Influence of disorder strength on phase-field models of interfacial growth

We study the influence of disorder strength on the interface roughening process in a phase-field model with locally conserved dynamics. We consider two cases where the mobility coefficient multiplying the locally conserved current is either constant throughout the system (the two-sided model) or becomes zero in the phase into which the interface advances (one-sided model). In the limit of weak disorder, both models are completely equivalent and can reproduce the physical process of a fluid diffusively invading a porous media, where super-rough scaling of the interface fluctuations occurs. On the other hand, increasing disorder causes the scaling properties to change to intrinsic anomalous scaling. In the limit of strong disorder this behavior prevails for the one-sided model, whereas for the two-sided case, nucleation of domains in front of the invading front are observed.

Side-branch growth in two-dimensional dendrits. Part II: Phase-field model

The development of side-branching in solidifying dendrites in a regime of large values of the Peclet number is studied by means of a phase-field model. We have compared our numerical results with experiments of the preceding paper and we obtain good qualitative agreement. The growth rate of each side branch shows a power-law behavior from the early stages of its life. From their birth, branches which finally succeed in the competition process of side-branching development have a greater growth exponent than branches which are stopped. Coarsening of branches is entirely defined by their geometrical position relative to their dominant neighbors. The winner branches escape from the diffusive field of the main dendrite and become independent dendrites.

Phase-field approach to spatial perturbations in normal Saffman-Taylor fingers

We make a numerical study of the effect that spatial perturbations have in normal Saffman-Taylor fingers driven at constant pressure gradients. We use a phase field model that allows for spatial variations in the Hele-Shaw cell. We find that, regardless of the specific way in which spatial perturbations are introduced, a lateral instability develops on the sides of the propagating Saffman-Taylor finger. Moreover, the instability exists regardless of the intensity of spatial perturbations in the cell as long as the perturbations are felt by the finger tip. If, as the finger propagates, the spatial perturbations felt by the tip change, the instability is nonperiodic. If, as the finger propagates, the spatial perturbations felt by the tip are persistent, the instability developed is periodic. In the later case, the instability is symmetrical or asymmetrical depending on the intensity of the perturbation.

Phase-field model for Hele-Shaw flows with arabitrary contrast II: numerical approach

We present a phase-field model for the dynamics of the interface between two inmiscible fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. With asymptotic matching techniques we check the model to yield the right Hele-Shaw equations in the sharp-interface limit, and compute the corrections to these equations to first order in the interface thickness. We also compute the effect of such corrections on the linear dispersion relation of the planar interface. We discuss in detail the conditions on the interface thickness to control the accuracy and convergence of the phase-field model to the limiting Hele-Shaw dynamics. In particular, the convergence appears to be slower for high viscosity contrasts.

Higher order Lagrangian systems: Geometric structures, Dynamics, and Constraints

In order to study the connections between Lagrangian and Hamiltonian formalisms constructed from aperhaps singularhigher-order Lagrangian, some geometric structures are constructed. Intermediate spaces between those of Lagrangian and Hamiltonian formalisms, partial Ostrogradskiis transformations and unambiguous evolution operators connecting these spaces are intrinsically defined, and some of their properties studied. Equations of motion, constraints, and arbitrary functions of Lagrangian and Hamiltonian formalisms are thoroughly studied. In particular, all the Lagrangian constraints are obtained from the Hamiltonian ones. Once the gauge transformations are taken into account, the true number of degrees of freedom is obtained, both in the Lagrangian and Hamiltonian formalisms, and also in all the intermediate formalisms herein defined.

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.

Heat transfer between nanoparticles: Thermal conductance for near-field interactions

We analyze the heat transfer between two nanoparticles separated by a distance lying in the near-field domain in which energy interchange is due to the Coulomb interactions. The thermal conductance is computed by assuming that the particles have charge distributions characterized by fluctuating multipole moments in equilibrium with heat baths at two different temperatures. This quantity follows from the fluctuation-dissipation theorem for the fluctuations of the multipolar moments. We compare the behavior of the conductance as a function of the distance between the particles with the result obtained by means of molecular dynamics simulations. The formalism proposed enables us to provide a comprehensive explanation of the marked growth of the conductance when decreasing the distance between the nanoparticles.

Vacuum decay in quantum field theory

We study the contribution to vacuum decay in field theory due to the interaction between the long- and short-wavelength modes of the field. The field model considered consists of a scalar field of mass M with a cubic term in the potential. The dynamics of the long-wavelength modes becomes diffusive in this interaction. The diffusive behavior is described by the reduced Wigner function that characterizes the state of the long-wavelength modes. This function is obtained from the whole Wigner function by integration of the degrees of freedom of the short-wavelength modes. The dynamical equation for the reduced Wigner function becomes a kind of Fokker-Planck equation which is solved with suitable boundary conditions enforcing an initial metastable vacuum state trapped in the potential well. As a result a finite activation rate is found, even at zero temperature, for the formation of true vacuum bubbles of size M-1. This effect makes a substantial contribution to the total decay rate.

Molecular dynamics study of orientational cooperativity in water

Recent experiments on liquid water show collective dipole orientation fluctuations dramatically slower than expected (with relaxation time >tation, the self-dipole randomization time tr, which is an upper limit on ta; we find that tr5ta. Third, to check if there are correlated domains of dipoles in water which have large relaxation times compared to the individual dipoles, we calculate the randomization time tbox of the site-dipole field, the net dipole moment formed by a set of molecules belonging to a box of edge Lbox. We find that the site-dipole randomization time tbox2.5ta for Lbox3 , i.e., it is shorter than the same quantity calculated for the self-dipole. Finally, we find that the orientational correlation length is short even at low T.

Relaxation dynamics in suspensions of ferromagnetic particles

We have studied the relaxation dynamics of a dilute assembly of ferromagnetic particles in suspension. A formalism based on the Smoluchowski equation, describing the evolution of the probability density for the directions of the magnetic moment and of the axis of easy magnetization of the particles, has been developed. We compute the rotational viscosity from a Green-Kubo formula and give an expression for the relaxation time of the particles which comes from the dynamic equations of the correlation functions. Concerning the relaxation time for the particles, our results agree quite well with experiments performed on different samples of ferromagnetic particles for which the magnetic energy, associated with the interaction between the magnetic moments and the external field, or the energy of anisotropy plays a dominant role.

Evidence of aging in spin glass mean-field models

We study numerically the out-of-equilibrium dynamics of the hypercubic cell spin glass in high dimensionalities. We obtain evidence of aging effects qualitatively similar both to experiments and to simulations of low-dimensional models. This suggests that the Sherrington-Kirkpatrick model as well as other mean-field finite connectivity lattices can be used to study these effects analytically.

Temporal and spatial dynamics of benthic invertebrate communities in an alpine glacier-fed alluvial system

Summary The present thesis work focused on the ecology of benthic invertebrates in the proglacial floodplain of the Rhone in the Swiss Alps. The main glacial Rhone River and a smaller glacial tributary, the Mutt River, joined and entered a braiding multi-thread area. A first part concentrated on the disruption of the longitudinal patterns of environmental conditions and benthic invertebrate fauna in the Rhone by its tributary the Mutt. The Mutt had less harsh environmental conditions, higher taxonomic richness and more abundant zoobenthos compared to the Rhone upstream of the confluence. Although the habitat conditions in the main stream were little modified by the tributary, the fauna was richer and more diverse below the confluence. Colonisation from the Mutt induced the occurrence of faunal elements uncommon of glacial streams in the upper Rhone, where water temperature remains below 4°C. Although the glacial Rhone dominated the system with regard to hydrology and certain environmental conditions, the Mutt tributary has to be seen as the faunal driver of the system. The second part of the study concerned the spatio-temporal differentiation of the habitats and the benthic communities along and across the flood plain. No longitudinal differentiation was found. The spatial transversal differentiation of three habitat types with different environmental characteristics was successfully reflected in the spatial variability of benthic assemblages. This typology separated marginal sites of the flood plain, left bank sites under the influence of the Mutt, and the right bank sites under the influence of the Rh6ne. Faunistic spatial differences were emphasized by the quantitative structure of the fauna, richness, abundances and Simpson index of diversity. Seasonal environmental variability was positively related with Simpson index of diversity and the total richness per site. Low flow conditions were the most favourable season for the fauna and November was characterized by low spatial environmental heterogeneity, high spatial heterogeneity of faunal assemblage, maximum taxonomic richness, a particular taxonomic composition, highest abundances, as well as the highest primary food resources. The third part studied the egg development of three species of Ephemeroptera in the laboratory at 1.5 to 7°C and the ecological implications in the field. Species revealed very contrasting development strategies. Baetis alpinus has a synchronous and efficient egg development, which is faster in warmer habitats, enabling it to exploit short periods of favourable conditions in the floodplain. Ecdyonurus picteti has a very long development time slightly decreasing in warmer conditions. The high degree of individual variation suggests a genetic determination of the degree-days demand. Combined with the glacial local conditions, this strategy leads to an extreme delay of hatching and allows it to develop in very unpredictable habitats. Rhithrogena nivata is the second cold adapted species in Ephemeroptera. The incubation duration is long and success largely depends on the timing of hatching and the discharge conditions. This species is able to exploit extremely unstable and cold habitats where other species are limited by low water temperatures. The fourth part dealt with larval development in different habitats of the floodplain. Addition of data on egg development allowed the description of the life histories of the species from oviposition until emergence. Rhithrogena nivata and loyolaea generally have a two-year development, with the first winter passed as eggs and the second one as larvae. Development of Ecdyonurus picteti is difficult to document but appears to be efficient in a harsh and unpredictable environment. Baetis alpinus was studied separately in four habitats of the floodplain system with contrasting thermal regimes. Differences in success and duration of larval development and in growth rates are emphasised. Subvention mechanisms between habitats by migration of young or grown larvae were demonstrated. Development success and persistence of the populations in the system were thus increased. Emergence was synchronised to the detriment of the optimisation of the adult's size and fecundity. These very different development strategies induce a spatial and temporal distribution in the use of food resources and ecological niches. The last part of this work aimed at the synthesis of the characteristics and the ecological features of three distinct compartments of the system that are the upper Rhone, the Mutt and the floodplain. Their particular role as well as their inter-dependence concerning the structure and the dynamics of the benthic communities was emphasised. Résumé Ce travail de thèse est consacré à l'écologie des invertébrés benthiques dans la zone alluviale proglaciaire du Rhône dans les Alpes suisses. Le Rhône, torrent glaciaire principal, reçoit les eaux de la Mutt, affluent glaciaire secondaire, puis pénètre dans une zone de tressage formée de plusieurs bras. La première partie de l'étude se concentre sur la disruption par la Mutt des processus longitudinaux, tant environnementaux que faunistiques, existants dans le Rhône. Les conditions environnementales régnant dans la Mutt sont moins rudes, la richesse taxonomique plus élevée et le zoobenthos plus abondant que dans le Rhône en amont de la confluence. Bien que les conditions environnementales dans le torrent principal soient peu modifiées par l'affluent, la faune s'avère être plus riche et plus diversifiée en aval de la confluence. La colonisation depuis la Mutt permet l'occurrence de taxons inhabituels dans le Rhône en amont de la confluence, où la température de l'eau se maintient en dessous de 4°C. Bien que le Rhône, torrent glaciaire principal, domine le système du point de vu de l'hydrologie et de certains paramètres environnementaux, l'affluent Mutt doit être considéré comme l'élément structurant la faune dans le système. La deuxième partie concerne la différentiation spatiale et temporelle des habitats et des communautés benthiques à travers la plaine alluviale. Aucune différentiation longitudinale n'a été mise en évidence. La différentiation transversale de trois types d'habitats sur la base des caractéristiques environnementales a été confirmée par la variabilité spatiale de la faune. Cette typologie sépare les sites marginaux de la plaine alluviale, ceux sous l'influence de la Mutt (en rive gauche) et ceux sous l'influence du Rhône amont (en rive droite). Les différences spatiales de la faune sont mises en évidence par la structure quantitative de la faune, la richesse, les abondances et l'indice de diversité de Simpson. La variabilité saisonnière du milieu est positivement liée avec l'indice de diversité de Simpson et la richesse totale par site. L'étiage correspond à la période la plus favorable pour la faune et novembre réunit des conditions de faible hétérogénéité spatiale du milieu, de forte hétérogénéité spatiale de la faune, une richesse taxonomique maximale, une composition faunistique particulière, les abondances ainsi que les ressources primaires les plus élevées. La troisième partie est consacrée à l'étude du développement des oeufs de trois espèces d'Ephémères au laboratoire à des températures de 1.5 à 7°C, ainsi qu'aux implications écologiques sur le terrain. Ces espèces présentent des stratégies de développement très contrastées. Baetis alpinus a un développement synchrone et efficace, plus rapide en milieu plus chaud et lui permettant d'exploiter les courtes périodes de conditions favorables. Ecdyonurus picteti présente une durée de développement très longue, diminuant légèrement dans des conditions plus chaudes. L'importante variation interindividuelle suggère un déterminisme génétique de la durée de développement. Cette stratégie, associée aux conditions locales, conduit à un décalage extrême des éclosions et permet à l'espèce de se développer dans des habitats imprévisibles. Rhithrogena nivata est la seconde espèce d'Ephémères présentant une adaptation au froid. L'incubation des oeufs est longue et son succès dépend de la période des éclosions et des conditions hydrologiques. Cette espèce est capable d'exploiter des habitats extrêmement instables et froids, où la température est facteur limitant pour d'autres espèces. La quatrième partie traite du développement larvaire dans différents habitats de la plaine alluviale. Le développement complet est décrit pour les espèces étudiées de la ponte jusqu'à l'émergence. Rhithrogena nivata et loyolaea atteignent généralement le stade adulte en deux ans, le premier hiver étant passé sous forme d'oeuf et le second sous forme de larve. Le développement de Ecdyonurus picteti est difficile à documenter, mais s'avère cependant efficace dans un environnement rude et imprévisible. Baetis alpinus a été étudié séparément dans quatre habitats de la plaine ayant des régimes thermiques contrastés. La réussite et la durée du développement embryonnaire ainsi que les taux de croissance y sont variables. Des mécanismes de subvention entre habitats sont possibles par la migration de larves juvéniles ou plus développées, augmentant ainsi la réussite du développement et le maintien des populations dans le système. L'émergence devient synchrone, au détriment de l'optimisation de la taille et de la fécondité des adultes. Ces stratégies très différentes induisent une distribution spatiale et temporelle dans l'usage des ressources et des niches écologiques. La dernière partie synthétise les caractéristiques écologiques des trois compartiments du système que sont le Rhône amont, la Mutt et la zone alluviale. Leurs rôles particuliers et leurs interdépendances du point de vue de la structure et de la dynamique des communautés benthiques sont mis en avant.

Nonequilibrium orientational patterns in two-component Langmuir monolayers

A model of a phase-separating two-component Langmuir monolayer in the presence of a photoinduced reaction interconverting two components is formulated. An interplay between phase separation, orientational ordering, and reaction is found to lead to a variety of nonequilibrium self-organized patterns, both stationary and traveling. Examples of the patterns, observed in numerical simulations, include flowing droplets, traveling stripes, wave sources, and vortex defects.

Influence of ohmic heating on the flow field in thin-layer electrodeposition

In thin-layer electrodeposition the dissipated electrical energy leads to a substantial heating of the ion solution. We measured the resulting temperature field by means of an infrared camera. The properties of the temperature field correspond closely with the development of the concentration field. In particular, we find that the thermal gradients at the electrodes act similar to a weak additional driving force to the convection rolls driven by concentration gradients.

Dynamics of a paramagnetic colloidal particle driven on a magnetic-bubble lattice

We present a theoretical study of the recently observed dynamical regimes of paramagnetic colloidal particles externally driven above a regular lattice of magnetic bubbles [P. Tierno, T. H. Johansen, and T. M. Fischer, Phys. Rev. Lett. 99, 038303 (2007)]. An external precessing magnetic field alters the potential generated by the surface of the film in such a way to either drive the particle circularly around one bubble, ballistically through the array, or in triangular orbits on the interstitial regions between the bubbles. In the ballistic regime, we observe different trajectories performed by the particles phase locked with the external driving. Superdiffusive motion, which was experimentally found bridging the localized and delocalized dynamics, emerge only by introducing a certain degree of randomness into the bubbles size distribution.