Defect dynamics in viscous fingering

We study the dynamics of Staffman-Taylor fingering in terms of topological defects of the flow field. The defects are created and/or annihilated at the interface. The route towards the single-finger steady state is characterized by a detailed mechanism for defect annihilation. For small viscosity contrast this mechanism is impeded, and creation of new defects leads the system away from a single-finger solution. Strong evidence for a drastic reduction of the basin of attraction of the Saffman-Taylor finger is presented.

Evaporation and coarsening dynamics with open boundaries

We present a study of the evaporation dynamics of a substance undergoing a coarsening process. The system is modeled by the Cahn-Hilliard equation with absorbing boundaries. We have found that the dynamics, although of a diffusive nature, is much slower than the usual one without coarsening. Analytical and simulation results are in reasonable agreement.

Dynamics of the two-dimensional gonihedric spin model

In this paper, we study dynamical aspects of the two-dimensional (2D) gonihedric spin model using both numerical and analytical methods. This spin model has vanishing microscopic surface tension and it actually describes an ensemble of loops living on a 2D surface. The self-avoidance of loops is parametrized by a parameter ¿. The ¿=0 model can be mapped to one of the six-vertex models discussed by Baxter, and it does not have critical behavior. We have found that allowing for ¿¿0 does not lead to critical behavior either. Finite-size effects are rather severe, and in order to understand these effects, a finite-volume calculation for non-self-avoiding loops is presented. This model, like his 3D counterpart, exhibits very slow dynamics, but a careful analysis of dynamical observables reveals nonglassy evolution (unlike its 3D counterpart). We find, also in this ¿=0 case, the law that governs the long-time, low-temperature evolution of the system, through a dual description in terms of defects. A power, rather than logarithmic, law for the approach to equilibrium has been found.

Fuzzy logic applied to the modeling of water dynamics in an Oxisol in northeastern Brazil

Modeling of water movement in non-saturated soil usually requires a large number of parameters and variables, such as initial soil water content, saturated water content and saturated hydraulic conductivity, which can be assessed relatively easily. Dimensional flow of water in the soil is usually modeled by a nonlinear partial differential equation, known as the Richards equation. Since this equation cannot be solved analytically in certain cases, one way to approach its solution is by numerical algorithms. The success of numerical models in describing the dynamics of water in the soil is closely related to the accuracy with which the water-physical parameters are determined. That has been a big challenge in the use of numerical models because these parameters are generally difficult to determine since they present great spatial variability in the soil. Therefore, it is necessary to develop and use methods that properly incorporate the uncertainties inherent to water displacement in soils. In this paper, a model based on fuzzy logic is used as an alternative to describe water flow in the vadose zone. This fuzzy model was developed to simulate the displacement of water in a non-vegetated crop soil during the period called the emergency phase. The principle of this model consists of a Mamdani fuzzy rule-based system in which the rules are based on the moisture content of adjacent soil layers. The performances of the results modeled by the fuzzy system were evaluated by the evolution of moisture profiles over time as compared to those obtained in the field. The results obtained through use of the fuzzy model provided satisfactory reproduction of soil moisture profiles.

Statistical dynamics of dislocation systems: The influence of dislocation-dislocation correlations.

During plastic deformation of crystalline materials, the collective dynamics of interacting dislocations gives rise to various patterning phenomena. A crucial and still open question is whether the long range dislocation-dislocation interactions which do not have an intrinsic range can lead to spatial patterns which may exhibit well-defined characteristic scales. It is demonstrated for a general model of two-dimensional dislocation systems that spontaneously emerging dislocation pair correlations introduce a length scale which is proportional to the mean dislocation spacing. General properties of the pair correlation functions are derived, and explicit calculations are performed for a simple special case, viz pair correlations in single-glide dislocation dynamics. It is shown that in this case the dislocation system exhibits a patterning instability leading to the formation of walls normal to the glide plane. The results are discussed in terms of their general implications for dislocation patterning.

Effect of management systems and cover crops on organic matter dynamics of soil under vegetables

Vegetable production in conservation tillage has increased in Brazil, with positive effects on the soil quality. Since management systems alter the quantity and quality of organic matter, this study evaluated the influence of different management systems and cover crops on the organic matter dynamics of a dystrophic Red Latosol under vegetables. The treatments consisted of the combination of three soil tillage systems: no-tillage (NT), reduced tillage (RT) and conventional tillage (CT) and of two cover crops: maize monoculture and maize-mucuna intercrop. Vegetables were grown in the winter and the cover crops in the summer for straw production. The experiment was arranged in a randomized block design with four replications. Soil samples were collected between the crop rows in three layers (0.0-0.05, 0.05-0.10, and 0.10-0.30 m) twice: in October, before planting cover crops for straw, and in July, during vegetable cultivation. The total organic carbon (TOC), microbial biomass carbon (MBC), oxidizable fractions, and the carbon fractions fulvic acid (C FA), humic acid (C HA) and humin (C HUM) were determined. The main changes in these properties occurred in the upper layers (0.0-0.05 and 0.05-0.10 m) where, in general, TOC levels were highest in NT with maize straw. The MBC levels were lowest in CT systems, indicating sensitivity to soil disturbance. Under mucuna, the levels of C HA were lower in RT than NT systems, while the C FA levels were lower in RT than CT. For vegetable production, the C HUM values were lowest in the 0.05-0.10 m layer under CT. With regard to the oxidizable fractions, the tillage systems differed only in the most labile C fractions, with higher levels in NT than CT in the 0.0-0.05 m layer in both summer and winter, with no differences between these systems in the other layers. The cabbage yield was not influenced by the soil management system, but benefited from the mulch production of the preceding maize-mucuna intercrop as cover plant.

Long-tailed trapping times and Lévy flights in a self-organized critical granular system

We present a continuous time random walk model for the scale-invariant transport found in a self-organized critical rice pile [K. Christensen et al., Phys. Rev. Lett. 77, 107 (1996)]. From our analytical results it is shown that the dynamics of the experiment can be explained in terms of Lvy flights for the grains and a long-tailed distribution of trapping times. Scaling relations for the exponents of these distributions are obtained. The predicted microscopic behavior is confirmed by means of a cellular automaton model.

Metastable liquid-liquid phase transition in a single-component system with only one crystal phase and no density anomaly

We investigate the phase behavior of a single-component system in three dimensions with spherically-symmetric, pairwise-additive, soft-core interactions with an attractive well at a long distance, a repulsive soft-core shoulder at an intermediate distance, and a hard-core repulsion at a short distance, similar to potentials used to describe liquid systems such as colloids, protein solutions, or liquid metals. We showed [Nature (London) 409, 692 (2001)] that, even with no evidence of the density anomaly, the phase diagram has two first-order fluid-fluid phase transitions, one ending in a gas¿low-density-liquid (LDL) critical point, and the other in a gas¿high-density-liquid (HDL) critical point, with a LDL-HDL phase transition at low temperatures. Here we use integral equation calculations to explore the three-parameter space of the soft-core potential and perform molecular dynamics simulations in the interesting region of parameters. For the equilibrium phase diagram, we analyze the structure of the crystal phase and find that, within the considered range of densities, the structure is independent of the density. Then, we analyze in detail the fluid metastable phases and, by explicit thermodynamic calculation in the supercooled phase, we show the absence of the density anomaly. We suggest that this absence is related to the presence of only one stable crystal structure.

Dynamics of Fréedericksz transition in a fluctuating magnetic field

Fréedericksz transition under twist deformation in a nematic layer is discussed when the magnetic field has a random component. A dynamical model which includes the thermal fluctuations of the system is presented. The randomness of the field produces a shift of the instability point. Beyond this instability point the time constant characteristic of the approach to the stationary stable state decreases because of the field fluctuations. The opposite happens for fields smaller than the critical one. The decay time of an unstable state, calculated as a mean first-passage time, is also decreased by the field fluctuations.

Evaporation and coarsening dynamics with open boundaries

We present a study of the evaporation dynamics of a substance undergoing a coarsening process. The system is modeled by the Cahn-Hilliard equation with absorbing boundaries. We have found that the dynamics, although of a diffusive nature, is much slower than the usual one without coarsening. Analytical and simulation results are in reasonable agreement.

Chemoconvection patterns in the Methylene-blue-glucose system: Weakly nonlinear analysis

The oxidation of solutions of glucose with methylene-blue as a catalyst in basic media can induce hydrodynamic overturning instabilities, termed chemoconvection in recognition of their similarity to convective instabilities. The phenomenon is due to gluconic acid, the marginally dense product of the reaction, which gradually builds an unstable density profile. Experiments indicate that dominant pattern wavenumbers initially increase before gradually decreasing or can even oscillate for long times. Here, we perform a weakly nonlinear analysis for an established model of the system with simple kinetics, and show that the resulting amplitude equation is analogous to that obtained in convection with insulating walls. We show that the amplitude description predicts that dominant pattern wavenumbers should decrease in the long term, but does not reproduce the aforementioned increasing wavenumber behavior in the initial stages of pattern development. We hypothesize that this is due to horizontally homogeneous steady states not being attained before pattern onset. We show that the behavior can be explained using a combination of pseudo-steady-state linear and steady-state weakly nonlinear theories. The results obtained are in qualitative agreement with the analysis of experiments.

Nonlinear chemoconvection in the Methylene-blue-glucose system

Interfacial hydrodynamic instabilities arise in a range of chemical systems. One mechanism for instability is the occurrence of unstable density gradients due to the accumulation of reaction products. In this paper we conduct two-dimensional nonlinear numerical simulations for a member of this class of system: the methylene-blue¿glucose reaction. The result of these reactions is the oxidation of glucose to a relatively, but marginally, dense product, gluconic acid, that accumulates at oxygen permeable interfaces, such as the surface open to the atmosphere. The reaction is catalyzed by methylene-blue. We show that simulations help to disassemble the mechanisms responsible for the onset of instability and evolution of patterns, and we demonstrate that some of the results are remarkably consistent with experiments. We probe the impact of the upper oxygen boundary condition, for fixed flux, fixed concentration, or mixed boundary conditions, and find significant qualitative differences in solution behavior; structures either attract or repel one another depending on the boundary condition imposed. We suggest that measurement of the form of the boundary condition is possible via observation of oxygen penetration, and improved product yields may be obtained via proper control of boundary conditions in an engineering setting. We also investigate the dependence on parameters such as the Rayleigh number and depth. Finally, we find that pseudo-steady linear and weakly nonlinear techniques described elsewhere are useful tools for predicting the behavior of instabilities beyond their formal range of validity, as good agreement is obtained with the simulations.

Simulation of interface dynamics across pore discontinuities

We study the dynamics of a water-oil meniscus moving from a smaller to a larger pore. The process is characterised by an abrupt change in the configuration, yielding a sudden energy release. A theoretic study for static conditions provides analytical solutions of the surface energy content of the system. Although the configuration after the sudden energy release is energetically more convenient, an energy barrier must be overcome before the process can happen spontaneously. The energy barrier depends on the system geometry and on the flow parameters. The analytical results are compared to numerical simulations that solve the full Navier-Stokes equation in the pore space and employ the Volume Of Fluid (VOF) method to track the evolution of the interface. First, the numerical simulations of a quasi-static process are validated by comparison with the analytical solutions for a static meniscus, then numerical simulations with varying injection velocity are used to investigate dynamic effects on the configuration change. During the sudden energy jump the system exhibits an oscillatory behaviour. Extension to more complex geometries might elucidate the mechanisms leading to a dynamic capillary pressure and to bifurcations in final distributions of fluid phases in porous

Information sharing and social network dynamics : a coevolutionary approach

The capacity to interact socially and share information underlies the success of many animal species, humans included. Researchers of many fields have emphasized the evo¬lutionary significance of how patterns of connections between individuals, or the social networks, and learning abilities affect the information obtained by animal societies. To date, studies have focused on the dynamics either of social networks, or of the spread of information. The present work aims to study them together. We make use of mathematical and computational models to study the dynamics of networks, where social learning and information sharing affect the structure of the population the individuals belong to. The number and strength of the relationships between individuals, in turn, impact the accessibility and the diffusion of the shared information. Moreover, we inves¬tigate how different strategies in the evaluation and choice of interacting partners impact the processes of knowledge acquisition and social structure rearrangement. First, we look at how different evaluations of social interactions affect the availability of the information and the network topology. We compare a first case, where individuals evaluate social exchanges by the amount of information that can be shared by the partner, with a second case, where they evaluate interactions by considering their partners' social status. We show that, even if both strategies take into account the knowledge endowments of the partners, they have very different effects on the system. In particular, we find that the first case generally enables individuals to accumulate higher amounts of information, thanks to the more efficient patterns of social connections they are able to build. Then, we study the effects that homophily, or the tendency to interact with similar partners, has on knowledge accumulation and social structure. We compare the case where individuals who know the same information are more likely to learn socially from each other, to the opposite case, where individuals who know different information are instead more likely to learn socially from each other. We find that it is not trivial to claim which strategy is better than the other. Depending on the possibility of forgetting information, the way new social partners can be chosen, and the population size, we delineate the conditions for which each strategy allows accumulating more information, or in a faster way For these conditions, we also discuss the topological characteristics of the resulting social structure, relating them to the information dynamics outcome. In conclusion, this work paves the road for modeling the joint dynamics of the spread of information among individuals and their social interactions. It also provides a formal framework to study jointly the effects of different strategies in the choice of partners on social structure, and how they favor the accumulation of knowledge in the population. - La capacité d'interagir socialement et de partager des informations est à la base de la réussite de nombreuses espèces animales, y compris les humains. Les chercheurs de nombreux domaines ont souligné l'importance évolutive de la façon dont les modes de connexions entre individus, ou réseaux sociaux et les capacités d'apprentissage affectent les informations obtenues par les sociétés animales. À ce jour, les études se sont concentrées sur la dynamique soit des réseaux sociaux, soit de la diffusion de l'information. Le présent travail a pour but de les étudier ensemble. Nous utilisons des modèles mathématiques et informatiques pour étudier la dynamique des réseaux, où l'apprentissage social et le partage d'information affectent la structure de la population à laquelle les individus appartiennent. Le nombre et la solidité des relations entre les individus ont à leurs tours un impact sur l'accessibilité et la diffusion de l'informa¬tion partagée. Par ailleurs, nous étudions comment les différentes stratégies d'évaluation et de choix des partenaires d'interaction ont une incidence sur les processus d'acquisition des connaissances ainsi que le réarrangement de la structure sociale. Tout d'abord, nous examinons comment des évaluations différentes des interactions sociales influent sur la disponibilité de l'information ainsi que sur la topologie du réseau. Nous comparons un premier cas, où les individus évaluent les échanges sociaux par la quantité d'information qui peut être partagée par le partenaire, avec un second cas, où ils évaluent les interactions en tenant compte du statut social de leurs partenaires. Nous montrons que, même si les deux stratégies prennent en compte le montant de connaissances des partenaires, elles ont des effets très différents sur le système. En particulier, nous constatons que le premier cas permet généralement aux individus d'accumuler de plus grandes quantités d'information, grâce à des modèles de connexions sociales plus efficaces qu'ils sont capables de construire. Ensuite, nous étudions les effets que l'homophilie, ou la tendance à interagir avec des partenaires similaires, a sur l'accumulation des connaissances et la structure sociale. Nous comparons le cas où des personnes qui connaissent les mêmes informations sont plus sus¬ceptibles d'apprendre socialement l'une de l'autre, au cas où les individus qui connaissent des informations différentes sont au contraire plus susceptibles d'apprendre socialement l'un de l'autre. Nous constatons qu'il n'est pas trivial de déterminer quelle stratégie est meilleure que l'autre. En fonction de la possibilité d'oublier l'information, la façon dont les nouveaux partenaires sociaux peuvent être choisis, et la taille de la population, nous déterminons les conditions pour lesquelles chaque stratégie permet d'accumuler plus d'in¬formations, ou d'une manière plus rapide. Pour ces conditions, nous discutons également les caractéristiques topologiques de la structure sociale qui en résulte, les reliant au résultat de la dynamique de l'information. En conclusion, ce travail ouvre la route pour la modélisation de la dynamique conjointe de la diffusion de l'information entre les individus et leurs interactions sociales. Il fournit également un cadre formel pour étudier conjointement les effets de différentes stratégies de choix des partenaires sur la structure sociale et comment elles favorisent l'accumulation de connaissances dans la population.

Roles of astrocytic sodium dynamics in the neurometabolic coupling : a study by cellular imaging

RESUME LARGE PUBLIC Le système nerveux central est principalement composé de deux types de cellules :les neurones et les cellules gliales. Ces dernières, bien que l'emportant en nombre sur les neurones, ont longtemps été considérées comme des cellules sans intérêts par les neuroscientifiques. Hors, les connaissances modernes à leurs sujets indiquent qu'elles participent à la plupart des tâches physiologiques du cerveau. Plus particulièrement, elles prennent part aux processus énergétiques cérébraux. Ceux-ci, en plus d'être vitaux, sont particulièrement intrigants puisque le cerveau représente seulement 2 % de la masse corporelle mais consomme environ 25 % du glucose (substrat énergétique) corporel. Les astrocytes, un type de cellules gliales, jouent un rôle primordial dans cette formidable utilisation de glucose par le cerveau. En effet, l'activité neuronale (transmission de l'influx nerveux) est accompagnée d'une augmentation de la capture de glucose, issu de la circulation sanguine, par les astrocytes. Ce phénomène est appelé le «couplage neurométabolique » entre neurones et astrocytes. L'ion sodium fait partie des mécanismes cellulaires entrant en fonction lors de ces processus. Ainsi, dans le cadre de cette thèse, les aspects dynamiques de la régulation du sodium astrocytaire et leurs implications dans le couplage neurométabolique ont été étudiés par des techniques d'imagerie cellulaires. Ces études ont démontré que les mitochondries, machineries cellulaires convertissant l'énergie contenue dans le glucose, participent à la régulation du sodium astrocytaire. De plus, ce travail de thèse a permis de découvrir que les astrocytes sont capables de se transmettre, sous forme de vagues de sodium se propageant de cellules en cellules, un message donnant l'ordre d'accroître leur consommation d'énergie. Cette voie de signalisation leur permettrait de fournir de l'énergie aux neurones suite à leur activation. RESUME Le glutamate libéré dans la fente synaptique pendant l'activité neuronale, est éliminé par les astrocytes environnants. Le glutamate est co-transporté avec des ions sodiques, induisant une augmentation intracellulaire de sodium (Na+i) dans les astrocytes. Cette élévation de Na+i déclenche une cascade de mécanismes moléculaires qui aboutissent à la production de substrats énergétiques pouvant être utilisés par les neurones. Durant cette thèse, la mesure simultanée du sodium mitochondrial (Na+mit) et cytosolique par des techniques d'imagerie utilisant des sondes fluorescentes spécifiques, a indiqué que les variations de Na+i induites par le transport du glutamate sont transmises aux mitochondries. De plus, les voies d'entrée et de sortie du sodium mitochondrial ont été identifiées. L'échangeur de Na+ et de Ca2+ mitochondrial semble jouer un rôle primordial dans l'influx de Na+mit, alors que l'efflux de Na+mit est pris en charge par l'échangeur de Na+ et de H+ mitochondrial. L'étude du Na+mit a nécessité l'utilisation d'un système de photoactivation. Les sources de lumière ultraviolette (UV) classiques utilisées à cet effet (lasers, lampes à flash) ayant plusieurs désavantages, une alternative efficace et peu coûteuse a été développée. Il s'agit d'un système compact utilisant une diode électroluminescente (LED) à haute puissance et de longueur d'onde de 365nm. En plus de leurs rôles dans le couplage neurométabolique, les astrocytes participent à la signalisation multicellulaire en transmettant des vagues intercellulaires de calcium. Ce travail de thèse démontre également que des vagues intercellulaires de sodium peuvent être évoquées en parallèle à ces vagues calciques. Le glutamate, suite à sa libération par un mécanisme dépendent du calcium, est réabsorbé par les transporteurs au glutamate. Ce mécanisme a pour conséquence la génération de vagues sodiques se propageant de cellules en cellules. De plus, ces vagues sodiques sont corrélées spatialement avec une consommation accrue de glucose par les astrocytes. En conclusion, ce travail de thèse a permis de montrer que le signal sodique astrocytaire, déclenché en réponse au glutamate, se propage à la fois de façon intracellulaire aux mitochondries et de façon intercellulaire. Ces résultats suggèrent que les astrocytes fonctionnent comme un réseau de cellules nécessaire au couplage énergétique concerté entre neurones et astrocytes et que le sodium est un élément clé dans les mécanismes de signalisations cellulaires sous-jacents. SUMMARY Glutamate, released in the synaptic cleft during neuronal activity, is removed by surrounding astrocytes. Glutamate is taken-up with Na+ ions by specific transporters, inducing an intracellular Na+ (Na+i) elevation in astrocytes which triggers a cascade of molecular mechanisms that provides metabolic substrates to neurons. Thus, astrocytic Na+i homeostasis represents a key component of the so-called neurometabolic coupling. In this context, the first part of this thesis work was aimed at investigating whether cytosolic Na+ changes are transmitted to mitochondria, which could therefore influence their function and contribute to the overall intracellular Na+ regulation. Simultaneous monitoring of both mitochondrial Na+ (Na+mit) and cytosolic Na+ changes with fluorescent dyes revealed that glutamate-evoked cytosolic Na+ elevations are indeed transmitted to mitochondria. The mitochondrial Na+/Ca2+ exchangers have a prominent role in the regulation of Na+mit influx pathway, and Na+mit extrusion appears to be mediated by Na+/H+ exchangers. To demonstrate the implication of Na+/Ca2+ exchangers, this study has required the technical development of an UV-flash photolysis system. Because light sources for flash photolysis have to be powerful and in the near UV range, the use of UV lasers or flash lamps is usually required. As an alternative to these UV sources that have several drawbaks, we developped a compact, efficient and lowcost flash photolysis system which employs a high power 365nm light emitting diode. In addition to their role in neurometabolic coupling, astrocytes participate in multicellular signaling by transmitting intercellular Ca2+ waves. The third part of this thesis show that intercellular Na+ waves can be evoked in parallel to Ca2+ waves. Glutamate released by a Ca2+ wave-dependent mechanism is taken up by glutamate transporters, resulting in a regenerative propagation of cytosolic Na+ increases. Na+ waves in turn lead to a spatially correlated increase in glucose uptake. In conclusion, the present thesis demonstrates that glutamate-induced Na+ changes occurring in the cytosol of astrocytes propagate to both the mitochondrial matrix and the astrocytic network. These results furthermore support the view that astrocytic Na+ is a signal coupled to the brain energy metabolism.