Relationships between structure and dynamics have been well studied in molecular fluids, both in computer simulations and in experiments. However, the development of simple structure-dynamics relationships would also be useful in understanding colloidal fluids. Colloidal fluids display differentiated component dynamics, are made of polydisperse particles, have soft interactions and have a separation of length and time scales. In this dissertation work, we have used computer simulations to generalize some structure-dynamics scaling laws, originally formulated for molecular fluids, in a way that successfully accounts for these important aspects of colloidal suspensions. To begin, we examine a two-component mixture of ultrasoft Gaussian-core particles through molecular dynamics simulations. This fluid shows an anomalous dynamic crossover where the larger particles become more diffusive than the smaller particles. However, this dynamic crossover is accompanied by a corresponding structural crossover for a component-specific structural order metric. In the light of this structural order metric, the fluid is non-anomalous with respect to the relationship between static structuring and diffusivity. Next, we show that accounting for the many-component nature of even modestly polydisperse fluids is important for accurately characterizing their structure-dynamics relationships. We demonstrate this for colloids with short-range attractions through new Monte Carlo simulation techniques and through theoretical calculations carried out in the dilute limit. From here, we present a new generalized framework to non-dimensionalize diffusivity so that it will have an approximately one-to-one relationship with excess entropy. This method involves rescaling diffusivity with dilute-limit analyses that can be analytically and systematically executed. We tested this framework through a combination of molecular dynamics simulations, Brownian dynamics simulations and Monte Carlo simulations. The results of the simulations demonstrate that this framework can account for particle size asymmetry, particle additivity, interaction strength and some solvent effects. Finally, we present a new, simple equation that relates non-dimensionalized forms of diffusivity from molecular dynamics and Brownian dynamics simulations. This simple relationship is tested for inverse power law fluids, as well as a suite of ultrasoft fluids that show structural and dynamic anomalies. / text

A multivariate generalization of mutual information, multi-information, is defined in the thermodynamic limit. The definition takes phase coexistence into account by taking the infimum over the translation-invariant Gibbs measures of an interaction potential. It is shown that this infimum is attained in a pure state. An explicit formula can be found for the Ising square lattice, where the quantity is proved to be maximized at the phase-transition point. By this, phase coexis-tence is linked to high model complexity in a rigorous way.

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Many complexity measures are defined as the size of a minimal representation in a specific model class. One such complexity measure, which is important because it is widely applied, is statistical complexity. It is defined for discrete-time, stationary stochastic processes within a theory called computational mechanics. Here, a mathematically rigorous, more general version of this theory is presented, and abstract properties of statistical complexity as a function on the space of processes are investigated. In particular, weak-* lower semi-continuity and concavity are shown, and it is argued that these properties should be shared by all sensible complexity measures. Furthermore, a formula for the ergodic decomposition is obtained. The same results are also proven for two other complexity measures that are defined by different model classes, namely process dimension and generative complexity. These two quantities, and also the information theoretic complexity measure called excess entropy, are related to statistical complexity, and this relation is discussed here. It is also shown that computational mechanics can be reformulated in terms of Frank Knight's prediction process, which is of both conceptual and technical interest. In particular, it allows for a unified treatment of different processes and facilitates topological considerations. Continuity of the Markov transition kernel of a discrete version of the prediction process is obtained as a new result.

Ce travail de thèse concerne les verres bioactifs purs et dopés pour des applications en tant que biomatériaux en site osseux. Ils sont synthétisés par fusion dans le système SiO₂-CaO-Na₂O-P₂O₅. Quatre éléments métalliques (Zn, Ti, Cu et Ag), présentant des caractéristiques chimiques et physiologiques intéressantes, ont été introduits dans la matrice vitreuse. Leur réactivité chimique et leur cytotoxicité ont été évalués lors de tests in vitro. L'introduction de ces éléments métalliques influe sur les caractéristiques thermiques des verres ainsi que sur la dissolution de la matrice vitreuse, la cinétique et la cristallisation de la couche d'hydroxyapatite. Une bonne prolifération cellulaire a été mise en évidence. En parallèle, une méthode de synthèse d'une vitrocéramique, présentant une microporosité, a été développée par réaction entre TiN et ZnO. Des essais in vitro ont montré un caractère bioactif après 60 jours d'immersion et une absence de cytotoxicité. Ce biomatériau a ensuite été implanté au niveau de la diaphyse fémorale de lapins. Différentes études structurales ont montré la résorption progressive du biomatériau jusqu'à 6 mois d'implantation. Des scaffolds chitosan / verre bioactif ont également été synthétisés et obtenus par lyophilisation. Ils ont été étudiés lors d'essais in vitro. Ils ont servi de support pour la vectorisation de gentamicine. Les résultats obtenus montrent que les teneurs en chitosan et en verre bioactif ont une influence sur la cristallisation de l'hydroxyapatite et le relargage du médicament. Les modèles mathématiques établis montrent que le temps de relaxation des scaffolds dépend de la concentration de départ en gentamicine. / This research work focuses on the pure and doped bioactive glasses for use as bone biomaterial. They are synthesized by the melting method in the system SiO₂-CaO-Na₂O-P₂O₅. Four metallic elements, presenting interesting chemical and physiological properties, have been introduced in the amorphous matrix. Their chemical reactivity and their cytotoxicity have been evaluated during in vitro assays in simulated body fluid and cell culture media. The introduction of these metallic elements influences their thermal characteristics, the glass matrix dissolution, the kinetic and the crystallization of the hydroxyapatite layer. A good cells proliferation have been showed. In parallel, a method of synthesis of a glass-ceramic, having a microporosity, have been developed by reaction between TiN and ZnO. In vitro assays have showed a bioactive character after 60 days of immersion and a non-cytotoxicity. This biomaterial was implanted in the femoral dyaphisis of rabbits. Different structural studies have showed the gradual resorption of the biomaterial up to 6 months of implantation. Finally, scaffolds chitosan/bioactive glass, obtained by freeze-drying, have also been studied during in vitro assays. They were used as support for the vectorization of gentamicin. The obtained results show that the content of chitosan and bioactive glass have an impact on the crystallization of hydroxyapatite et the release of drug. Mathematic models show that the relaxation time depend on the starting concentration of gentamicin.

Many complexity measures are defined as the size of a minimal representation in a specific model class. One such complexity measure, which is important because it is widely applied, is statistical complexity. It is defined for discrete-time, stationary stochastic processes within a theory called computational mechanics. Here, a mathematically rigorous, more general version of this theory is presented, and abstract properties of statistical complexity as a function on the space of processes are investigated. In particular, weak-* lower semi-continuity and concavity are shown, and it is argued that these properties should be shared by all sensible complexity measures. Furthermore, a formula for the ergodic decomposition is obtained. The same results are also proven for two other complexity measures that are defined by different model classes, namely process dimension and generative complexity. These two quantities, and also the information theoretic complexity measure called excess entropy, are related to statistical complexity, and this relation is discussed here. It is also shown that computational mechanics can be reformulated in terms of Frank Knight''s prediction process, which is of both conceptual and technical interest. In particular, it allows for a unified treatment of different processes and facilitates topological considerations. Continuity of the Markov transition kernel of a discrete version of the prediction process is obtained as a new result.