Considere um meio caracterizado por $N$ pontos cujas coordenadas são geradas aleatoriamente de maneira uniforme nas arestas unitárias de um hipercubo $d$-dimensional. Um caminhante parte de cada ponto deste meio desordenado e se movimenta obedecendo à regra determinista de ir para o ponto mais próximo que não tenha sido visitado nos últimos $mu$ passos. Este processo foi denominado de caminhada determinista do turista. Cada trajetória gerada por esta dinâmica possui uma parte inicial não-periódica de $t$ passos (transiente) e uma parte final periódica de $p$ passos (atrator). As probabilidades de vizinhança são expressas através da fórmula de Cox, que é parametrizada pela função beta incompleta normalizada $I_d = I_{1/4}[1/2,(d+1)/2]$. Enfati-zamos aqui que a distribuição relevante é $S_{mu,d}^{(N)}(t,p)$, a distribuição conjunta de $t$ e $p$, que tem como casos particulares as distribuições marginais, previamente estudadas. O objetivo deste estudo é obter analiticamente estas distribuições para a caminhada determinista do turista sem memória no espaço euclideano, no modelo de distâncias aleatórias (que corresponde ao limite $d ightarrow infty$) e no modelo de mapeamento aleatório (que é um caso limite das redes de Kauffman). As distribuições analíticas obtidas foram validadas através de experimentos numéricos. A distribuição conjunta de tempos de transiente e período de atratores, no limite termodinâmico para uma dimensionalidade arbitrária vale: $S_{1,d}^{(infty)}(t,p) = [Gamma(1+I_d^{-1}) cdot (t+I_d^{-1})/Gamma(t+p+I_d^{-1})] cdot delta_{p,2}$, onde $t=0,1,2,ldots,infty$; $Gamma(z)$ é a função gama e $delta_{i,j}$ é o delta de Kronecker. A caminhada determinista do turista sem memória no modelo de mapeamento aleatório produz uma distribuição de períodos não-trivial ($S_{0,rm}^{(N)}(p) propto p^{-1}$), que é obtida de $S_{0,rm}^{(N)}(t,p) = Gamma(N)/{Gamma[N+1-(t+p)]N^{t+p}}$, onde enfatizamos que o número de pontos explorados $n_e=t+p$ é a grandeza fundamental nos problemas considerados. / Consider a medium characterized by $N$ points whose coordinates are randomly generated by a uniform distribution along the unitary edges of a $d$-dimensional hypercube. A walker leaves from each point of this disordered medium and moves according to the deterministic rule to go the nearest point which has not been visited in the preceding $mu$ steps. This process has been called the deterministic tourist walk. Each trajectory generated by this dynamics has an initial non-periodic part of $t$ steps (transient) and a final periodic part of $p$ steps (attractor). The neighborhood probabilities are given by the Cox formula, which is parameterized by the normalized incomplete beta function $I_d = I_{1/4}[1/2,(d+1)/2]$. Here we stress that the relevant distribution is the joint $t$ and $p$ distribution $S_{mu,d}^{(N)}(t,p)$, which has as particular cases, the marginal distributions previously studied. The objective of this study is to obtain analytically these distributions for the memoryless deterministic tourist walk in the euclidean space, random link model (which corresponds to $d ightarrow infty$ limit) and random map model (which is a limiting case of the Kauffman model). The obtained distributions have been validated by numerical experiments. The joint transient time and attractor period distribution in the thermodynamic limit for an arbitrary dimensionality is: $S_{1,d}^{(infty)}(t,p) = [Gamma(1+I_d^{-1}) cdot (t+I_d^{-1})/Gamma(t+p+I_d^{-1})] cdot delta_{p,2}$, where $t=0,1,2,ldots,infty$; $Gamma(z)$ is the gamma function and $delta_{i,j}$ is the Kronecker's delta. The memoryless deterministic tourist walk in the random map leads to a non-trivial cycle distribution ($S_{0,rm}^{(N)}(p) propto p^{-1}$), which is obtained from $S_{0,rm}^{(N)}(t,p) = Gamma(N)/{Gamma[N+1-(t+p)]N^{t+p}}$, where we stress that the number of explored points $n_e=t+p$ is the fundamental quantity in the considered problems.

Considere um meio desordenado constituído por $N$ pontos cujas coordenadas são geradas aleatoriamente de maneira uniforme e independente nas arestas unitárias de um hipercubo $d$-dimensional. As probabilidades de vizinhança entre os pares de pontos deste meio são expressas através da fórmula de Cox. Um caminhante parte de um dado ponto deste meio desordenado e se movimenta obedecendo à regra determinista de ir para o ponto mais próximo que não tenha sido visitado nos últimos $\\mu$ passos. Este processo foi denominado de caminhada determinista do turista. Cada trajetória gerada por esta dinâmica possui uma parte inicial não-periódica de $t$ passos (transiente) e uma parte final periódica de $p$ passos (atrator). Neste trabalho, obtemos analiticamente algumas distribuições estatísticas para a caminhada determinista do turista com memória $\\mu$ arbitrária em sistemas unidimensionais e com memória $\\mu=2$ no modelo Random Link (que corresponde ao limite $d ightarrow 1$). Estes resultados nos permitiram compreender o papel da memória no comportamento exploratório do turista e explicar a equivalência não-trivial entre o modelo Random Link e o modelo Random Map (que é um caso limite das redes de Kauffman). Enfatizamos que o número de pontos explorados pelo turista é a grandeza fundamental nos problemas considerados. As distribuições analíticas obtidas foram validadas através de experimentos numéricos. Também obtivemos uma dedução alternativa para a fórmula de Cox, apresentando os resultados finais em termos de distribuições estatísticas elementares. / Consider a medium characterized by $N$ points whose coordinates are randomly and independently generated by a uniform distribution along the unitary edges of a $d$-dimensional hypercube. The neighborhood probabilities between any pair of points in this medium are given by the Cox formula. A walker leaves from each point of this disordered medium and moves according to the deterministic rule to go the nearest point which has not been visited in the preceding $\\mu$ steps. This process has been called the deterministic tourist walk. Each trajectory generated by this dynamics has an initial non-periodic part of $t$ steps (transient) and a final periodic part of $p$ steps (attractor). In this work, we obtain analytically some statistical distributions for the deterministic tourist walk with arbitrary memory $\\mu$ in one-dimensional systems and with memory $\\mu=2$ in the random link model (which corresponds to $d ightarrow 1$ limit). These results enable us to understand the main role played by the memory on the tourist\'s exploratory behavior and explain the non-trivial equivalence between the random link model and the random map model (which is a limiting case of the Kauffman model). We stress that the number of explored points is the fundamental quantity in the considered problems. The obtained distributions have been validated by numerical experiments. We also obtain an alternative derivation for the Cox formula, writing the final results in terms of known statistical distributions.

Cette thèse porte sur la compréhension et le contrôle des interactions dynamiques entre les mécanismes physiques et biologiques en considérant un procédé alternatif de séparation membranaire pour les bioprocédés industriels. L’objectif premier est un apport de connaissances scientifiques liées à la maîtrise de la bioréaction en considérant l'hydrodynamique complexe et les verrous rétention-perméation. Une technologie de filtration dynamique, appelée Rotating and Vibrating Filtration (RVF), a été spécifiquement étudiée. Elle se compose de cellules de filtration en série comprenant deux membranes circulaires planes fixées sur des supports poreux au voisinage d'un agitateur à trois pales planes attachées à un arbre central. Ce dispositif mécanique simple fonctionne en continu et génère une contrainte de cisaillement élevée ainsi qu'une perturbation hydrodynamique dans un entrefer étroit (pale-membrane). Les verrous scientifiques et techniques qui motivent ce travail, sont la caractérisation et la quantification (i) des champs de vitesse locaux et instantanés, (2) des contraintes pariétales de cisaillement à la surface de la membrane et (3) l'impact mécanique sur les cellules microbiennes.Dans ce but, des expériences et des simulations numériques ont été réalisées pour étudier l'hydrodynamique à des échelles globales et locales, en régimes laminaire et turbulent avec des fluides newtoniens dans des environnements biotique et abiotique. Pour l'approche globale, la distribution des temps de séjour (RTD) et le bilan thermique ont été réalisés et comparés aux précédentes études globales (courbes de consommation de puissance et de frottement). Une étude analytique des fonctions de distribution a été effectuée et les moments statistiques ont été calculés et discutés. Une analyse systémique a été utilisée pour décrire les comportements hydrodynamiques du module RVF. En combinant la simulation des écoulements (CFD) et les observations (RTD), les conditions et les zones de dysfonctionnement des cellules de filtration sont éclairées. Pour l'approche locale, la vélocimétrie laser (PIV) a été réalisée dans les plans horizontaux et verticaux et comparée à la simulation numérique (CFD). Une étude préliminaire basée sur une synchronisation entre la prise d’image et la position de l’agitateur (résolution angulaire) a permis d’accéder aux champs de vitesse moyens. Une campagne de mesure PIV a été réalisée sans synchronisation afin d’appliquer une décomposition orthogonale aux valeurs propres (POD) pour 'identifier les composantes moyennes, organisées et turbulentes des champs de vitesse (énergie cinétique). Pour l'application aux bioprocédés, un travail exploratoire a caractérisé l'effet de la filtration dynamique sur des cellules procaryotes (E. coli) en quantifiant l'intégrité cellulaire ou leur dégradation en fonction du temps et de la vitesse de rotation. / This thesis focuses on the understanding and the control of dynamic interactions between physical and biological mechanisms considering an alternative membrane separation into industrial bioprocess. It aims to carry scientific knowledge related to the control of bioreaction considering complex hydrodynamics and retention-permeation locks specific to membrane separation. A dynamic filtration technology, called Rotating and Vibrating Filtration (RVF), was investigated. It consists of filtration cells in series including two flat disc membranes fixed onto porous substrates in the vicinity of a three-blade impeller attached to a central shaft. This simple mechanical device runs continuously and generates a high shear stress as well as a hydrodynamic perturbation in the narrow membrane-blade gap. Several scientific and technical locks motivating this work are to characterize and to quantify (i) the velocity fields locally and instantaneously, (2) the shear stresses at membrane surface and (3) the mechanical impact on microbial cells.To this end, experiments and numerical simulations have been performed to investigate the hydrodynamics at global and local scales under laminar and turbulent regimes with Newtonian fluids under biotic and abiotic environment. For global approach, investigation of Residence Time Distribution (RTD) and thermal balance was carried out and compared to the previous global study (power consumption and friction curves). Analytical study of distribution functions was conducted and statistical moments were calculated and discussed. A systemic analysis was used to describe the hydrodynamic behaviors of the RVF module. Combining Computational Fluid Dynamics (CFD) and RTD observations, it leads to demonstrate dysfunctioning conditions and area. For the local approach, Particle Image Velocimetry (PIV) was be carried out in both horizontal and vertical planes and compared to CFD simulation. PIV preliminary study was conducted with a trigger strategy to access through angle-resolved measurements to an averaged velocity field. PIV further study were performed with a non-trigger strategy and applied to Proper Orthogonal Decomposition (POD) analysis in order to identify the coherent structure of the flow by decomposing the organized and turbulent fluctuations. For the bioprocess application, an exploratory work characterized the effect of Dynamic Filtration on prokaryote cell population (Escherichia coli) by quantifying cell integrity or damage as a function of time and rotation speed during filtration process in turbulent regime.

In my doctoral thesis I have investigated earthquake swarms from two com- pletely different tectonic areas, West Bohemia/Vogtland and Southwest Iceland, with the aim of gaining a deeper insight into the nature of earthquake swarms in diverse tectonic environments. I analysed swarm-like activities from West Bo- hemia and Southwest Iceland from the perspective of statistical characteristics (magnitude-frequency distribution, interevent time distribution), seismic moment release, and space-time distribution of events. I found that the ratio of small to large events and the event rates are similar for all the activities in both areas, while the rate of the seismic moment release is significantly higher for the South- west Icelandic swarms. Seismic moment released step by step is characterised for the West Bohemia swarms, whereas seismic moment released in one dominant short-term phase is typical of Southwest Icelandic earthquake swarms. All the West Bohemian swarms took place in a bounded focal zone Nový Kostel that is fairly complex, consisting of several fault segments. The Southwest Icelandic swarms are distributed at much larger area along the Mid Atlantic Ridge up to its branching in the Hengill triple junction, the individual swarms clearly reflect a tectonic structure of respective focal areas. I have...

Des procédés innovants basés sur l’extrusion à haute vitesse et l’irradiation sous rayonnement γ, ont été étudiés en vue d’améliorer la compatibilisation de deux polyoléfines non miscibles : le polypropylène PP et le polyéthylène PE. Dans un premier temps, l’étude de la distribution des temps de séjour de polypropylènes dans l’extrudeuse à haute vitesse a été réalisée. L’impact des conditions opératoires (débit et vitesse de rotation des vis) ainsi que l’impact du profil de vis et de la viscosité du polypropylène d’étude ont été mis en avant. Certains résultats expérimentaux sont souvent en accord avec ceux du logiciel de simulation d’extrusion bi-vis Ludovic, bien qu’il puisse y avoir des écarts pour les hautes vitesses de rotation des vis. Dans un deuxième temps, une fois l’écoulement caractérisé, nous avons réalisé des mélanges PP/PE, les paramètres qui ont varié sont la quantité d’énergie apportée durant le mélange (vitesse de rotation des vis) ainsi que la présence ou non de copolymère préformé et le type d’atmosphère utilisée durant l’extrusion. Faire varier le taux de cisaillement ne permet pas la modulation des propriétés finales du mélange surtout lorsque l’on extrude sous atmosphère inerte. L’utilisation de copolymère préformé, de type éthylène-octène, permet d’améliorer considérablement les propriétés de notre mélange en créant une interphase "cœur-couronne" entre la matrice PP, le compatibilisant et la phase dispersée PE. Pour terminer, une étape d’irradiation γ a été ajoutée au procédé de mise en œuvre classique de nos mélanges. En première partie de cette étude, la simulation de spectres RPE a permis d’identifier et quantifier les différentes espèces radicalaires créées. Dans la deuxième partie, l’influence de la place de la séquence d’irradiation a été étudiée : avant extrusion, entre extrusion et injection, après injection et avant recuit. Les meilleures améliorations ont été obtenues lorsque l’irradiation est suivie d’un traitement thermique. En conclusion, il est possible d’améliorer la compatibilité d’un mélange PP/PE en jouant essentiellement sur l’ordre des étapes de production sans avoir à modifier la formulation de ce dernier. / Innovative processes, based on high shear twin screw extrusion and γ-irradiation, have been used to increase the compatibility of two immiscible polyolefins: polypropylene PP and polyethylene PE. In a first part, the residence time distribution of polypropylenes in the twin screw extruder (TSE) has been investigated. The impact of the processing conditions (throughput and screw rotation speed), the screw profile and the polypropylene viscosity were underlined. Some of the experimental results are often in good agreement with those predicted by simulation software of twin screw extrusion (Ludovic), except for some experiments at high screw rotation rates. In a second part, once polymer flow was characterised in the TSE, we realized PP/PE blends. The impact of the mechanical energy (screw rotation speed), the presence or absence of copolymers and the nature of the extrusion atmosphere were analysed. Using high shear rate does not allow modulating the final properties of the blends particularly once inert atmosphere is used. The use of ethylene-octene copolymers increases significantly the final properties of the PP/PE blends by creating a “core-shell” morphology between the PP matrix, the copolymer and the PE dispersed phase. To finish, a γ-irradiation process step has been added to the classical processing of PP/PE blends. In a first part of this study, the simulations of ESR spectra have permitted to identify and quantify the different radicals created. In a second part, the sequence order of the γ-irradiation has been investigated: before extrusion, between extrusion and injection, and after injection followed by a thermal treatment. The best results were obtained once γ-irradiation is followed by a heat treatment. As a conclusion, the compatibility of immiscible polyolefins can be improved only by changing the order of the different processing steps without changing the formulation.