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1
Imoto, Yu, and Takashi Odagaki. "Diffusion on diffusing particles." Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-193282.
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We investigate random walk of a particle constrained on cells, where cells behave as a lattice gas on a two dimensional square lattice. By Monte Carlo simulation, we obtain the mean first passage time of the particle as a function of the density and temperature of the
lattice gas. We find that the transportation of the particle becomes anomalously slow in a certain range of parameters because of the cross over in dynamics between the low and high density regimes; for low densities the dynamics of cells plays the essential role, and
for high densities, the dynamics of the particle plays the dominant role.
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Imoto, Yu, and Takashi Odagaki. "Diffusion on diffusing particles." Diffusion fundamentals 6 (2007) 11, S. 1-7, 2007. https://ul.qucosa.de/id/qucosa%3A14185.
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We investigate random walk of a particle constrained on cells, where cells behave as a lattice gas on a two dimensional square lattice. By Monte Carlo simulation, we obtain the mean first passage time of the particle as a function of the density and temperature of the
lattice gas. We find that the transportation of the particle becomes anomalously slow in a certain range of parameters because of the cross over in dynamics between the low and high density regimes; for low densities the dynamics of cells plays the essential role, and
for high densities, the dynamics of the particle plays the dominant role.
3
Bernhardt, Thomas. "Reflected diffusions and piecewise diffusion approximations of Levy processes." Thesis, London School of Economics and Political Science (University of London), 2017. http://etheses.lse.ac.uk/3659/.
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In the first part of the thesis, the solvability of stochastic differential equations with reflecting boundary conditions is studied. Such equations arise in singular stochastic control problems as a way for determining the optimal strategies. The stochastic differential equations represent homogeneous one-dimensional diffusions while the boundaries are given by c`adl`ag functions. Pathwise solutions are constructed under mild assumptions on the coefficients of the equations. In particular, the solutions are derived as the diffusions’ scale functions composed with appropriately time-changed reflected Brownian motions. Several probabilistic properties are addressed and analysed. In the second part of the thesis, piecewise diffusion approximations of Levy processes are studied. Such approximating processes have been called Itˆo semi-diffusions. While keeping the statistical fit to Levy processes, this class of processes has the analytical tractability of Ito diffusions. At a given time grid, their distribution is the same as the one of the underlying Levy processes. At times outside the grid, they evolve like homogeneous diffusions. The analysis identifies conditions under which Itˆo semi-diffusions can be used as an alternative to Levy processes for modelling financial asset prices. In particular, for a sequence of Itˆo semi-diffusions determined by a given Levy process, conditions for the convergence of their finite-dimensional distributions to the ones of the Levy process are established. Furthermore, for a single Ito semi-diffusion, conditions for the existence of pricing measures are established.
4
Prehl, Janett Hoffmann Karl-Heinz. "Diffusion on fractals Diffusion auf Fraktalen /." [S.l. : s.n.], 2007.
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5
Rane, Swati. "Diffusion tensor imaging at long diffusion time." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29708.
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Thesis (Ph.D)--Biomedical Engineering, Georgia Institute of Technology, 2009.<br>Committee Chair: Hu, Xiaoping; Committee Member: Brummer, Marijn; Committee Member: Duong, Tim; Committee Member: Keilholz, Shella; Committee Member: Schumacher, Eric. Part of the SMARTech Electronic Thesis and Dissertation Collection.
6
Coulon, Anne-Charline. "Propagation in reaction-diffusion equations with fractional diffusion." Doctoral thesis, Universitat Politècnica de Catalunya, 2014. http://hdl.handle.net/10803/277576.
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This thesis focuses on the long time behaviour of solutions to Fisher-KPP reaction-diffusion equations involving fractional diffusion. This type of equation arises, for example, in spatial propagation or spreading of biological species (rats, insects,...). In population dynamics,
the quantity under study stands for the density of the population.
It is well-known that, under some specific assumptions, the solution tends to a stable state of the evolution problem, as time goes to infinity. In other words, the population invades the medium, which corresponds to the survival of the species, and we want to understand at which speed this invasion takes place. To answer this question, we set up a new method to study the speed of propagation when fractional diffusion is at stake and apply it on three different problems.
Part I of the thesis is devoted to an analysis of the asymptotic location of the level sets of the solution to two different problems : Fisher-KPP models in periodic media and cooperative systems, both including fractional diffusion. On the first model, we prove that, under some assumptions on the periodic medium, the solution spreads exponentially fast in time and we find the precise exponent that appears in this exponential speed of propagation. We also carry out numerical simulations to investigate the dependence of the speed of propagation on the initial condition. On the second model, we prove that the speed of propagation is once again exponential in time, with an exponent depending on the smallest index of the fractional Laplacians at stake and on the reaction term.
Part II of the thesis deals with a two dimensional environment, where reproduction of Fisher-KPP type and usual diffusion occur, except on a line of the plane, on which fractional diffusion takes place. The plane is referred to as 'the field' and the line to 'the road', as a reference to the biological situations we have in mind. Indeed, it has long been known that fast diffusion on roads can have a driving effect on the spread of epidemics. We prove that the speed of propagation is exponential in time on the road, whereas it depends linearly on time in the field. Contrary to the precise asymptotics obtained in Part I, for this model, we are not able to give a sharp location of the level sets on the road and in the field. The expansion shape of the level sets in the field is investigated through numerical simulations.<br>Esta tesis se centra en el comportamiento en tiempos grandes de las soluciones de la ecuación de Fisher- KPP de reacción-difusión con difusión fraccionaria. Este tipo de ecuación surge, por ejemplo, en la propagación espacial o en la propagación de especies biológicas (ratas, insectos,...). En la dinámica de poblaciones, la cantidad que se estudia representa la densidad de la población. Es conocido que, bajo algunas hipótesis específicas, la solución tiende a un estado estable del problema de evolución, cuando el tiempo tiende a infinito. En otras palabras, la población invade el medio, lo que corresponde a la supervivencia de la especie, y nosotros queremos entender con qué velocidad se lleva a cabo esta invasión. Para responder a esta pregunta, hemos creado un nuevo método para estudiar la velocidad de propagación cuando se consideran difusiones fraccionarias, además hemos aplicado este método en tres problemas diferentes. La Parte I de la tesis está dedicada al análisis de la ubicación asintótica de los conjuntos de nivel de la solución de dos problemas diferentes: modelos de Fisher- KPP en medios periódicos y sistemas cooperativos, ambos consideran difusión fraccionaria. En el primer modelo, se prueba que, bajo ciertas hipótesis sobre el medio periódico, la solución se propaga exponencialmente rápido en el tiempo, además encontramos el exponente exacto que aparece en esta velocidad de propagación exponencial. También llevamos a cabo simulaciones numéricas para investigar la dependencia de la velocidad de propagación con la condición inicial. En el segundo modelo, se prueba que la velocidad de propagación es nuevamente exponencial en el tiempo, con un exponente que depende del índice más pequeño de los Laplacianos fraccionarios y también del término de reacción. La Parte II de la tesis ocurre en un entorno de dos dimensiones, donde se reproduce un tipo ecuación de Fisher- KPP con difusión estándar, excepto en una línea del plano, en el que la difusión fraccionada aparece. El plano será llamado "campo" y la línea "camino", como una referencia a las situaciones biológicas que tenemos en mente. De hecho, desde hace tiempo se sabe que la difusión rápida en los caminos puede causar un efecto en la propagación de epidemias. Probamos que la velocidad de propagación es exponencial en el tiempo en el camino, mientras que depende linealmente del tiempo en el campo. Contrariamente a los precisos exponentes obtenidos en la Parte I, para este modelo, no fuimos capaces de dar una localización exacta de los conjuntos de nivel en la carretera y en el campo. La forma de propagación de los conjuntos de nivel en el campo se investiga a través de simulaciones numéricas
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Benson, Debbie Lisa. "Reaction diffusion models with spatially inhomogeneous diffusion coefficients." Thesis, University of Oxford, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239337.
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Prehl, Janett. "Diffusion on fractals and space-fractional diffusion equations." Doctoral thesis, Universitätsbibliothek Chemnitz, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-201001068.
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Ziel dieser Arbeit ist die Untersuchung der Sub- und Superdiffusion in fraktalen Strukturen. Der Fokus liegt auf zwei separaten Ansätzen, die entsprechend des Diffusionbereiches gewählt und variiert werden. Dadurch erhält man ein tieferes Verständnis und eine bessere Beschreibungsweise für beide Bereiche. Im ersten Teil betrachten wir subdiffusive Prozesse, die vor allem bei Transportvorgängen, z. B. in lebenden Geweben, eine grundlegende Rolle spielen. Hierbei modellieren wir den fraktalen Zustandsraum durch endliche Sierpinski Teppiche mit absorbierenden Randbedingungen und lösen dann die Mastergleichung zur Berechnung der Zeitentwicklung der Wahrscheinlichkeitsverteilung. Zur Charakterisierung der Diffusion auf regelmäßigen und zufälligen Teppichen bestimmen wir die Abfallzeit der Wahrscheinlichkeitsverteilung, die mittlere Austrittszeit und die Random Walk Dimension. Somit können wir den Einfluss zufälliger Strukturen auf die Diffusion aufzeigen. Superdiffusive Prozesse werden im zweiten Teil der Arbeit mit Hilfe der Diffusionsgleichung untersucht. Deren zweite Ableitung im Ort erweitern wir auf nichtganzzahlige Ordnungen, um die fraktalen Eigenschaften der Umgebung darzustellen. Die resultierende raum-fraktionale Diffusionsgleichung spannt ein Übergangsregime von der irreversiblen Diffusionsgleichung zur reversiblen Wellengleichung auf. Deren Lösungen untersuchen wir mittels verschiedener Entropien, wie Shannon, Tsallis oder Rényi Entropien, und deren Entropieproduktionsraten, welche natürliche Maße für die Irreversibilität sind. Das dabei gefundene Entropieproduktions-Paradoxon, d. h. ein unerwarteter Anstieg der Entropieproduktionsrate bei sinkender Irreversibilität des Prozesses, können wir nach geeigneter Reskalierung der Entropien auflösen<br>The aim of this thesis is the examination of sub- and superdiffusive processes in fractal structures. The focus of the work concentrates on two separate approaches that are chosen and varied according to the corresponding regime. Thus, we obtain new insights about the underlying mechanisms and a more appropriate way of description for both regimes. In the first part subdiffusion is considered, which plays a crucial role for transport processes, as in living tissues. First, we model the fractal state space via finite Sierpinski carpets with absorbing boundary conditions and we solve the master equation to compute the time development of the probability distribution. To characterize the diffusion on regular as well as random carpets we determine the longest decay time of the probability distribution, the mean exit time and the Random walk dimension. Thus, we can verify the influence of random structures on the diffusive dynamics. In the second part of this thesis superdiffusive processes are studied by means of the diffusion equation. Its second order space derivative is extended to fractional order, which represents the fractal properties of the surrounding media. The resulting space-fractional diffusion equations span a linking regime from the irreversible diffusion equation to the reversible (half) wave equation. The corresponding solutions are analyzed by different entropies, as the Shannon, Tsallis or Rényi entropies and their entropy production rates, which are natural measures of irreversibility. We find an entropy production paradox, i. e. an unexpected increase of the entropy production rate by decreasing irreversibility of the processes. Due to an appropriate rescaling of the entropy we are able to resolve the paradox
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Kuchel, Philip W., and Guilhem Pages. "NMR diffusion diffraction and diffusion interference from cells." Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-194150.
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Pulsed field gradient spin-echo (PGSE) NMR spectroscopy is the definitive means for measuring translational motion of molecules in free solution and in heterogeneous systems. A unique ‘twist’ on the method is that in some systems in which diffusion is restricted
the PGSE experiment yields information on the geometrical properties of the confining boundaries. When applied to red blood cells (RBCs) in suspensions, using intense magnetic field gradients (around 10 T m-1), the graph of normalized NMR-signal intensity versus the magnitude of the field gradients has the form of the diffraction and interference patterns that are seen in physical optics. We review here the nature of these so called q-space plots and discuss a data-processing method that adds objectivity to estimates of the mean RBC diameter. Convection potentially interferes with the veracity of these measurements so an experiment is reported in which a cell-free sample was deliberately made to flow. The very simple analysis of flow diffraction yielded estimates of flow that were in remarkable agreement with gravimetric measurements. Finally, in a theoretical study using a model of uniformly arrayed octagonal
prisms that were ‘morphed’ in a systematic way, the dependence of the form of q-space plots on prism shape and packing density was obtained. This showed that elaborately shaped q-space plots can be obtained from simple periodic arrays of ‘cells’. The uniqueness or otherwise of shapes of q-space plots, and the prospect of generally solving the inverse problem whereby q-space analysis yields detailed information on packing arrangements is poised for further detailed investigations.
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Kuchel, Philip W., and Guilhem Pages. "NMR diffusion diffraction and diffusion interference from cells." Diffusion fundamentals 6 (2007) 74, S. 1-16, 2007. https://ul.qucosa.de/id/qucosa%3A14254.
Full textAbstract:
Pulsed field gradient spin-echo (PGSE) NMR spectroscopy is the definitive means for measuring translational motion of molecules in free solution and in heterogeneous systems. A unique ‘twist’ on the method is that in some systems in which diffusion is restricted
the PGSE experiment yields information on the geometrical properties of the confining boundaries. When applied to red blood cells (RBCs) in suspensions, using intense magnetic field gradients (around 10 T m-1), the graph of normalized NMR-signal intensity versus the magnitude of the field gradients has the form of the diffraction and interference patterns that are seen in physical optics. We review here the nature of these so called q-space plots and discuss a data-processing method that adds objectivity to estimates of the mean RBC diameter. Convection potentially interferes with the veracity of these measurements so an experiment is reported in which a cell-free sample was deliberately made to flow. The very simple analysis of flow diffraction yielded estimates of flow that were in remarkable agreement with gravimetric measurements. Finally, in a theoretical study using a model of uniformly arrayed octagonal
prisms that were ‘morphed’ in a systematic way, the dependence of the form of q-space plots on prism shape and packing density was obtained. This showed that elaborately shaped q-space plots can be obtained from simple periodic arrays of ‘cells’. The uniqueness or otherwise of shapes of q-space plots, and the prospect of generally solving the inverse problem whereby q-space analysis yields detailed information on packing arrangements is poised for further detailed investigations.
11
Hinchcliffe, Owen G. "Diffusion algebras." Thesis, University of Sheffield, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.425565.
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Cussler, Edward L. "Diffusion barriers." Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-194127.
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Cussler, Edward L. "Diffusion barriers." Diffusion fundamentals 6 (2007) 72, S. 1-12, 2007. https://ul.qucosa.de/id/qucosa%3A14252.
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Chakraborty, Jay. "Diffusion in stressed thin films = Diffusion in dünnen Schichten." Stuttgart Max-Planck-Inst. für Metallforschung, 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=975753460.
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Coulon, Chalmin Anne-Charline. "Fast propagation in reaction-diffusion equations with fractional diffusion." Toulouse 3, 2014. http://thesesups.ups-tlse.fr/2427/.
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Cette thèse est consacrée à l'étude du comportement en temps long, et plus précisément de phénomènes de propagation rapide, des équations de réaction-diffusion de type Kisher-KPP avec diffusion fractionnaire. Ces équations modélisent, par exemple, la propagation d'espèces biologiques. Sous certaines hypothèses, la population envahit le milieu et nous voulons comprendre à quelle vitesse cette invasion a lieu. Pour répondre à cette question, nous avons mis en place une nouvelle méthode et nous l'appliquons à différents modèles. Dans une première partie, nous étudions deux problèmes d'évolution comprenant une diffusion fractionnaire : un modèle de type Fisher-KPP en milieu périodique et un système coopératif. Dans les deux cas, nous montrons, sous certaines conditions, que la vitesse de propagation est exponentielle en temps, et nous donnons une expression précise de l'exposant de propagation. Nous menons des simulations numériques pour étudier la dépendance de cette vitesse de propagation en la donnée initiale. Dans une seconde partie, nous traitons un environnement bidimensionnel, dans lequel le terme de reproduction est de type Fisher-KPP et le terme diffusif est donné par un laplacien standard, excepté sur une ligne du plan où une diffusion fractionnaire intervient. Le plan est nommé "le champ" et la ligne "la route", en référence aux situations biologiques que nous voulons modéliser. Nous prouvons que la vitesse de propagation est exponentielle en temps sur la route, alors qu'elle dépend linéairement du temps dans le champ. La forme des lignes de niveau dans le champ est étudiée au travers de simulations numériques<br>This thesis focuses on the long time behaviour, and more precisely on fast propagation, in Fisher-KPP reaction diffusion equations involving fractional diffusion. This type of equation arises, for example, in spreading of biological species. Under some specific assumptions, the population invades the medium and we want to understand at which speed this invasion takes place when fractional diffusion is at stake. To answer this question, we set up a new method and apply it on different models. In a first part, we study two different problems, both including fractional diffusion : Fisher-KPP models in periodic media and cooperative systems. In both cases, we prove, under additional assumptions, that the solution spreads exponentially fast in time and we find the precise exponent of propagation. We also carry out numerical simulations to investigate the dependence of the speed of propagation on the initial condition. In a second part, we deal with a two dimensional environment, where reproduction of Fisher-KPP type and usual diffusion occur, except on a line of the plane, on which fractional diffusion takes place. The plane is referred to as "the field" and the line to "the road", as a reference to the biological situations we have in mind. We prove that the speed of propagation is exponential in time on the road, whereas it depends linearly on time in the field. The expansion shape of the level sets in the field is investigated through numerical simulations
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Pavlin, Tina, and John Georg Seland. "Investigating effects from restricted diffusion in multi-component diffusion data." Universitätsbibliothek Leipzig, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-178775.
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We have investigated model systems in which effects from non-Gaussian restricted diffusion could be separated from effects caused by multiple diffusion coefficients. We applied various models to analyze the experimental data. An analysis based on multi-exponential models does not account correctly for effects caused by restricted diffusion in a system with multiple compartments. However, separating the components due to differences in dynamic behavior prior to the diffusion analysis, combined with a diffusion analysis based on the second cumulant approximation, was more robust, and was able to handle effects from restricted diffusion in the presence of multi-component diffusion.
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Pavlin, Tina, and John Georg Seland. "Investigating effects from restricted diffusion in multi-component diffusion data." Diffusion fundamentals 22 (2014) 9, S. 1-6, 2014. https://ul.qucosa.de/id/qucosa%3A13489.
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We have investigated model systems in which effects from non-Gaussian restricted diffusion could be separated from effects caused by multiple diffusion coefficients. We applied various models to analyze the experimental data. An analysis based on multi-exponential models does not account correctly for effects caused by restricted diffusion in a system with multiple compartments. However, separating the components due to differences in dynamic behavior prior to the diffusion analysis, combined with a diffusion analysis based on the second cumulant approximation, was more robust, and was able to handle effects from restricted diffusion in the presence of multi-component diffusion.
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JONCKHEERE, THIBAUT. "Diffusion d'ondes en milieu atomique : chaos quantique et diffusion multiple." Paris 6, 2001. http://www.theses.fr/2001PA066126.
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Ce travail de these comporte deux parties distinctes, concernant la diffusion d'ondes en milieu atomique. La premiere partie etudie le probleme des niveaux excites d'un atome non-hydrogenoide en champ exterieur. Ce systeme est tres similaire au cas de l'hydrogene dans le meme champ exterieur, mais est plus complexe a cause de la diffusion de l'onde electronique sur le cur ionique non-hydrogenoide. On montre dans cette premiere partie que la presence du cur ionique est mathematiquement equivalente a celle d'un ou plusieurs diffuseurs ponctuels. Ceci permet d'obtenir une equation qui, d'une part, autorise un calcul efficace des niveaux d'energie du systeme a partir de ceux pour l'atome d'hydrogene dans le meme champ exterieur, et qui d'autre part mene a la prediction des proprietes statistiques des niveaux d'energie du systeme, en fonction de celles du systeme hydrogenoide correspondant. La deuxieme partie est consacree au probleme de la diffusion multiple d'une onde lumineuse en milieu atomique, et en particulier a l'etude de l'augmentation coherente de la retrodiffusion par un gaz d'atomes refroidis. L'augmentation coherente de la retrodiffusion est un effet d'interference entre des paires de chemins de diffusion multiple, et est un phenomene bien etudie pour des diffuseurs classiques. Dans cette deuxieme partie, nous montrons que la prise en compte de la structure interne atomique est essentielle pour la comprehension de la retrodiffusion coherente par un milieu atomique, et mene a une diminution significative des facteurs d'augmentation observables. Un calcul explicite de la diffusion simple et de la diffusion double par des atomes est donne, et les resultats sont compares a des donnees experimentales recentes.
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Prehl, geb Balg Janett. "Diffusion on Fractals." Master's thesis, Universitätsbibliothek Chemnitz, 2007. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200701033.
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We study anomalous diffusion on fractals with a static external field applied. We utilise the master equation to calculate particle distributions and from that important quantities as for example the mean square displacement . Applying different bias amplitudes on several regular Sierpinski carpets we obtain maximal drift velocities for weak field strengths. According to ~t^(2/d_w), we determine random walk dimensions of d_w<2 for applied external fields. These d_w corresponds to superdiffusion, although diffusion is hindered by the structure of the carpet, containing dangling ends. This seems to result from two competing effects arising within an external field. Though the particles prefer to move along the biased direction, some particles get trapped by dangling ends. To escape from there they have to move against the field direction. Due to the by the bias accelerated particles and the trapped ones the probability distribution gets wider and thus d_w<2<br>In dieser Arbeit untersuchen wir anomale Diffusion auf Fraktalen unter Einwirkung eines statisches äußeres Feldes. Wir benutzen die Mastergleichung, um die Wahrscheinlichkeitsverteilung der Teilchen zu berechnen, um daraus wichtige Größen wie das mittlere Abstandsquadrat zu bestimmen. Wir wenden unterschiedliche Feldstärken bei verschiedenen regelmäßigen Sierpinski-Teppichen an und erhalten maximale Driftgeschwindigkeiten für schwache Feldstärken. Über ~t^{2/d_w} bestimmen wir die Random-Walk-Dimension d_w als d_w<2. Dieser Wert für d_w entspricht der Superdiffusion, obwohl der Diffusionsprozess durch Strukturen des Teppichs, wie Sackgassen, behindert wird. Es schient, dass dies das Ergebnis zweier konkurrierender Effekte ist, die durch das Anlegen eines äußeren Feldes entstehen. Einerseits bewegen sich die Teilchen bevorzugt entlang der Feldrichtung. Andererseits gelangen einige Teilchen in Sackgassen. Um die Sackgassen, die in Feldrichtung liegen, zu verlassen, müssen sich die Teilchen entgegen der Feldrichtung bewegen. Somit sind die Teilchen eine gewisse Zeit in der Sackgasse gefangen. Infolge der durch das äußere Feld beschleunigten und der gefangenen Teilchen, verbreitert sich die Wahrscheinlichkeitsverteilung der Teilchen und somit ist d_w<2
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Bowen, Mark. "High order diffusion." Thesis, University of Nottingham, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.267628.
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Barker, John A. "Diffusion in hydrogeology." Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-193862.
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The field of hydrogeology is primarily concerned with the flow of water below the ground surface and with transport, normally of solutes and heat, within that water. Many disciplines have contributed to this endeavor which requires skills from across the spectrum
of science, engineering and beyond. The diffusion equation describes not only solute transport but also the flow of water, via Darcy’s law. Of particular interest is transport in fractured rock where most of the flow is through the fractures while most of the storage is in the rock pores: a ‘double-porosity’ system. Hydrogeology remains a field that welcomes those who bring techniques from other areas
of science to address problems as varied as water supply, radioactive waste disposal and geothermal energy.
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Heinke, Lars. "Diffusion in MOFs." Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-198185.
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Eloul, Shaltiel. "Diffusion to electrodes." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:88c5f1d0-9f2f-49d5-b46d-6eeb5b7d4bfe.
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This thesis develops diffusion models for modern electrochemical experiments involving the transport of particles to electrodes and adsorbing surfaces. In particular, the models are related to the 'impact' method where particles stochastically arrive at an electrode and detected electrochemically. The studies are carried out using numerical simulations and also analytical methods. Chapter 1 is introductory and outlines some fundamental concepts in mass transport and kinetics, and their relation to electrochemical measurements which are of importance for the reader. Chapter 2 describes the numerical methods which are used for electrochemical simulations. Chapter 3 focuses on a specific two dimensional simulation system and the development of a high performance voltammetry simulation. Chapters 4 and 5 study the stochastic impacts of particles at an electrode surface. In Chapter 4, a 'diffusion only' model is developed using a probabilistic study and random walk simulations in order to provide expressions that can be used in so-called `impact' experiments. In Chapter 5, the practical cases of microdisc and microwire electrodes are investigated. Expressions for the number of impacts are developed and the concept of the lower limit of detection in ultra-dilute solutions is introduced. Then, a comparison study between the microwire electrode and the microdisc electrode explores a geometrical effect and its implications for experimental setups. In Chapter 6, a numerical and analytical study is developed to examine the effect of hindered diffusion as a particle moves close to an adsorbing surface. The study identifies the conditions under which this hindered diffusion is signiffcant even in a non-confined space. The study shows that the domination of hindered diffusion is strongly dependant on the sizes of both the particle and the target. The study focuses on a variety of target shapes and allows the number of hits/impacts to be estimated in practical 'impact' experiments. Moreover, a drastic effect on the calculation of the mean first passage time is observed for a sub-micron sized target, showing the importance of this effect not only for electrochemistry but also in biological systems. Chapters 7 and 8 investigate the properties of an adsorbing insulating surface adjacent to an electrode. In Chapter 7, a numerical study of the effect of 'shielding' by the insulating sheath is carried out. The study examines the in uence of this effect on the magnitude of the current in chronoamperometry experiments. Chapter 8 explores the case of reversible adsorption on the insulating surface for voltammetric enhancement by pre-concentration on the sheath surface. The results identify the conditions under which enhancement of the voltammetric signal can be observed. Finally, Chapter 9 looks at geometrical effects on the current response of insulating particles modified with an electroactive surface layer. Numerical models are developed to model the diffusion of charge transfer between electro-active sites on a modified surface of insulating particles. The current-time responses are simulated for particles with the shape of a sphere, a cube/cuboid, and a cylinder on an electrode. The characteristic currenttime responses are calculated for the various shapes. The observations show that the model can be utilised in experiments to determine the coverage or the diffusion coeficient of charge dissipation on modified insulating particles and, in some situations to identify the particle shape.
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Barker, John A. "Diffusion in hydrogeology." Diffusion fundamentals 6 (2007) 50, S. 1-18, 2007. https://ul.qucosa.de/id/qucosa%3A14229.
Full textAbstract:
The field of hydrogeology is primarily concerned with the flow of water below the ground surface and with transport, normally of solutes and heat, within that water. Many disciplines have contributed to this endeavor which requires skills from across the spectrum
of science, engineering and beyond. The diffusion equation describes not only solute transport but also the flow of water, via Darcy’s law. Of particular interest is transport in fractured rock where most of the flow is through the fractures while most of the storage is in the rock pores: a ‘double-porosity’ system. Hydrogeology remains a field that welcomes those who bring techniques from other areas
of science to address problems as varied as water supply, radioactive waste disposal and geothermal energy.
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Подолкова, Світлана Віталіївна, Светлана Витальевна Подолкова, Svitlana Vitaliivna Podolkova, and Y. Mykula. "Diffusion of innovation." Thesis, Вид-во СумДУ, 2009. http://essuir.sumdu.edu.ua/handle/123456789/16772.
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Agrawal, Mani Kant. "Diffusion activity networks." Raleigh, NC : North Carolina State University, 1999. http://www.lib.ncsu.edu/etd/public/etd-52301811109943140/etd.pdf.
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Zerhouni, Abder Rahim. "Diffusion et feuilletages." Grenoble 2 : ANRT, 1986. http://catalogue.bnf.fr/ark:/12148/cb37601925f.
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Harris, John William. "Branching diffusion processes." Thesis, University of Bath, 2006. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.428379.
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Molkenthin, Nora. "Advection-diffusion-networks." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2014. http://dx.doi.org/10.18452/17064.
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Das globale Klimasystem ist ein ausgesprochen komplexes und hochgradig nichtlineares System mit einer Vielzahl von Einflüssen und Interaktionen zwischen Variablen und Parametern. Komplementär zu der Beschreibung des Systems mit globalen Klimamodellen, kann Klima anhand der Interaktionsstruktur des Gesamtsystems durch Netzwerke beschrieben werden. Statt Details so genau wie möglich zu modellieren, werden hier Zeitreihendaten verwendet um zugrundeliegende Strukturen zu finden. Die Herausforderung liegt dann in der Interpretation dieser Strukturen. Um mich der Frage nach der Interpretation von Netzwerkmaßen zu nähern, suche ich nach einem allgemeinen Zusammenhang zwischen Eigenschaften der Netzwerktopologie und Eigenschaften des zugrundeliegenden physikalischen Systems. Dafür werden im Wesentlichen zwei Methoden entwickelt, die auf der Analyse von Temperaturentwicklungen gemäß der Advektions-Diffusions-Gleichung (ADE) basieren. Für die erste Methode wird die ADE mit offenen Randbedingungen und δ-peak Anfangsbedingungen gelöst. Die resultierenden lokalen Temperaturprofile werden verwendet um eine Korrelationsfunktion und damit ein Netzwerk zu definieren. Diese Netzwerke werden analysiert und mit Klimanetzen aus Daten verglichen. Die zweite Methode basiert auf der Diskretisierung der stochastischen ADE. Die resultierende lineare, stochastische Rekursionsgleichung wird verwendet um eine Korrelationsmatrix zu definieren, die nur von der Übergangsmatrix und der Varianz des stochastischen Störungsterms abhängt. Ich konstruiere gewichtete und ungewichtete Netzwerke für vier verschiedene Fälle und schlage Netzwerkmaße vor, die zwischen diesen Systemen zu unterscheiden helfen, wenn nur das Netzwerk und die Knotenpositionen gegeben sind. Die präsentierten Rekonstruktionsmethoden generieren Netzwerke, die konzeptionell und strukturell Klimanetzwerken ähneln und können somit als "proof of concept" der Methode der Klimanetzwerke, sowie als Interpretationshilfe betrachtet werden.<br>The earth’s climate is an extraordinarily complex, highly non-linear system with a multitude of influences and interactions between a very large number of variables and parameters. Complementary to the description of the system using global climate models, in recent years, a description based on the system’s interaction structure has been developed. Rather than modelling the system in as much detail as possible, here time series data is used to identify underlying large scale structures. The challenge then lies in the interpretation of these structures. In this thesis I approach the question of the interpretation of network measures from a general perspective, in order to derive a correspondence between properties of the network topology and properties of the underlying physical system. To this end I develop two methods of network construction from a velocity field, using the advection-diffusion-equation (ADE) for temperature-dissipation in the system. For the first method, the ADE is solved for δ-peak-shaped initial and open boundary conditions. The resulting local temperature profiles are used to define a correlation function and thereby a network. Those networks are analysed and compared to climate networks from data. Despite the simplicity of the model, it captures some of the most salient features of climate networks. The second network construction method relies on a discretisation of the ADE with a stochastic term. I construct weighted and unweighted networks for four different cases and suggest network measures, that can be used to distinguish between the different systems, based on the topology of the network and the node locations. The reconstruction methods presented in this thesis successfully model many features, found in climate networks from well-understood physical mechanisms. This can be regarded as a justification of the use of climate networks, as well as a tool for their interpretation.
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Golshani, Fariborz. "Boron doping of diamond powder by enhanced diffusion and forced diffusion : diffusion concentrations, mechanical, chemical and optical properties /." free to MU campus, to others for purchase, 1997. http://wwwlib.umi.com/cr/mo/fullcit?p9842530.
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Pablo, Hélène. "Diffusion chimique dans les verres borosilicates d'intérêt nucléaire." Thesis, Paris, Muséum national d'histoire naturelle, 2017. http://www.theses.fr/2017MNHN0014/document.
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La diffusion chimique est un phénomène clé dans l’élaboration des verres d’intérêt nucléaire. A haute température, dans le liquide, elle permet l’homogénéisation des flux de matière (précurseurs vitreux et déchets) et conduit à la formation d’un verre homogène après refroidissement. A contrario, dans le liquide surfondu, elle peut être à l’origine de processus de séparation de phase ou de cristallisation qui doivent être contrôlés pour le bon fonctionnement du procédé. Dans cette thèse, l’influence de la diffusion chimique sur les processus de cristallisation et d’homogénéisation du liquide est étudiée pour un verre simplifié de type borosilicate de sodium entre sa température de transition vitreuse et sa température d’élaboration. Pour ce type de système, qualifié de multicomposants, la description des phénomènes diffusifs nécessite le calcul d’une matrice de diffusion prenant en compte la diffusion couplée des espèces. Ces couplages sont retranscrits au travers de mécanismes de diffusion ou « échanges diffusifs » qui sont invariants avec la température. Les énergies d’activation associées à ces échanges sont proches de l’énergie d’activation de l’écoulement visqueux ce qui montre que le flux visqueux et la diffusion chimique sont pilotés par un seul et même mécanisme en lien avec la fréquence de rupture des liaisons Si-O et B-O. Nous mettons également en évidence que dans le liquide surfondu, les échanges diffusifs primaire (SiO2-Na2O) et secondaire (SiO2-B2O3) jouent un rôle prépondérant sur la cinétique de cristallisation et la direction de croissance des phases cristallines (cristobalite et tridymite) formées dans nos systèmes. Ces résultats permettent de justifier l’évolution des gradients de compositions à proximité et loin des cristaux. Dans la dernière partie du manuscrit, une complexification des verres a été initiée en ajoutant du lanthane pour simuler un des lanthanides majoritairement présents dans la composition du verre nucléaire de référence R7T7. Les données obtenues ont révélé un couplage diffusif entre le lanthane et le silicium qui entre en compétition avec les autres couplages mis en évidence dans le ternaire SiO2-Na2O-B2O3. Ce couplage, combiné aux autres résultats de la thèse, permet d’expliquer la formation d’une phase de type borosilicate de lanthane (LaBSiO5)<br>Chemical diffusion is a key-phenomenon during nuclear glass synthesis. At high temperature, diffusion leads to homogenization of the melt contributing to the transformation of heterogeneous waste and frit precursors to a homogeneous glass after cooling. In contrast, in the supercooled liquid, diffusion is a critical factor affecting phase separation and/or crystallization processes that must be avoided when producing a high quality final product.In this manuscript, the impact of chemical diffusion on crystallization and liquid homogenization is studied for a simplified sodium borosilicate glass between its glass transition temperature and its synthesis temperature. For this kind of system, qualified as multicomponent, the description of diffusive phenomena requires the calculation of a diffusion matrix that takes into account diffusive couplings between species. These couplings can be written in the form of diffusive mechanisms or “diffusive exchanges” that are invariant with temperature. The activation energies associated with these exchanges are close to the activation energy of shear viscosity which suggests that viscous flow and chemical diffusion are driven by a single mechanism related to the frequency of Si-O and B-O bond breaking. It is also highlighted that in the supercooled liquid, the principal diffusive exchange (SiO2-Na2O) and the secondary diffusive exchange (SiO2-B2O3) play a significant role on the kinetics and direction of growth of crystalline phases which are formed in our system. These results are used to rationalise the evolution of compositional gradients in the vicinity and far from crystals. In the last part of this work, a complexification of the glasses was initiated by adding lanthanum to simulate one of the main lanthanides of the R7T7 nuclear glass composition. The data collected reveal diffusive couplings between lanthanum and silicon. These couplings, combined with the other results explain the formation of a lanthanum borosilicate phase (LaBSiO5)
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Mukherjee, Sayak. "Applications of Field Theory to Reaction Diffusion Models and Driven Diffusive Systems." Diss., Virginia Tech, 2009. http://hdl.handle.net/10919/39293.
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In this thesis, we focus on the steady state properties of two systems which are genuinely out of equilibrium. The first project is an application of dynamic field theory to a specific non equilibrium critical phenomenon, while the second project involves both simulations and analytical calculations. The methods of field theory are used on both these projects. In the first part of this thesis, we investigate a generalization of the well-known field theory for directed percolation (DP). The DP theory is known to describe an evolving population, near extinction. We have coupled this evolving population to an environment with its own nontrivial spatio-temporal dynamics. Here, we consider the special case where the environment follows a simple relaxational (model A) dynamics. We find two marginal couplings with upper critical dimension of four, which couple the two theories in a nontrivial way. While the Wilson-Fisher fixed point remains completely unaffected, a mismatch of time scales destabilizes the usual DP fixed point. Some open questions and future work remain.
In the second project, we focus on a simple particle transport model far from equilibrium, namely, the totally asymmetric simple exclusion process (TASEP). While its stationary properties are well studied, many of its dynamic features remain unexplored. Here, we focus on the power spectrum of the total particle occupancy in the system. This quantity exhibits unexpected oscillations in the low density phase. Using standard Monte Carlo simulations and analytic calculations, we probe the dependence of these oscillations on boundary effects, the system size, and the overall particle density. Our simulations are fitted to the predictions of a linearized theory for the fluctuation of the particle density. Two of the fit parameters, namely the diffusion constant and the noise strength, deviate from their naive bare values [6]. In particular, the former increases significantly with the system size. Since this behavior can only be caused by nonlinear effects, we calculate the lowest order corrections in perturbation theory. Several open questions and future work are discussed.<br>Ph. D.
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Jonckheere, Thibaut. "Diffusion d'ondes dans un milieu atomique : chaos quantique et diffusion multiple." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2000. http://tel.archives-ouvertes.fr/tel-00000410.
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Ce travail de thèse comporte deux parties distinctes, concernant la diffusion d'ondes en milieu atomique.<br />La première partie étudie le problème<br />des niveaux excités d'un atome non-hydrogenoide en champ extérieur. Ce système est très similaire<br />au cas de l'hydrogène dans le même champ extérieur, mais est plus complexe à cause de la diffusion<br />de l'onde électronique sur le coeur ionique non-hydrogenoide. On montre dans cette première partie que la <br />présence du coeur ionique est mathématiquement équivalente à celle d'un ou plusieurs diffuseurs<br />ponctuels. Ceci permet d'obtenir une équation qui, d'une part, autorise un calcul efficace des niveaux <br />d'énergie du système à partir de ceux pour l'atome d'hydrogène dans le même champ extérieur,<br />et qui d'autre part mène à la prédiction des propriétés statistiques des niveaux d'énergie<br />du système, en fonction de celles du système hydrogenoide correspondant. <br /><br />La deuxième partie est consacrée au problème <br />de la diffusion multiple d'une onde lumineuse en milieu atomique, et en particulier à l'étude de l'augmentation<br />cohérente de la rétrodiffusion par un gaz d'atomes refroidis. L'augmentation cohérente de la rétrodiffusion <br />est un effet d'interférence entre des paires de chemins de diffusion multiple, et est un phénomène <br />bien étudié pour des diffuseurs classiques. Dans cette deuxième partie, nous montrons que la prise <br />en compte de la structure interne atomique est essentielle pour la compréhension de la rétrodiffusion cohérente<br />par un milieu atomique,<br />et mène à une diminution significative des facteurs d'augmentation observables. Un calcul explicite de la <br />diffusion simple et de la diffusion double par des atomes est donné, et les résultats sont comparés à des données<br /> expérimentales récentes.
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Endal, Jørgen. "Nonlinear fractional convection-diffusion equations, with nonlocal and nonlinear fractional diffusion." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2013. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-22955.
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We study nonlinear fractional convection-diffusion equations with nonlocal and nonlinear fractional diffusion. By the idea of Kru\v{z}kov (1970), entropy sub- and supersolutions are defined in order to prove well-posedness under the assumption that the solutions are elements in $L^{\infty}(\mathbb{R}^d\times (0,T))\cap C([0,T];L_\text{loc}^1(\mathbb{R}^d))$. Based on the work of Alibaud (2007) and Cifani and Jakobsen (2011), a local contraction is obtained for this type of equations for a certain class of L\'evy measures. In the end, this leads to an existence proof for initial data in $L^{\infty}(\mathbb{R}^d)$
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Hrabetova, Sabina. "Extracellular diffusion in brain: distinct diffusion regimes at different spatial scales." Diffusion fundamentals 16 (2011) 3, S. 1-2, 2011. https://ul.qucosa.de/id/qucosa%3A13731.
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Shah, Milap. "Parallel Aes diffusion inter block diffusion at bit level and compression." Thesis, Högskolan i Halmstad, Akademin för informationsteknologi, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-42449.
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Information is an intelligent data through which knowledgeable and usable things can be convicted or interpreted in a proper manner. With the advancement of technology, transmission of information over the network has come a trend. This information must be transmitted securely over the network. Data security was not a problem if a secure channel was provided for single transmission. It is a necessity to convert the information into an unintelligible form for transmitting it over an unsecured channel. Encryption is a technique through which original information can be converted into unintelligible form. As time has elapsed, various encryption algorithms are employed so that information can be transmitted securely over an unsecured channel. Unless an intruder accesses the encrypted text, he / she cannot gain any information from that text. But as the new algorithms are designed, all the algorithms are challenged and their cryptanalysis is available. In the year 1998, Advanced Encryption Standards (A (S)) were proposed and later it was widely accepted as the most secure encryption algorithm that can be used to encrypt the information so that it can be transmitted securely and unsecured. fixed to a new scheme called Parallel AЕS, was an employee who takes four blocks of 16 bytes at a time to generate four blocks of 16 bytes of text thus providing diffusion of blocks at exchange. than all sequential AЕs. All the algorithms are challenged and their cryptanalysis is available. In the year 1998, To make A morS more fixed to a new scheme called Parallel AЕS, was an employee who took four blocks of 16 bytes at a time to generate four blocks of 16 bytes of text, thus providing diffusion of blocks at exchange. By doing this parallel A stoodS stood to be much firmer than sequential AЕS. Advanced Encryption Standards (AЕS) was proposed and later it was widely accepted as the most secure encryption algorithm that can be used to encrypt the information so that it can be transmitted securely over an unsecured channel. To make A morS more fixed to a new scheme called Parallel AЕS, was an employee who took four blocks of 16 bytes at a time to generate four blocks of 16 bytes of text, thus providing diffusion of blocks at exchange. By doing this parallel A stoodS stood to be much firmer than sequential AЕS. Advanced Encryption Standards (AЕS) was proposed and later it was widely accepted as the most secure encryption algorithm that can be used to encrypt the information so that it can be transmitted securely over an unsecured channel. To make A morS more fixed to a new scheme called Parallel AЕS, was an employee who took four blocks of 16 bytes at a time to generate four blocks of 16 bytes of text, thus providing diffusion of blocks at exchange. By doing this parallel A stoodS stood to be much firmer than sequential AЕS. was an employee who took four blocks of 16 bytes at a time to generate four blocks of 16 bytes of text, thus providing diffusion of blocks at exchange. By doing this parallel A stoodS stood to be much firmer than sequential AЕS. was an employee who took four blocks of 16 bytes at a time to generate four blocks of 16 bytes of text, thus providing diffusion of blocks at exchange. By doing this parallel A stoodS stood to be much firmer than sequential AЕS.
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Kharchenko, Andriy V. "La diffusion de la lumière par les gaz : de la diffusion incohérente à la diffusion exacerbée ; application à la vélocimétrie." Palaiseau, Ecole polytechnique, 2000. http://www.theses.fr/2000EPXX0013.
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La diffusion exacerbée de la lumière par un gaz utilise la diffusion élastique et se produit lorsque la distribution spatiale de la densité du gaz n'est pas uniforme. Le champ électrique de cette diffusion est proportionnel à une transformée de Fourier spatiale de la distribution des molécules au vecteur d'onde k, et son intensité mesure le facteur de forme s(k). Dans ce travail, on a mesuré le facteur de forme s(k) dans l'écoulement turbulent d'un jet d'air en fonction du module du vecteur d'onde k depuis les échelles des mouvements microscopiques (10 microns) jusqu'à l'échelle macroscopique de l'écoulement (1 millimètre). Entre ces deux échelles le facteur de forme passe de la valeur unité, caractéristique du gaz parfait, jusqu'à des intensités multipliées par un facteur très important atteignant douze ordres de grandeur. On a observé de façon continue cette transition depuis la diffusion incohérente jusqu'à la diffusion exacerbée. Lorsque la lumière incidente est une lumière visible, l'intensité de la diffusion exacerbée permet l'observation à l'oeil nu. L'amplitude complexe du champ électrique diffusé a été enregistrée en utilisant la détection hétérodyne, et les propriétés d'analycité mathématique de ce signal ont été etudiées en fonction de la variable temps. On utilise cette propriété d'analycité pour extraire une mesure continue de la vitesse du gaz. En outre le signal complexe contient aussi une information sur les mouvements microscopiques : on a mis en évidence cette information et on l'a utilisée pour mesurer un coefficient de diffusion moléculaire en très bon accord avec les données tabulées.
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Euschen, Andreas. "Diffusion in flüssigkristallinen Silastomeren : e. Beitr. zur Kontrolle d. Arzneistofffreisetzung durch Diffusion /." Saarbrücken, 1988. http://www.gbv.de/dms/bs/toc/016585976.pdf.
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Zhang, Qiaofu. "Use Diffusion Multiples to Investigate Diffusion and Precipitation Behavior in Binary Systems." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1483702959561522.
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Euschen, Andreas. "Diffusion in flüssigkristallinen Silastomeren : e. Beitrag zur Kontrolle d. Arzneistofffreisetzung durch Diffusion /." [S.l.], 1988. http://www.gbv.de/dms/bs/toc/016585976.pdf.
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Heim, Susanne. "Statistical Diffusion Tensor Imaging." Diss., lmu, 2007. http://nbn-resolving.de/urn:nbn:de:bvb:19-72610.
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Fredriksson, Lars. "Normal and anomalous diffusion." Thesis, Karlstads universitet, Fakulteten för teknik- och naturvetenskap, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-6561.
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Diffusion can be classified as either normal or anomalous. A variety of experimental systems are evaluated to classify diffusion. Potential regressions and step size distributions are analysed. Nor-mal diffusion holds except where flocculation takes place, or where concentrations of cationic starches are high or with cationic starches and latex together. In these cases, subdiffusion takes place. Furthermore, limiting values are used to calculate diffusion coefficients. Diffusion of non-spherical particles is covered as well, here tested on microcrystalline cellulose.
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Hariz, Jakob. "Diffusion in fractal globules." Thesis, Umeå universitet, Institutionen för fysik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-126570.
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Recent experiments suggest that the human genome (all of our DNA) is organised as a so-called fractal globule. The fractal globule is a knot--free dense polymer that easily folds and unfolds any genomic locus, for example a group of nearby genes. Proteins often need to locate specific target sites on the DNA, for instance to activate a gene. To understand how proteins move through the DNA polymer, we simulate diffusion of particles through a fractal globule. The fractal globule was generated on a cubic lattice as spheres connected by cylinders. With the structure in place, we simulate particle diffusion and measure how their mean squared displacement ($\langle R^2(t)\rangle$) grows as function of time $t$ for different particle radii. This quantity allows us to better understand how the three dimensional structure of DNA affects the protein's motion. From our simulations we found that $\langle R^2(t)/t\rangle$ is a decaying function when the particle is sufficiently large. This means that the particles diffuse slower than if they were free. Assuming that $\langle R^2(t) \rangle \propto t^\alpha$ for long times, we calculated the growth exponent $\alpha$ as a function of particle radius $r_p$. When $r_p$ is small compared to the average distance between two polymer segments $d$, we find that $\alpha \approx 1$. This means the polymer network does not affect the particle's motion. However, in the opposite limit $r_p\sim d$ we find that $\alpha<1$ which means that the polymer strongly slows down the particle's motion. This behaviour is indicative of sub-diffusive dynamics and has potentially far reaching consequences for target finding processes and biochemical reactions in the cell.
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Ta, Thi nguyet nga. "Sub-gradient diffusion equations." Thesis, Limoges, 2015. http://www.theses.fr/2015LIMO0137/document.
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Ce mémoire de thèse est consacrée à l'étude des problèmes d'évolution où la dynamique est régi par l'opérateur de diffusion de sous-gradient. Nous nous intéressons à deux types de problèmes d'évolution. Le premier problème est régi par un opérateur local de type Leray-Lions avec un domaine borné. Dans ce problème, l'opérateur est maximal monotone et ne satisfait pas la condition standard de contrôle de la croissance polynomiale. Des exemples typiques apparaît dans l'étude de fluide non-Neutonian et aussi dans la description de la dynamique du flux de sous-gradient. Pour étudier le problème nous traitons l'équation dans le contexte de l'EDP non linéaire avec le flux singulier. Nous utilisons la théorie de gradient tangentiel pour caractériser l'équation d'état qui donne la relation entre le flux et le gradient de la solution. Dans le problème stationnaire, nous avons l'existence de la solution, nous avons également l'équivalence entre le problème minimisation initial, le problème dual et l'EDP. Dans l'équation de l'évolution, nous proposons l'existence, l'unicité de la solution. Le deuxième problème est régi par un opérateur discret. Nous étudions l'équation d'évolution discrète qui décrivent le processus d'effondrement du tas de sable. Ceci est un exemple typique de phénomènes auto-organisés critiques exposées par une slope critique. Nous considérons l'équation d'évolution discrète où la dynamique est régie par sous-gradient de la fonction d'indicateur de la boule unité. Nous commençons par établir le modèle, nous prouvons existence et l'unicité de la solution. Ensuite, en utilisant arguments de dualité nous étudions le calcul numérique de la solution et nous présentons quelques simulations numériques<br>This thesis is devoted to the study of evolution problems where the dynamic is governed by sub-gradient diffusion operator. We are interest in two kind of evolution problems. The first problem is governed by local operator of Leray-Lions type with a bounded domain. In this problem, the operator is maximal monotone and does not satisfied the standard polynomial growth control condition. Typical examples appears in the study of non-Neutonian fluid and also in the description of sub-gradient flows dynamics. To study the problem we handle the equation in the context of nonlinear PDE with singular flux. We use the theory of tangential gradient to characterize the state equation that gives the connection between the flux and the gradient of the solution. In the stationary problem, we have the existence of solution, we also get the equivalence between the initial minimization problem, the dual problem and the PDE. In the evolution one, we provide the existence, uniqueness of solution and the contractions. The second problem is governed by a discrete operator. We study the discrete evolution equation which describe the process of collapsing sandpile. This is a typical example of Self-organized critical phenomena exhibited by a critical slop. We consider the discrete evolution equation where the dynamic is governed by sub-gradient of indicator function of the unit ball. We begin by establish the model, we prove existence and uniqueness of the solution. Then by using dual arguments we study the numerical computation of the solution and we present some numerical simulations
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Palmieri, Benoit. "Diffusion in channeled structures." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=18269.
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The theory of Ronis and Vertenstein [J. Chem. Phys. vol. 85, 1628, (1986)] is used to calculate the permeability of Xenon in Theta-1 and of Argon in alpha-quartz, both crystalline sodalites containing large, one-dimensional channels in the first case and narrow interconnected channels in the second. The simulated dynamics of a small part of the crystal atoms exactly reproduce those of the full crystal by the means of a generalized Langevin classical equation of motion. An approximate expression for the potential of mean force inside the crystal is derived. The Theta-1 energy landscape is smooth with small energy barriers while the alpha-quartz has large energy barriers to diffusion. The permeability is reported for both systems and compared in detail with that obtained from transition state theory. The role of the lattice vibrations is also investigated. For Xenon in Theta-1, transition state theory does not properly describe the diffusion process and the lattice vibrations do not play a large role. For Argon in alpha-quartz, transition state theory is more appropriate but there, the lattice vibrations cannot be neglected. For systems where the lattice vibrations play a role, the quantum mechanical corrections to the diffusion are computed. The diffusion is studied using the path integral formalism. Forward-Backward path integrals are combined and, using the MSR [Phys. Rev. A., vol. 8, 423 (1973)] formalism, are transformed to a set of generalized Langevin equations that reduce to the classical equations of motion at high temperatures. The quantum mechanical treatment of the lattice vibrations results in a decreased permeability. The quantum corrections to the potential of mean force are computed from an approximate density matrix. A modification to the original Feynman-Kleinert variational method[Phys. Rev. A., vol. 34, 5080 (1986)] to calculate quantum mechanical partition functions is sugges<br>La méthode dévelopée par Ronis et Vertenstein [J. Chem. Phys. vol. 85, 1628, (1986)] est utilisée pour calculer la perméabilité du Xénon à l'intérieur du zéolite Theta-1 et de l'Argon à l'intérieur d'un cristal d'alpha-quartz. Ces deux sodalites contiennent des canaux qui sont larges et unidimensionnels dans le premier cas et étroits et interconnectés dans le deuxième. La dynamique d'une petite partie des atomes du cristal est explicitement simulée. Cette dynamique est décrite à partir d'équations de Langevin généralisées qui reproduisent l'effet du reste du cristal. L'énergie libre du gaz absorbé à l'intérieur du cristal est approximée. Le profil énergétique à l'intérieur du zéolite Theta-1 est presque plat et contient des barrières énergétiques peu élevées. Celui à l'intérieur du quartz contient de larges barrières à la diffusion. La perméabilité des deux systèmes est rapportée et comparée en détail avec celle obtenue à partir de la théorie dite des états de transitions. Le rôle qu'ont les modes de vibrations du cristal sur la diffusion est aussi étudié. Pour le Xénon à l'intérieur du zéolite Theta-1, la théorie des états de transitions ne décrit pas adéquatement la diffusion du gaz et les vibrations du cristal ne jouent pas un grand rôle. Pour l'argon dans le quartz, la théorie des états de transitions est plus appropriée et les vibrations du cristal ne peuvent être négligées. Pour les systèmes où les vibrations du cristal jouent un rôle, les premières corrections quantiques sont calculées. Dans ce cas, la diffusion est étudiée à partir de la formulation des intégrales de chemins. Les intégrales de chemins sont combinées et, en utilisant la théorie développée par Martin, Siggia et Rose [Phys. Rev. A., vol. 8, 423 (1973)], réduites à un système d'équations de Langevin généralisées q
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Abdullatif, Tawfik A. "Turbulent diffusion impinging flames." Thesis, University of Manchester, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.488402.
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Kallioras, Panagiotis. "Diffusion Through Multilayer Networks." Thesis, Uppsala universitet, Institutionen för informationsteknologi, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-251289.
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Population of earth is increasing rapidly, generating more and more situations which allow us to study the mechanisms behind humans. Previous studies have found evidence of important network effects. When network effects are present, the value of a product or service is dependent on the number of others using them; however there is a lack of empirical research concerning them. The goal of this thesis is to examine and analyze such networks and try through a simulation model of a diffusion process to identify the determinant that can predict the result. We investigate these networks in terms of the probability of the virus to be spread to the neighbors of the receiver needed to reach a given percentage of the nodes in the network. Moreover, we are going to answer to questions like how these parameters change when we change the structure of the networks and their relationships. Finally, the provided results after a number of tests performed on our data will demonstrate how they effect in networks. The study of previous literature will help us to obtain a more depth understanding of multilayer networks. Verification of the model on real data is an objective of the thesis but it is not guaranteed, given the difficulty in retrieving real data.
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Allen, Elizabeth D. "Diffusion through strained semiconductors." Thesis, University of Nottingham, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.267629.
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Gandhi, U. P. "Diffusion in cellulose derivatives." Thesis, Cardiff University, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.376555.
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Dray, A. E. "Diffusion bonding of aluminium." Thesis, University of Cambridge, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.382557.
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