properties allows the formulation of competing hypotheses about these processes. Reducing the number of these hypotheses by analyzing the convergence between their associated population patterns and investigating the stability of their convergence along a landscape gradient appears to be a necessary tep towards a better knowledge about ecological processes. In a first step, we propose a heuristic method based on the simulation of reaction-diffusion models carrying these competing hypotheses. Comparing the population patterns allowed to set a model typology according to their response to the landscape variable, through a classification algorithm, thus reducing the initial number of competing hypotheses. The selection of the most likely hypothesis from this irreducible set must rely on the observation of population patterns on the field. This implies that population patterns are described with spatial and temporal resolutions that are fine enough to select a unique hypothesis among the ones in competition. In the second part, we propose a heuristic method that allows determining a priori sampling strategies that maximize the robustness of ecological hypotheses selection. The simulation of reaction-diffusion models carrying the ecological hypotheses allows to generate virtual population data in space and time. These data are then sampled using strategies differing in the total effort, number of sampling locations, dates and landscape replicates. Population patterns are described from these samples. The sampling strategies are assessed through a classification algorithm that classifies the models according to the associated patterns. The analysis of classification performances, i.e. the ability of the algorithm to discriminate the ecological processes, allows the selection of optimal sampling designs. We also show that the way the sampling effort is distributed between its spatial and temporal components is strongly impacting the ecological processes inference. Reducing the number of competing ecological hypotheses, along with the selection of sampling strategies for optimal model inference both meet a strong need in the process of knowledge improvement about the ecological processes for the exploration of landscape scenarios favoring ecosystem services. In the last chapter, we discuss the implications and future prospects of our work
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ORCIL, KERVAJAN LOUISIANE. "Etude de l'influence des cinetiques d'echange sur les processus de transport dans les electrolytes." Paris 6, 1987. http://www.theses.fr/1987PA066561.
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Jiménez, Oviedo Byron. "Processus d’exclusion avec des sauts longs en contact avec des réservoirs." Thesis, Université Côte d'Azur (ComUE), 2018. http://www.theses.fr/2018AZUR4000/document.
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Mourragui, Mustapha. "Comportement hydrodynamique des processus de sauts, de naissances et de morts." Rouen, 1993. http://www.theses.fr/1993ROUES002.
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Dans cette thèse, nous étudions la limite hydrodynamique des processus de sauts, de naissances et de morts qui décrivent l'évolution de particules indistingables sur le tore. Dans ces systèmes, les particules sautent indépendamment les unes des autres, elles sont créées et détruites selon des taux non linéaires. En utilisant différentes méthodes : la méthode de l'estimation surexponentielle de C. Kipnis, S. Olla et S. R. S. Varadhan, la méthode de production d'entropie de M. Z. Guo, G. C. Papanicolaou et S. R. S. Varadhan et la méthode d'entropie relative de H. T. Yau, nous démontrons que sous certaines conditions sur les taux de naissance et de mort, et par passage à la limite, nos systèmes évoluent selon des équations de réaction-diffusion non linéaires
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PAPASEIT, CYRIL. "Formation de motifs microtubulaires in vitro et dans l'embryon de drosophile par des processus dissipatifs de type réaction-diffusion." Université Joseph Fourier (Grenoble), 1998. http://www.theses.fr/1998GRE10190.
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Les processus physico-chimiques de reaction-diffusion ont ete proposes par turing comme une explication possible de l'auto-organisation et de la morphogenese biologique. La theorie prevoit que des systemes chimiques ou biochimiques loin de l'equilibre thermodynamique peuvent former des structures complexes a partir d'un etat initialement homogene. Les processus impliques sont non-lineaires, irreversibles, et consomment continuellement de l'energie. Dans certaines conditions, des solutions de microtubules in vitro se comportent ainsi. La prediction principale de cette theorie consiste en ce que les motifs doivent etre constitues de differences de concentration en reactifs. Dans cette these nous montrons que les motifs macroscopiques stries formes spontanement par les microtubules in vitro, contiennent des variations periodiques dans la concentration en microtubules. Les techniques employees sont la diffusion des neutrons aux petits angles et la fluorescence. C'est la premiere demonstration experimentale de la formation de structures de turing dans un systeme biologique in vitro. Reprenant l'idee initiale de turing, nous nous sommes demandes si ces processus peuvent se produire in vivo pendant l'embryogenese. Un motif microtubulaire strie, mis en evidence par immunofluorescence, apparait dans l'uf de la mouche drosophile au moment de la gastrulation. Une caracteristique des motifs formes par des processus de reaction-diffusion est leur sensibilite aux dimensions de l'echantillon. Nous avons trouve que le motif microtubulaire forme dans des ufs ligatures varie avec la longueur du fragment de la meme maniere que celui apparaissant in vitro dans des recipients de longueurs differentes. Ces resultats sont egalement en accord avec la theorie et apportent un element de preuve que les processus de reaction-diffusion peuvent se produire pendant l'embryogenese de la drosophile. Enfin, la comparaison du motif microtubulaire avec le motif d'expression d'un gene reconnu jouer un role dans la segmentation, suggere qu'il pourrait exister un lien entre les deux systemes.
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Kuchi, Venkateswarlu. "Development of an innovative ISOL system for the production of short-lived neutron-deficient ions." Thesis, Normandie, 2018. http://www.theses.fr/2018NORMC233/document.
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Dans le cadre de l'installation GANIL / SPIRAL-1, un système innovant de source d'ions cible (TISS) a été conçu pour produire des nouveaux faisceaux d'ions radioactifs compétitifs et déterminer dans quelle mesure il est possible d'améliorer les performances de production par l’optimisation de l’ensemble cible-source (ECS) d’ions dédié à la production d'un faisceau d'ions radioactifs spécifique.L'isotope d'alcalin de courte durée de 74Rb ( demi-vie = 64.8 ms) a été choisi comme cas d’école.En étudiant et en améliorant les processus impliqués dans le fonctionnement de l’ECS, i.e. production dans la cible par réaction fusion-évaporation, implantation dans- et sortie du graphite, effusion et ionisation, une efficacité de transformation atome-ion de 75% est attendue, menant à un taux d'ions de l'ordre de 104 pps à la sortie de l’ECS.Les performances estimées permettraient à l'installation GANIL / SPIRAL-1 de délivrer des faisceaux de 74Rb et 114Cs avec des intensités compétitives, jamais atteintes dans d'autres installations.Le dispositif de production a été développé sur la base de mon travail, pour répondre aux objectifs de physique et aux conditions d'opération de SPIRAL-1. L'efficacité, la fiabilité et donc la simplicité étaient essentielles. Le système répond à ces exigences<br>In the frame of GANIL/SPIRAL-1 facility, an innovative target ion source system (TISS) has been designed in order to produce new competitive radioactive ion beams, and to determine to which extent it is possible to improve the production performances by optimizing a target ion source system dedicated to the production of a specific radioactive ion beam.The short-lived alkali isotope of 74Rb (half-life = 64.8 ms) has been chosen as a challenging case study.By studying and improving the processes involved in the TISS designed, i.e. in-target production by fusion-evaporation, implantation in and release out of graphite, effusion, and ionization, an atom-to-ion transformation efficiency of 75% was predicted, leading to an ion rate of the order of 104 pps at the exit of the TISS.The estimated performances would allow the GANIL / SPIRAL-1 installation to deliver beams of 74Rb and 114Cs with competitive intensities never reached in other installations.The production device was developed based on my work, to cope with physics objectives and with the conditions of the SPIRAL-1 operation. Efficiency, reliability and thus simplicity were essential. The system meets these requirements.The instrumentation needed for tests existed or have been specifically designed. The TISS has been built, assembled and partly tested.In parallel, issues have been addressed to answer related questions about sticking times, resistivity, and emissivity, to get inputs for the design of the TISS.Expected results with alkali allow thinking that the transposition of the principle to the production of neutron-deficient short-lived isotopes of noble gases and eventually metals could be performing
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Rodrigues, Daiana Aparecida. "Modelagem e solução numérica de equações reação-difusão em processos biológicos." Universidade Federal de Juiz de Fora, 2013. https://repositorio.ufjf.br/jspui/handle/ufjf/1153.
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Previous issue date: 2013-08-29<br>CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>Fenômenos biológicos são todo e qualquer evento que possa ser observado nos seres vivos.
O estudo desses fenômenos permite propor explicações para o seu mecanismo, a m
de entender as causas e efeitos. Pode-se citar como exemplos de fenômenos biológicos o
comportamento das células como respiração, reprodução, metabolismo e morte celular.
Equações de reação-difusão são frequentemente utilizadas para modelar fenômenos bioló-
gicos. Sistemas de reação-difusão podem produzir padrões espaciais estáveis a partir de
uma distribuição inicial uniforme esse fenômeno é conhecido como instabilidade de Turing.
Este trabalho apresenta a análise da instabilidade de Turing bem como resultados
numéricos para a solução de três modelos biológicos, modelo de Schnakenberg, modelo de
glicólise e modelo da coagulação sanguínea. O modelo de Schnakenberg é utilizado para
descrever uma reação química autocatalítica e o modelo de glicólise é relativo ao processo
de degradação metabólica da molécula de glicose para proporcionar energia para o metabolismo
celular, esses dois modelos são frequentemente relatados na literatura. O terceiro
modelo é mais recente e descreve o fenômeno da coagulação sanguínea. Nas soluções
numéricas se utiliza o método das linhas onde a discretização espacial é feita através de
um esquema de diferenças nitas. O sistema de equações diferencias ordinárias resultante
é resolvido por um esquema de integração adaptativo, com a utilização de pacote para
computação cientí ca da linguagem Python, Scipy.<br>Biological phenomena are all and any event that can be observed in living beings. The
study of these phenomena enables us to propose explanations for its mechanisms in order
to understand causes and e ects. One can cite as examples of biological phenomena
the behavior of cells as respiration, reproduction, metabolism and cell death. Reactiondi
usion equations are often used to model biological phenomena. Reaction-di usion
systems can produce stable spatial patterns from a uniform initial distribution, this phenomenon
is known as Turing instability. This dissertation presents an analysis of the
Turing instability as well as numerical results for the solution of three biological models,
model Schnakenberg, model of glycolysis and model of blood coagulation. The Schnakenberg
model is used to describe an autocatalytic chemical reaction and glycolysis model
refers to the process of metabolic breakdown of the glucose molecule to provide energy for
cellular metabolism, these two models are frequently reported in the literature. The third
model is newer and describes the phenomenon of blood coagulation. The method of lines
is used in the numerical solutions, where the spatial discretization is done through a nite
di erence scheme. The resulting system of ordinary di erential equations is then solved
by an adaptive integration scheme with the use of the package for scienti c computing of
Python language, Scipy.
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Wadi, Hicham. "Géométrie globale du transport dans l'espace des phases (Systèmes à deux degrés de liberté) : application à l'étude de la réactivité chimique." Université Joseph Fourier (Grenoble), 1997. http://www.theses.fr/1997GRE10239.
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Le cadre de cette these est strictement celui des systemes hamiltoniens a deux degres de liberte, invariants par renversement du temps. Notre resultat principal est d'etre parvenus a construire des sections de poincare globalement transverses au flot. A partir de ces sections il devient possible d'analyser d'une maniere globale l'organisation geometrique des trajectoires dans l'espace des phases. Notre construction repose essentiellement sur le concept de pods (periodic orbit dividing surface) ; il s'agit de trajectoires periodiques dont la trace sur l'espace des configurations ne dessine pas de boucles. Nous montrons que ces pods generalisent aux systemes a 2d les idees de puits et de barrieres de potentiel. Bien que de multiples applications soient a priori envisageables, nous nous sommes exclusivement penches sur le cas des reactions chimiques de la forme : ab + c abc a + bc a partir de nos sections globales, nous avons developpe une methode generale pour d'ecrire et analyser la dynamique de ces reactions ; en particulier afin d'obtenir des moyennes d'observables et les probabilites de reaction. Quant au chaos de diffusion, nous avons pu en donner une interpretation totalement nouvelle (le theoreme des enroulements), mais surtout, nous avons montre qu'il n'y a pas lieu de le distinguer du chaos dit borne.
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Orellana, Esbel Tomás Valero. "Um modelo de duas escalas da resposta elétrica de tecido muscular induzida por ativação de mastócitos." Laboratório Nacional de Computação Científica, 2010. http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=205.
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O estudo dos mecanismos que desencadeiam as reações alérgicas é um tema de grande interesse científico na atualidade. A anafilaxia, reação alérgica sistêmica severa, tem ocupado um lugar de destaque nas pesquisas. Diferentes experimentos em laboratório, tanto in vivo quanto in vitro, assim como diferentes modelos matemáticos baseados nos resultados experimentais, têm procurado investigar a participação ou não dos mastócitos nesse mecanismo. No entanto, os resultados obtidos não são conclusivos, dividindo a comunidade científica em dois grupos: os que consideram determinante o papel dos mastócitos responsáveis pela liberação de histamina e os que consideram que a histamina não é o neurotransmissor determinante na reação anafilática. Trabalhos anteriores propuseram modelos diferenciais para simular processos relacionados com a reação anafilática na escala celular para o mecanismo de geração de potencial na membrana das células. Mais recentemente foi proposto, a nível de tecido, um modelo probabilístico para simular a resposta in vitro a antígenos. A nível de organismo têm sido propostos modelos de multi compartimentos para a cinética da histamina no fluido sanguíneo. Contudo, nenhum trabalho até o momento abordou a construção de um modelo capaz de descrever os processos que participam no mecanismo de reação anafilática nas diversas escalas. Neste trabalho propomos um modelo que integra as escalas celular e do tecido, que permite modelar experimentos in vitro, e que pode ser estendido para escala do organismo incluindo o fluxo sanguíneo para modelar experimentos in vivo. O modelo proposto integra o mecanismo de resposta elétrica a nível celular com o processo de reação-difusão da histamina e dos antígenos no tecido, considerando o mecanismo de reação mediado por mastócitos. Para integrar as duas escalas propomos uma relação constitutiva baseada em resultados experimentais da resposta mecânica (contração do tecido) a estímulos elétricos. Este modelo permite o desenho de novos experimentos especificamente direcionados ao estudo da reação anafilática, indicando os parâmetros a serem estimados. Utilizando-se o modelo proposto, foram realizadas simulações numéricas para uma ampla faixa de variação dos parâmetros visando identificar domínios com diferentes comportamentos do modelo. Uma análise dos resultados obtidos baseada em parâmetros adimensionais é apresentada.<br>The study of the mechanisms that set off allergic reactions is being a subject of great scientific interest. Anaphylaxis, severe systemic allergic reaction, occupies a prominence place in researches. Different laboratory experiments, in vivo as well as in vitro, and also different mathematical models based on experimental results, tries to investigate if mast cells takes part in those mechanisms or not. However, the obtained results are inconclusive, dividing the scientific community in two groups: one considering that mast cells have a prime role in releasing histamine, and another one which considers that histamine is not the determinative neurotransmitter in the anaphylactic reaction. Previous works proposed differential models to simulate processes related to anaphylactic reactions in the cellular scale for the cell membrane potential generation mechanism. More recently, it has been proposed a probabilistic model, in the tissue scale, to simulate an in vitro antigen response. In the organism level scale, multi-compartimental models have been proposed for the kinetics of histamine in the blood. Nevertheless, no work, until now, has proposed the construction of a model that is able to describe the processes that participate in the mechanism of anaphylactic reaction in different scales.
In this work, a model is proposed that integrates the cellular and the tissue scales, allowing to model in vitro experiments, being capable to be extended to the organism scale by the inclusion of the blood flow to model in vivo experiments. The proposed model couples the electric response in the cellular level with the reaction-diffusion of histamine and antigens in the tissue, considering the reaction mechanism mediated by the mast cells. To integrate these two scales, it is proposed here a constitutive relation based on experimental results for the mechanical response (tissue contraction) to electric stimulus. This model allows to design experiments specifically related to the anaphylaxis reaction, indicating the parameters that should be estimated. With this model, numerical simulations have been performed for a wide variation range of the parameters to identify the different domains of the model. A dimensionless parameter based analysis is presented for the obtained results.
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Baptestini, Elizabeth Machado. "Um sistema presa-predador com evasão mediada por feromônio de alarme." Universidade Federal de Viçosa, 2006. http://locus.ufv.br/handle/123456789/4276.
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Previous issue date: 2006-03-20<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>Pattern, structure and emergent collective properties are ubiquitous in systems with many units (alive or inanimated) coupled through nonlinear interactions. Within this context, the study of cooperative phenomena in population dynamics of ecological interest has attracted the attention of the mathematicians and physicists since Lotka and Volterra in the 1920s. Thenceforth, in addition to differential equations, theoretical ecology has continuously incorporated powerful and well-established techniques of contacts processes, cellular automata models and others, developed in the fields of condensed matter physics, statistical physics and computational physics. In the present work, a predator-prey model with pursuit and escape triggered by alarm pheromones is proposed and studied through analytical methods and computer simulations. Such models can show oscillatory behavior of the population density, phase transitions that belong to distinct universality classes and rich stationary phase diagrams. Two distinct levels of description were used. In a first approach, we consider a model of cellular automata in which predators and preys walk on a square lattice, according specific rules for each species, in a homogeneous environment and with periodic boundary conditions. The second part of our study is based on the analysis of partial differential equations that also describes the dynamics of a prey-predator system with the same characteristics above. Both, spatially uniform or mean field like and explicit spatio-temporal partial differential equations were considered. These models can represent relevant tools to design better strategies of biological control of pests by predators. In successful cases, the pests and its predators must persist in stable interactions at a low level of pest density.<br>Padrões, estruturas, propriedades coletivas emergentes são ubíquas em sistemas com muitas unidades (vivas ou inanimadas) acopladas por meio de interações não-lineares. Dentro desse contexto, o estudo de fenômenos cooperativos em dinâmica de populações de interesse ecológico tem atraído a atenção de físicos e matemáticos desde os anos de 1920 com Lotka e Volterra. Portanto, além de equações diferenciais, a teoria ecológica tem continuamente incorporado poderosas e bem-estabelecidas técnicas dos processos de contatos, modelos de autômatos celulares e outros, desenvolvidos no campo de física da matéria condensada, física estatística e física computacional. No presente trabalho, um modelo presa-predador com perseguição e fuga mediada por um feromônio de alarme é proposto e estudado através de métodos analíticos e simulações computacionais. Tais modelos podem exibir comportamentos oscilatórios da densidade de população, transições de fases que pertencem a classes de universalidade distintas e um diagrama de fases rico. Duas abordagens distintas de descrição foram usadas. Numa primeira abordagem, propomos um modelo de Autômato Celular (AC) onde predadores e presas se movimentam, segundo regras específicas para cada espécie, num ambiente homogêneo e com condições de contorno periódicas. A outra parte do nosso estudo é baseado na análise de EDP s que também descrevem a dinâmica de um sistema presa-predador com as mesmas características citadas acima. É feito um estudo considerando as equações sem termos espaciais, isto é, tipo campo médio e depois considerando esses termos. Esses modelos podem representar ferramentas relevantes para o estudo das melhores estratégias para o controle biológico de pragas por predadores. Em casos bem sucedidos, as pestes e seus predadores devem persistir em interações estáveis e com uma baixa densidade da população de pragas.
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Nguepedja, Nankep Mac jugal. "Modélisation stochastique de systèmes biologiques multi-échelles et inhomogènes en espace." Thesis, Rennes, École normale supérieure, 2018. http://www.theses.fr/2018ENSR0012/document.
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Les besoins grandissants de prévisions robustes pour des systèmes complexes conduisent à introduire des modèles mathématiques considérant un nombre croissant de paramètres. Au temps s'ajoutent l'espace, l'aléa, les échelles de dynamiques, donnant lieu à des modèles stochastiques multi-échelles avec dépendance spatiale (modèles spatiaux). Cependant, l'explosion du temps de simulation de tels modèles complique leur utilisation. Leur analyse difficile a néanmoins permis, pour les modèles à une échelle, de développer des outils puissants: loi des grands nombres (LGN), théorème central limite (TCL), ..., puis d'en dériver des modèles simplifiés et algorithmes accélérés. Dans le processus de dérivation, des modèles et algorithmes dits hybrides ont vu le jour dans le cas multi-échelle, mais sans analyse rigoureuse préalable, soulevant ainsi la question d'approximation hybride dont la consistance constitue l'une des motivations principales de cette thèse.En 2012, Crudu, Debussche, Muller et Radulescu établissent des critères d'approximation hybride pour des modèles homogènes en espace de réseaux de régulation de gènes. Le but de cette thèse est de compléter leur travail et le généraliser à un cadre spatial.Nous avons développé et simplifié différents modèles, tous des processus de Markov de sauts pures à temps continu. La démarche met en avant, d'une part, des conditions d'approximations déterministes par des solutions d'équations d'évolution (type réaction-advection-diffusion), et, d'autre part, des conditions d'approximations hybrides par des processus stochastiques hybrides. Dans le cadre des réseaux de réactions biochimiques, un TCL est établi. Il correspond à une approximation hybride d'un modèle homogène simplifié à deux échelles de temps (suivant Crudu et al.). Puis, une LGN est obtenue pour un modèle spatial à deux échelles de temps. Ensuite, une approximation hybride est établie pour un modèle spatial à deux échelles de dynamique en temps et en espace. Enfin, des comportements asymptotiques en grandes populations et en temps long sont présentés pour un modèle d'épidémie de choléra, via une LGN suivie d'une borne supérieure pour les sous-ensembles compacts, dans le cadre d'un principe de grande déviation (PGD) correspondant.À l'avenir, il serait intéressant, entre autres, de varier la géométrie spatiale, de généraliser le TCL, de compléter les estimations du PGD, et d'explorer des systèmes complexes issus d'autres domaines<br>The growing needs of precise predictions for complex systems lead to introducing stronger mathematical models, taking into account an increasing number of parameters added to time: space, stochasticity, scales of dynamics. Combining these parameters gives rise to spatial --or spatially inhomogeneous-- multiscale stochastic models. However, such models are difficult to study and their simulation is extremely time consuming, making their use not easy. Still, their analysis has allowed one to develop powerful tools for one scale models, among which are the law of large numbers (LLN) and the central limit theorem (CLT), and, afterward, to derive simpler models and accelrated algorithms. In that deduction process, the so-called hybrid models and algorithms have arisen in the multiscale case, but without any prior rigorous analysis. The question of hybrid approximation then shows up, and its consistency is a particularly important motivation of this PhD thesis.In 2012, criteria for hybrid approximations of some homogeneous regulation gene network models were established by Crudu, Debussche, Muller and Radulescu. The aim of this PhD thesis is to complete their work and generalize it afterward to a spatial framework.We have developed and simplified different models. They all are time continuous pure jump Markov processes. The approach points out the conditions allowing on the the one hand deterministic approximations by solutions of evolution equations of type reaction-advection-diffusion, and, on the other hand, hybrid approximations by hybrid stochastic processes. In the field of biochemical reaction networks, we establish a CLT. It corresponds to a hybrid approximation of a simplified homogeneous model (due to Crudu et al.). Then a LLN is obtained for a spatial model with two time scales. Afterward, a hybrid approximation is established, for a two time-space scales spatial model. Finally, the asymptotic behaviour in large population and long time are respectively presented for a model of cholera epidemic, through a LLN followed by the upper bound for compact sets, in the context of a corresponding large deviation principle (LDP).Interesting future works would be, among others, to study other spatial geometries, to generalize the CLT, to complete the LDP estimates, and to study complex systems from other fields
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El, kettani Perla. "Équations d'évolution stochastiques locales et non locales dans des problèmes de transition de phase." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS494/document.
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Le but de cette thèse est de développer des méthodes de démonstration d’existence et d’unicité de solutions d’équations d’évolution stochastiques locales ou non locales dans les problèmes de transition de phase. Au chapitre 1, nous étudions un problème à valeur initiale pour une ´équation de réaction-diffusion stochastique non locale avec des conditions aux limites de Neumann homogènes dans un ouvert borné de ℝn de frontière suffisamment régulière. On considère le cas d’un opérateur elliptique non linéaire assez général et on suppose que le bruit est additif et induit par un processus Q-Wiener. Le problème déterministe modélise la séparation de phases dans des alliages binaires. La démonstration d’existence de la solution du problème stochastique est basée sur un changement de fonction qui fait intervenir la solution de l’équation de la chaleur stochastique avec un terme de diffusion non linéaire. On est ainsi conduit à l'étude d’un problème sans terme de bruit, ce qui facilite l’application de la méthode de monotonie pour identifier la limite des termes non linéaires. Au chapitre 2, nous démontrons l’existence et l’unicité de la solution d’un système de champ de phase stochastique avec des bruits multiplicatifs induits par des processus Q-Wiener. Les problèmes de champ de phase sont utilisés pour d´écrire des modèles où deux phases distinctes interviennent comme par exemple l’eau et la glace. Dans ce but, nous appliquons la méthode de Galerkin et nous établissons des estimations a priori pour la solution approchée. Nous nous appuyons ensuite sur la méthode de monotonie stochastique pour identifier la limite du terme non linéaire. Finalement, au chapitre 3, nous démontrons l’existence et l’unicité d’une solution trajectorielle en dimension d’espace d ≤ 6 pour l’équation d’Allen-Cahn non locale stochastique avec un bruit multiplicatif induit par un processus Q-Wiener. La présence d’une variable supplémentaire empêche l’application des théorèmes de compacité usuels utilisés dans les problèmes déterministes. C’est ce qui nous amène à appliquer la méthode de compacité stochastique<br>The aim of this thesis is to develop methods for proving the existence and uniqueness of solutionsof local and nonlocal stochastic evolution equations in phase transition problems. In chapter 1, we studyan initial value problem for a nonlocal stochastic reaction-diffusion equation with homogeneous Neumannboundary conditions in an open bounded set of ℝn, with a smooth boundary. We consider the case of ageneral nonlinear elliptic operator and we suppose that the noise is additive and induced by a Q-Wiener process.The deterministic problem with a linear diffusion term is used to model phase separation in a binarymixture. The proof of existence for the stochastic problem is based on a change of function which involvesthe solution of the stochastic heat equation with a nonlinear diffusion term. We obtain a problem withoutthe noise term. This simplifies the application of the monotonicity method, which we use to identify thelimit of the nonlinear terms. In chapter 2, we prove the existence and uniqueness of the solution for a phasefield problem with multiplicative noises induced by Q-Wiener processes. This problem models for instancethe process of melting and solidification. To that purpose we apply the Galerkin method and derive a prioriestimates for the approximate solutions. The last step is to identify the limit of the nonlinear terms whichwe do by the so-called stochastic monotonicity method. Finally, in chapter 3, we prove the existence anduniqueness of a pathwise solution in space dimension up to 6 for the stochastic nonlocal Allen-Cahn equationwith a multiplicative noise induced by a Q-Wiener process. The usual compactness method for deterministicproblems cannot be applied in a stochastic context because of the additional probability variable. Therefore,we apply the stochastic compactness method
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"Computational models of signaling processes in cells with applications: Influence of stochastic and spatial effects." Thesis, 2012. http://hdl.handle.net/1911/70209.
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The usual approach to the study of signaling pathways in biological systems is to assume that high numbers of cells and of perfectly mixed molecules within cells are involved. To study the temporal evolution of the system averaged over the cell population, ordinary differential equations are usually used. However, this approach has been shown to be inadequate if few copies of molecules and/or cells are present. In such situation, a stochastic or a hybrid stochastic/deterministic approach needs to be used. Moreover, considering a perfectly mixed system in cases where spatial effects are present can be an over-simplifying assumption. This can be corrected by adding diffusion terms to the ordinary differential equations describing chemical reactions and proliferation kinetics. However, there exist cases in which both stochastic and spatial effects have to be considered. We study the relevance of differential equations, stochastic Gillespie algorithm, and deterministic and stochastic reaction-diffusion models for the study of important biological processes, such as viral infection and early carcinogenesis. To that end we have developed two optimized libraries of C functions for R (r-project.org) to simulate biological systems using Petri Nets, in a pure deterministic, pure stochastic, or hybrid deterministic/stochastic fashion, with and without spatial effects. We discuss our findings in the terms of specific biological systems including signaling in innate immune response, early carcinogenesis and spatial spread of viral infection.
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Chacón-Acosta, Guillermo, Mayra Núnez-López, and José A. Santiago. "Curvature effects on a simplified reaction-diffusion model of biodegradation." 2017. https://ul.qucosa.de/id/qucosa%3A31634.
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The biodegradation process of some types of polymers occurs due to many different factors including
their morphology, structure and chemical composition. Although this is a complicated process, most
of its important stages like the diffusion of monomers and the hydrolysis reactions have been modeled
phenomenologically through reaction-diffusion equations, where the properties of the polymers were
encompassed. Using a simplified reaction-diffusion model for the biodegradation of polymers,
in this contribution we study the possible effects of the curvature of the system’s geometry in the
degradation process, which is characterized by the interaction of the corresponding reaction rate and
the diffusion coefficient. To illustrate the problem of diffusion on a curved surface we consider the
surface of a cylinder and of the so-called Gaussian bump. We show how the degradation process is
affected by the curvature of the system for the simplified model.