Thesis (Ph.D) - University of Queensland, 2006. / Includes bibliography.

Cette recherche doctorale est consacrée à l'analyse des perceptions de la citoyenneté française chez les immigrés originaires de Turquie et leurs enfants en lien avec leurs parcours migratoires. S'appuyant sur les différentes appartenances identitaires de ces immigrés, elle propose une analyse de l'articulation des appartenances particulières et de l'appartenance citoyenne qui se produit pendant les parcours migratoires. Cette analyse révèle les modes de compositions identitaires qui se réalisent d'une manière variée par rapport à des appartenances culturelles et politiques dans le cas des immigrés originaires de Turquie et leurs enfants. Les perceptions de la citoyenneté des enquêtés sont affectées, à la fois pour les immigrés et leurs enfants, non seulement par le lien établi avec la France du point de vue juridique, économique, social, culturel et identitaire mais aussi avec leur pays et leur culture d'origine via les activités associatives. Ce qui nous montre que l'appartenance citoyenne dans le parcours migratoire doit être analysée comme un processus qui débute en Turquie et qui continue en France, provoquant parfois des ruptures identitaires. / This doctoral research tried to analyze the perceptions of French citizenship among immigrants from Turkey and their children in relation with their migratory paths. Based on the different identities belonging, it studies the articulation of particular belongings and the citizenship belonging during the migratory paths. In the example of immigrants originated from Turkey, this analysis reveals the patterns of identity compositions that are realized in different ways in relation with cultural and political affiliations. The immigrant's perceptions of the citizenship are affected, for both the immigrants and their children, not only by the legal, economic, social, cultural and identity link with France but also with their country of origin and their native culture through associative activities. So that, citizenship belonging in the migratory process must be taken as a process that is beginning in Turkey and continuing in France, and sometimes causes identity disruption.

Le groupe de recherche Instabilités et Méthodes Numériques Spécifiques mène ses activités dans le développement d’outils numé- riques pour la résolution de problèmes non linéaires en utilisant, no- tamment, la Méthode Asymptotique Numérique (MAN). Basée sur le couplage d’une méthode de perturbation et de discrétisation spa- tiale, la MAN est efficace et permet de déterminer précisément les transitions telles que, par exemple, la perte d’unicité de la solution. L’objectif de ce travail de thèse est de proposer des méthodes numé- riques alternatives à la fois robustes, performantes pour la résolution des équations de Navier-Stokes. Nous nous intéressons à l’analyse de bifurcation stationnaire, mais aussi à la simulation d’écoulement dépendant du temps. Dans un premier temps, des techniques d’analyse de bifurcation nu- mérique pour des problèmes stationnaires à très grand nombre de degrés de liberté sont décrites. Nous implémentons ces techniques, basées sur la MAN, dans le logiciel open-source multi-physique ELMER . Nous détaillons l’implémentation des méthodes d’analyse de bifurcation stationnaire telles que la continuation de branches solutions, les techniques de détection des valeurs critiques du pa- ramètre de charge et les changements de branche en un point de bifurcation stationnaire. L’émergence d’une progression géométrique dans les termes de séries MAN à l’approche d’une singularité est dé- crite. Des discussions sont proposées pour le cas de bifurcations par brisure de symétrie. Les méthodes proposées dans ce travail sont validées en utilisant des cas référencés dans la littérature, tels que des écoulements dans des conduites à expansion/contraction sou- daine. Une étude paramétrique permet de présenter de nouveaux ré- sultats pour les écoulements tridimensionnels dans une expansion brusque. L’utilisation de librairies de calculs intensifs rend possible la réalisation d’analyse de bifurcation pour des modèles à très grand nombre de degrés de liberté, en des temps de calcul abordables. Dans un deuxième temps, des solveurs d’ordre élevé sont proposés pour la simulation d’écoulements instationnaires. Une technique d’homotopie à combinaison convexe et une technique de pertur- bation, sont couplées à un schéma d’intégration temporelle pour résoudre les équations instationnaires de Navier-Stokes. Le cas d’un écoulement bidimensionnel autour d’un cylindre fixe est étudié. Ce problème de référence nous permet de valider et discuter des amélio- rations proposées. De cette manière, nous confirmons, au cours des essais numériques, qu’il est possible de réduire les temps de cal- cul en évitant des assemblages d’opérateurs et des résolutions de systèmes linéaires qui n’apportent aucune information supplémen- taire pour la qualité des solutions. De plus, un nouvel éclairage est apporté sur l’utilisation des approximants de Padé par rapport aux travaux antérieurs. L’utilisation de ces solveurs non linéaires nous permet de réduire significativement le nombre de factorisations de matrice en les conservant valides pour un grand nombre de pas de temps, et parfois sur le domaine temporel complet. De nombreuses perspectives sont envisagées, notamment pour l’analyse des séries pour le cas d’un point limite, la bifurcation de Hopf, l’étude d’autre cas d’écoulements tridimensionnels, le couplage fluide-structure. De même, l’association des techniques MAN aux techniques de réductions de modèles et l’analyse de stabilité des orbites périodiques sont envisageables. / The research group "Instabilités et Méthodes Numériques Spéci-fiques" operates in the development of numerical tools for solving nonlinear problems by using, in particluar, the Asymptotic Numer- ical Method (ANM). Based on coupling a perturbation method and a spatial discretization, the ANM is effective and makes it possible to precisely determine the transitions such as, for example, loss of uniqueness of the solution. The objective of this thesis is to offer al- ternative numerical methods both robust and effective, for solving the Navier-Stokes equations. We are interested in steady bifurcation analysis, and in time dependent flow simulation .Initially, numerical bifurcation analysis techniques for steady flow problems in very large number of degrees of freedom are de- scribed. These techniques, based on the ANM, are implemented in the multiphysics ELMER open-source software. We detail the im- plementation of the steady bifurcation analysis methods such as continuation of solution branches, detection of load parameter critical values and branch switching at steady bifurcation point. The emer- gence of a geometric progression in ANM series terms in the vicinity of a singularity is described. Discussions are proposed for the case of symmetry breaking bifurcations. The methods described in this the- sis are validated using reference cases of the literature, such as flow in pipe with sudden expansion/contraction. New results for three- dimensional flow in a sudden expansion, are obtained according to a parametric study. The use of high performance computing libraries makes possible the bifurcation analysis for models with high number of degrees of freedom, in affordable computing times. Secondly, high-order solvers are proposed for the simulation of un- steady flows. Homotopy with convex combination and a perturba- tion technique, are coupled to a time integration scheme in order to solve the unsteady Navier-Stokes equations. The case of two- dimensional flow around a fixed cylinder is studied. This reference problem allows us to validate and discuss proposed improvements. In this way, we confirm, in the numerical tests, that it is possible to reduce the computation time by avoiding operators assembly and resolution of unuseful linear systems in respect to the solution quality. In addition, new lighting is provided on the use of Padé approximants over previous work. The use of these nonlinear solvers allows us to significantly reduce the number of matrix factorization retaining them valid for many time steps, and sometimes on the complete time do- main. Many opportunities are envisaged, in particular the analysis of ANM series for the case of limit point, the Hopf bifurcation, the study of other cases of three-dimensional flow, the fluid-structure interaction. Similarly, the combination of ANM models with reduction techniques f stable periodic orbits are possible.

[résumé trop long] / The important relationship between structure and function has always been a fundamental question in neuroscience research. In particular in the case of movement, brain controls large groups of muscles and combines it with sensory informations from the environment to execute purposeful motor behavior. Mapping dynamics encoded in a high dimensional neural space onto low-dimensional behavioral space has always been a difficult challenge as far as theory is concerned. Here, we develope a framework to study spike/burst dynamics having low dimensional phase description, which can readily be extended under certain biological constraints on the coupling to low dimensional functional descriptions. In general, phase models are amongst the simplest of neuron models reproducing spike-burst behavior, excitability and bifurcations towards periodic firing. However, the coupling among neurons has only been considered using generic arguments valid close to the bifurcation point, and the distinction between electric and synaptic coupling remains an open question. In this thesis we aim to address this question and derive a mathematical formulation for the various forms of biologically realistic coupling. We begin by constructing a mathematical model based on a planar simplification of the Morris-Lecar model. Using geometric arguments we then derive a phase description of a network of neurons with biologically realistic electric coupling and subsequently with chemical coupling under the fast synapse approximation. We then demonstrate that electric and synaptic coupling are expressed differently on the level of the network’s phase description, exhibiting qualitatively different dynamics. Our numerical investigations confirm these findings and show excellent correspondence between the dynamics of the full network and the network’s phase description. Following the success of the phase description of the spiking neural network, we extend this approach in order to propose a generating mechanism for parabolic bursting captured by only a single phase variable. This is the first model in the literature which captures bursting dynamics in one dimension. In order to study the emergent behavior we extend this to a network of bursters with global coupling and analytically reduce a high dimensional system to only two dimensions. Further, we investigate the bifurcation properties numerically as well as analytically. One of the key conclusion is that the stability states remain invariant to the increasing number of spikes per burst. Finally we investigate a spikeburst neuron network coupled via mean field type of fast synapses developed in this thesis and systematically carry out a detailed bifurcation analysis of the model, for a tractable special case. Numerical simulations investigate this mean field model beyond special case and clearly reveals qualitative correspondence with the full network model. Moreover, these network displays rich collective dynamics as a function of two parameters, mainly the synaptic coupling strength and the width of the distribution in applied stimulus. Besides incoherence, frequency locking, and oscillator death (a total cessation of firing caused by excessively strong coupling), there exist multistable solutions in the full and the phase network of neurons.

Ce travail de recherche est une contribution à l'étude des transitoires d'attaque dans les instruments de type clarinette. L'objectif est d'analyser le comportement de l'instrument en réponse à une variation lente et linéaire de la pression dans la bouche du musicien.Dans des simulations numériques ou des expériences in vitro, lorsque la pression dans la bouche du musicien varie lentement et linéairement dans le temps, on observe en général l'apparition du son lorsque la pression dans la bouche atteint une valeur, appelée seuil d’oscillation dynamique, supérieure au seuil d'oscillation statique. L'apport principal de ce travail est d'interpréter ce phénomène par la présence d'un retard à la bifurcation.L'approche analytique est privilégiée. La contribution majeure de ce doctorat est de comprendre les fondements de la théorie de la bifurcation dynamique afin d’étudier le retard à la bifurcation dans le modèle de clarinette dit "de Raman". Les propriétés du seuil dynamique d’oscillation sont ainsi reliées aux caractéristiques de la variation temporelle de la pression dans la bouche (sa valeur initiale et sa pente). L'une des caractéristiques notoires du retard à la bifurcation est sa grande dépendance au bruit, même s’il provient des erreurs d’arrondi de l’ordinateur. Les propriétés du seuil dynamique changent selon que le bruit peut être ignoré ou non.Nous montrons ensuite expérimentalement à l'aide d’une bouche artificielle et d'une clarinette de laboratoire que le retard à la bifurcation n'est pas qu'un phénomène numérique. Il est ainsi mis en évidence expérimentalement et ses propriétés sont également étudiés et comparées avec celles obtenues dans le cas numérique. / This research is a contribution to the study of attack transients in clarinet-like instruments. The main objective is to understand the behavior of the instrument when the mouth pressure is increased slowly through time at a constant rate.Although previous research proves that oscillations can appear at a value of the static oscillation threshold, numerical simulations and in vitro experiments show that for gradual increases of the mouth pressure, the audible sound generally appears when mouth pressure reaches a much higher value, called the dynamic oscillation threshold. This phenomenon is referred to as bifurcation delay in this work.A major part of this work follows an analytical approach, using the foundations of dynamic bifurcation theory to study the bifurcation delay in the simple "Raman" clarinet model. The properties of the dynamic oscillation threshold are related to indicators of the time variation of the mouth pressure such as its initial value and its slope. One of the remarkable features of the bifurcation delay is its strong dependence on noise, including that arising from round-off errors of the computer. The properties of the dynamic threshold are different according to whether the noise can be ignored or not.Additionally, an artificial mouth is used on a clarinet-like instrument to show that the bifurcation delay is not only a numerical phenomenon. Experimental observations performed on a clarinet-like instrument blown by an artificial mouth prove that bifurcation delay exists also on real-life systems. These observations show that the properties of the bifurcation delay observed in low-precision simulations are similar to experimental ones.

abstract: Cancer is a worldwide burden in every aspect: physically, emotionally, and financially. A need for innovation in cancer research has led to a vast interdisciplinary effort to search for the next breakthrough. Mathematical modeling allows for a unique look into the underlying cellular dynamics and allows for testing treatment strategies without the need for clinical trials. This dissertation explores several iterations of a dendritic cell (DC) therapy model and correspondingly investigates what each iteration teaches about response to treatment. In Chapter 2, motivated by the work of de Pillis et al. (2013), a mathematical model employing six ordinary differential (ODEs) and delay differential equations (DDEs) is formulated to understand the effectiveness of DC vaccines, accounting for cell trafficking with a blood and tumor compartment. A preliminary analysis is performed, with numerical simulations used to show the existence of oscillatory behavior. The model is then reduced to a system of four ODEs. Both models are validated using experimental data from melanoma-induced mice. Conditions under which the model admits rich dynamics observed in a clinical setting, such as periodic solutions and bistability, are established. Mathematical analysis proves the existence of a backward bifurcation and establishes thresholds for R0 that ensure tumor elimination or existence. A sensitivity analysis determines which parameters most significantly impact the reproduction number R0. Identifiability analysis reveals parameters of interest for estimation. Results are framed in terms of treatment implications, including effective combination and monotherapy strategies. In Chapter 3, a study of whether the observed complexity can be represented with a simplified model is conducted. The DC model of Chapter 2 is reduced to a non-dimensional system of two DDEs. Mathematical and numerical analysis explore the impact of immune response time on the stability and eradication of the tumor, including an analytical proof of conditions necessary for the existence of a Hopf bifurcation. In a limiting case, conditions for global stability of the tumor-free equilibrium are outlined. Lastly, Chapter 4 discusses future directions to explore. There still remain open questions to investigate and much work to be done, particularly involving uncertainty analysis. An outline of these steps is provided for future undertakings. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics 2020

Dans la configuration de Rayleigh-Bénard, on considère une fine couche de fluide placée entre deux parois horizontales, chauffée par le bas et refroidie par le haut. Cette couche peut être le siège d'une instabilité si le gradient thermique est suffisamment important : on passe alors de l'état conductif à l'état convectif et on parle de bifurcation primaire pour qualifier cette première transition. Cette mise en mouvement du fluide se fait de manière ordonnée : on constate ainsi l'émergence de différents motifs de convection comme des rouleaux, des carrés ou encore des hexagones. Ces structures vont à leur tour subir des instabilités qualifiées de secondaires qui vont limiter la gamme de nombres d'onde stables. On étudie ici théoriquement ces instabilités d'une part à proximité du seuil de la convection grâce à une approche faiblement non linéaire, d'autre part loin des conditions critiques grâce à une approche fortement non linéaire. Le fluide est rhéofluidifiant, ce qui correspond au comportement rhéologique le plus fréquemment rencontré, et est décrit par le modèle de Carreau. À proximité du seuil, on considère deux situations : la première correspond au cas où les plaques ont une conductivité finie, la seconde à celui d'un fluide thermodépendant. Dans chaque cas, l'influence du caractère rhéofluidifiant sur la nature du motif émergeant à la bifurcation primaire et sur les instabilités secondaires est mise en évidence. Pour étudier les motifs de convection loin des conditions critiques, on a recours à une procédure de continuation permettant de déterminer de proche en proche les caractéristiques de l'écoulement comme les champs de vitesse ou de température ainsi que le nombre de Nusselt. / In the Rayleigh-Bénard configuration, we consider a thin layer of fluid confined between two horizontal slabs which is heated from below and cooled from above. This layer undergoes an instability if the thermal gradient is strong enough: a transition from the conductive state to the convective state and called _ primary bifurcation _occurs. Moreover, it happens in an ordered way: we can notice the emergence of various convection patterns such as rolls, squares or hexagons. In their turn, these patterns undergo _ secondary instabilities _ that limit the range of stable wavenumbers. These instabilities are studied theoretically _firstly near the threshold thanks to a weakly nonlinear approach, and secondly far from critical conditions thanks to a strongly nonlinear approach. We consider a shear thinning fluid, the most common rheological behavior, which is described by the Carreau model. Near the threshold, two situations are considered: the first corresponds to finite conductivity plates, the second corresponds to a thermodependent fluid. In each case, the influence of the shear thinning effect on the nature of the pattern emerging at the primary bifurcation and on secondary instabilities is highlighted. To study the convection patterns far from the critical conditions, a continuation procedure is used to determine, step-by-step, the characteristics of the flow, such as the velocity or temperature fields and the Nusselt number.

Made available in DSpace on 2014-06-11T19:26:56Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-02-29Bitstream added on 2014-06-13T20:55:43Z : No. of bitstreams: 1 arakawa_vat_me_sjrp.pdf: 795168 bytes, checksum: 1ce40af6d71942f94c4c2bb678ce986f (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Nesse trabalho são apresentados alguns resultados importantes sobre bifurcações de codimensão dois de campos de vetores. O resultado principal dessa dissertação e o teorema que d a o diagrama de bifurcação e os retratos de fase da Bifurcação de Bogdanov-Takens. Para a demonstracão são usadas algumas técnicas basicas de Sistemas Dinâmicos e Teoria das Singularidades, tais como Integrais Abelianas, desdobramentos de Sistemas Hamiltonianos, desdobramentos versais, Teorema de Preparação de Malgrange, entre outros. Outra importante bifurcação clássica apresentada e a Bifurca cão do tipo Hopf-Zero, quando a matriz Jacobiana possui um autovalor simples nulo e um par de autovalores imagin arios puros. Foram usadas algumas hipóteses que garantem propriedades de simetria do sistema, dentre elas, assumiuse que o sistema era revers vel. Assim como na Bifurcação de Bogdanov-Takens, foram apresentados o diagrama de bifurcao e os retratos de fase da Bifurcação Hopf-zero bifurcação reversível. As técnicas usadas para esse estudo foram a forma normal de Belitskii e o método do Blow-up polar. / In this work is presented some important results about codimension two bifurcations of vector elds. The main result of this work is the theorem that gives the local bifurcation diagram and the phase portraits of the Bogdanov-Takens bifurcation. In order to give the proof, some classic tools in Dynamical System and Singularities Theory are used, such as Abelian Integral, versal deformation, Hamiltonian Systems, Malgrange Preparation Theorem, etc. Another classic bifurcation phenomena, known as the Hopf-Zero bifurcation, when the Jacobian matrix has a simple zero and a pair of purely imaginary eigenvalues, is presented. In here, is added the hypothesis that the system is reversible, which gives some symmetry in the problem. Like in Bogdanov-Takens bifurcation, the bifurcation diagram and the local phase portraits of the reversible Hopf-zero bifurcation were presented. The main techniques used are the Belitskii theory to nd a normal forms and the polar Blow-up method.

published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

Dynamical systems theory and bifurcation are used to analyze some simple models of nutrient limited phytoplankton growth. The models are restricted to batch culture type conditions allowing the use of a mass balance constraint. Two popular models from the literature, the Michaelis-Menton-Monod or M³ model, and the Droop internal nutrient model are analyzed and found to yield unreasonable predictions for certain ambient environmental conditions. The M³ model predicts that the population size becomes unbounded at equilibrium for certain values of the parameters. The Droop model predicts that the amount of nutrient left over during a nutrient uptake experiment would be very small, regardless of how large the initial external nutrient concentration is. Numerical comparisons of data with the predictions from both models demonstrate that the conditions for unreasonable behavior could occur both in cultures and in natural aquatic ecosystems. In the predicted nutrient concentration at uptake equilibrium is several orders of magnitude off. Two specific enzyme mechanisms for nutrient transport are proposed as alternatives to current models. The models differ in the assumptions made about how the backflow reaction with the enzymes responsible for transport proceeds. A nutrient uptake equation for each model is derived directly from the enzyme kinetics, while the equation for growth in population size is taken from the Droop model. The dynamics of both models are analyzed, treating the nutrient uptake equations with the singular perturbation assumption. The simple model predicts that the external nutrient concentration at uptake equilibrium should be a constant percentage of the internal concentration, while in the inhibition uptake model, the population size could exhibit relaxation type oscillations during the batch culture steady state. Qualitative evidence supporting both models is discussed. Applications of these models to water quality simulation and implications for theoretical ecology are discussed.