An important phenomenon of systems driven far-from-equilibrium is spatiotemporal chaos where the dynamics are aperiodic in both time and space. We explored this numerically for three systems: the Lorenz-96 model, the Swift-Hohenberg equation, and Rayleigh-Bénard convection. The Lorenz-96 model is a continuous in time and discrete in space phenomenological model that captures important features of atmosphere dynamics. We computed the fractal dimension as a function of system size and external forcing to estimate characteristic length and time scales describing the chaotic dynamics. We found extensive chaos with significant deviations from extensivity for small changes in system size and also the power-law growth of the dimension with increasing forcing. The Swift-Hohenberg equation is a partial differential equation for a scalar field, which has been widely used as a model for the study of pattern formation. We found that the magnitude of the mean flow in this model must be sufficiently large for spiral defect chaos to occur. We also explored the spatiotemporal chaos in experimentally accessible Rayleigh-Bénard convection using large-scale numerical simulations of the Boussinesq equations and the corresponding tangent space equations. We performed a careful study analyzing the impact of variations in the domain size, Rayleigh number, and Prandtl number on the system dynamics and fractal dimension. In addition, we quantified the dynamics of the spectrum of Lyapunov exponents and the leading order Lyapunov vector in an effort to connect directly with the dynamics of the flow field patterns. Further, we numerically studied the synchronization of chaos in convective flows by imposing time-dependent boundary conditions from a principal domain onto an initially quiescent target domain. We identified a synchronization length scale to quantify the size of a chaotic element using only information from the pattern dynamics. We also explored the relationship of this length scale with the pattern wavelength. Finally, we analyzed bioconvection which occurs as the result of the collective behavior of a suspension of swimming microorganisms. We developed a series of simulations to capture the gyrotactic pattern formation of the swimming algae. The results can be compared with the corresponding trend of pattern instabilities observed in the experimental studies. / Ph. D.

La plupart du temps, les bactéries vivent au sein de biofilms : un tissu biologique accroché sur des surfaces (molles ou solides), qui est composé de bactéries et de matrice extracellulaire. Lors de cette thèse nous avons étudié les mécanismes qui contrôlent la formation d’un biofilm à l’interface eau-air par Bacillus subtilis (BS). D’abord, nous avons observé l’évolution phénotypique de BS au cours du développement de sa population en milieu liquide, dans des conditions de culture standard (pas de biofilm in fine). Nous avons constaté que la population exhibe différents types cellulaires (phénotypes) au cours du temps. Puis, afin d’observer les étapes de la formation d’un biofilm, nous avons créé une expérience qui permet de suivre l’évolution macroscopique de la concentration des bactéries et sa répartition spatiale au sein du milieu de culture. Nous constatons qu’une accumulation de bactéries se forme en dessous de l’interface eau-air avant même l’apparition d’un biofilms. Cette accumulation est concomitante avec de la convection dans le fluide (bioconvection). Le biofilm apparait lors de la phase de croissance de la population en bactérie pour une concentration moyenne dans le milieu de culture de l’ordre de 10¹³ bactéries/m³. Ensuite, nous avons formulé un modèle continu qui renseigne sur l’évolution de l’environnement des bactéries. Ce modèle reproduit la bioconvection observée dans les expériences et révèle son effet sur la concentration en dioxygène dissous dans la culture. Enfin, nous avons construit un modèle hybride continu-discret qui décrit la transition de bactéries déconnectées (nomades) vers des bactéries connectées formant un biofilm solide (sédentaires). Chaque bactérie est considérée comme une particule individuelle. Le modèle tient compte des forces de contact, ainsi que les forces élastiques qui peuvent s’établir entre les bactéries lorsqu’elles sont liées par de la matrice. Un nombre minimal d’aptitudes biologiques a été utilisé pour modéliser les bactéries : la division cellulaire qui leur permet de coloniser le milieu de culture, la motilité et l’aérotactisme qui explique leur migration vers la surface liquide, le quorum sensing (QS) et la différenciation cellulaire qui leur permet de passer du phénotype nomade (motile) au phénotype sédentaire (producteur de matrice). L’environnement en dioxygène des bactéries et les propriétés hydrodynamiques du milieu sont décrits par des champs continus. Le modèle reproduit toutes les étapes de la formation d'un biofilm observées dans nos expériences et confirme la nécessité de certaines aptitudes biologiques. Il montre que le seuil de QS joue un rôle majeur dans la morphologie du biofilm et sa cinétique de formation. En revanche, le taux de consommation de dioxygène par les bactéries ne semble pas avoir de rôle important. Enfin, nous avons établi que la bioconvection agit comme un retardateur de la formation du biofilm. / Most of the time, the bacteria live inside the biofilm: the biological tissue that is attached to the surface (soft or solid), is made of the bacteria and of extracellular matrix. According to this thesis we study the mechanics that control the formation of a biofilm at the interface water-air by Bacillus subtilis (BS). First, we absorbed the phenotype evolution of the BS during the development of its population in liquid medium, under the conditions of a standard culture (no of biofilm in fine). We noticed that the population exhibits different cellular types (phenotypes) during this time. Then, after absorbing the different stages of the development in the formation of a biofilm, we created an experience that allows us to follow the macroscopic evolution of the concentration of the bacteria and its special distribution in the middle of the culture. We found that an accumulation of the bacteria forms under the surface water-air, even before the appearance of a biofilm. This accumulation is concomitant with the conservation in the liquid (bioconvection). The biofilm appears during the growth phase of the bacterial population in an average concentration in the culture medium of about 10¹³ bacteria / m³. Then, we formed a continuous model that shows us the evolution of the environment of the bacteria. This model reproduced the bioconvection that was observed in the experiments and reveals its effect on the concentration of oxygen in the biological culture. Finally we built a hybrid continuous-discreet model that described the transition of the disconnected bacteria (nomads) through the connected bacteria that form a solid biofilm (sedentary). Each bacteria is considered as an individual particle. The model takes the contact forces under consideration, as well as the elastic forces that can settle between the bacteria when linked by the matrix. A minimum number of biological skills were used to form a model from the bacteria; the cellular division that allowed it to colonize the medium biological culture, the motility and the aerotaxi that explains its migration towards the liquid surface, the quorum sensing (QS) and the cellular differentiation that allows them to spend nomadic phenotype (motile) sedentary phenotype (producer of matrix). The dioxygen environment of the bacteria and its middle hydrodynamic properties are described by continuous fields. The model reproduces all the formation steps of an observed biofilm in our experiment and confirms the need of certain biological skills. It shows that the threshold of QS plays a major role in the morphology and biofilm formation kinetics. On the other hand, the rate of diocygen consumption by the bacteria does not seem to have any significant role. Finally, we established that the bioconvection reacts as a retardant in the biofilm formation.

The main aim of this work is to study the thermal conductivity of base fluid with mild inclusion of nanoparticles. We perform numerical study for transportation of Maxwell nanofluids with activation energy and Cattaneo–Christov flux over an extending sheet along with mass transpiration. Further, bioconvection of microorganisms may support avoiding the possible settling of nanoentities. We formulate the theoretical study as a nonlinear coupled boundary value problem involving partial derivatives. Then ordinary differential equations are obtained from the leading partial differential equations with the help of appropriate similarity transformations. We obtain numerical results by using the Runge–Kutta fourth-order method with shooting technique. The effects of various physical parameters such as mixed convection, buoyancy ratio, Raleigh number, Lewis number, Prandtl number, magnetic parameter, mass transpiration on bulk flow, temperature, concentration, and distributions of microorganisms are presented in graphical form. Also, the skin friction coefficient, Nusselt number, Sherwood number, and motile density number are calculated and presented in the form of tables. The validation of numerical procedure is confirmed through its comparison with the existing results. The computation is carried out for suitable inputs of the controlling parameters.