Statistical mechanics of two-dimensional foams: Physical foundations of the model

In a recent series of papers [1--3], a statistical model that accounts for correlations between topological and geometrical properties of a two-dimensional shuffled foam has been proposed and compared with experimental and numerical data. Here, the various assumptions on which the model is based are exposed and justified: the equiprobability hypothesis of the foam configurations is argued. The range of correlations between bubbles is discussed, and the mean field approximation that is used in the model is detailed. The two self-consistency equations associated with this mean field description can be interpreted as the conservation laws of number of sides and bubble curvature, respectively. Finally, the use of a '' Grand-Canonical '' description, in which the foam constitutes a reservoir of sides and curvature, is justified

Architecture of optimal transport networks

We analyze the structure of networks minimizing the global resistance to flow (or dissipated energy) with respect to two different constraints: fixed total channel volume and fixed total channel surface area. First, we determine the shape of channels in such optimal networks and show that they must be straight with uniform cross-sectional areas. Then, we establish a relation between the cross-sectional areas of adjoining channels at each junction. Indeed, this relation is a generalization of Murray's law, originally established in the context of local optimization. Moreover, we establish a relation between angles and cross-sectional areas of adjoining channels at each junction, which can be represented as a vectorial force balance equation, where the force weight depends on the channel cross-sectional area. A scaling law between the minimal resistance value and the total volume or surface area value is also derived from the analysis. Furthermore, we show that no more than three or four channels meet in one junction of optimal bi-dimensional networks, depending on the flow profile (e.g.: Poiseuille-like or plug-like) and the considered constraint (fixed volume or surface area). In particular, we show that sources are directly connected to wells, without intermediate junctions, for minimal resistance networks preserving the total channel volume in case of plug flow regime. Finally, all these results are illustrated with a simple example, and compared with the structure of natural networks

Optimizing the bulk modulus of cellular networks

We present an alternative derivation of upper-bounds for the bulk modulus of both two-dimensional and three-dimensional cellular materials. For two-dimensional materials, we recover exactly the expression of the Hashin-Shtrikman (HS) upper-bound in the low-density limit, while for three-dimensional materials we even improve the HS bound. Furthermore, we establish necessary and sufficient conditions on the cellular structure for maximizing the bulk modulus, for a given solid volume fraction. These conditions are found to be exactly those under which the electrical (or thermal) conductivity of the material reaches its maximal value as well. These results provide a set of straightforward criteria allowing to address the design of optimized cellular materials, and shed light on recent studies of structures with both maximal bulk modulus and maximal conductivity. Finally, we discuss the compatibility of the criteria presented here with the geometrical constraints caused by minimization of surface energy in a real foam

Frame tension governs the thermal fluctuations of a fluid membrane: new evidence

Two different tensions can be defined for a fluid membrane: the internal tension, $\gamma$, conjugated to the real membrane area in the Hamiltonian, and the frame tension, $\tau$, conjugated to the projected (or frame) area. According to the standard statistical description of a membrane, the fluctuation spectrum is governed by $\gamma$. However, using rotational invariance arguments, several studies argued that fluctuation spectrum must be governed by the frame tension $\tau$ instead. These studies disagree on the origin of the result obtained with the standard description yet: either a miscounting of configurations, quantified with the integration measure, or the use of a quadratic approximation of the Helfrich Hamiltonian. Analyzing the simplest case of a one-dimensional membrane, for which arc length offers a natural parametrization, we give a new proof that the fluctuations are driven by $\tau$, and show that the origin of the issue with the standard description is a miscounting of membrane configurations. The origin itself of this miscounting depends on the thermodynamic ensemble in which calculations are made

Concevoir des contenus de formations des enseignants à partir de l'analyse du système d'activité en classe

Cette communication présente une réflexion relative à la conception de formations issues de l'analyse de l'activité en classe. Les résultats d'une étude portant sur une séquence de lecture orale et collective au Cycle 2 du primaire montrent que l'action de l'enseignante et des élèves s'articulent localement et que ces articulations font émerger une organisation collective que nous dénommons configuration d'activité. Cette configuration est organisée au sens où un ordre émerge de ces interactions locales, et organisante dans la mesure où les actions individuelles sont contraintes par elle en retour. La discussion porte sur la possibilité de concevoir des contenus de formation d'enseignants sur l'analyse de l'activité réelle en classe, et notamment sur le (ou les) niveau(x) d'organisation de l'activité pertinent(s) pour la conception de ces contenus

Les préoccupations et la tonalité émotionnelle des enseignants débutants lors de leurs premières expériences en classe

International audienceThis study describes and interprets the beginning teacher's experience in Physical Education during her first teaching year. The method to describe and interpret her experience is based on a primacy allowed to her emotions during her experience, to her preoccupations in front of their students, and to the way she copes with her preoccupations into action. The results indicate how teacher's emotional tonality and preoccupations format her action during ordinary teaching situations. They show the usefulness of revealing the subjective dimension of beginning teacher's professional experience in teacher education programs.Cette recherche décrit et interprète l'expérience d'une enseignante débutante en Éducation Physique lors de sa première année d'enseignement. La méthode pour décrire et interpréter son expérience accorde le primat à ses émotions durant son expérience, à ses préoccupations face aux élèves, et à la manière de concrétiser ses préoccupations dans l'action. Les résultats montrent combien la tonalité émotionnelle et les préoccupations de l'enseignante influencent son action lors de situations d'enseignement ordinaires. Ils montrent la nécessité de dévoiler la dimension subjective de l'expérience professionnelle des enseignants débutants en formation initiale

La formation d’enseignants entre utilitarisme et cycles de Don : illustration en éducation physique

La formation des enseignants est généralement conçue en termes de transmission/construction utilitaire de connaissances et de compétences, et les formateurs valorisent le plus souvent l’adhésion, au moins formelle, à une logique utilitariste. Cependant, certains faits significatifs ne sont pas explicables dans cette logique. Ces faits sont analysés à partir de la théorie du Don dans des cas d’aide spontanée et des dispositifs de conseil chez des étudiants, des enseignants stagiaires et des formateurs. L’analyse montre que la nature des liens de confiance ou de défiance qui se tissent entre formateurs et formés pourrait avoir une influence dans la formation des enseignants. Ces liens permettent la réalisation de cycles de don ou de vengeance qui autorisent ou non le transfert de connaissances chez les enseignants nouveaux venus.In general, teacher training is envisaged in terms of transmission/construction of knowledge and competencies, and trainers most often place value on a utilitarian logic, as least in a formal sense. However, certain significant events are not explained using this logic. These situations are analyzed based on the theory of the “Gift” in cases of spontaneous help and advice between students, teacher mentors, and teacher trainers. The analysis shows that nature of relationships, being either those of confidence or defiance, that develop between trainers and their students can impact on teacher training. These links show the presence of cycles of gift and of vengeance that facilitate or prevent the transfer of knowledge to newly arrived teachers.La formación docente se concibe en general en términos de transmisión/construcción utilitaria de conocimientos y de competencias, y los formadores habitualmente valoran la adhesión, por lo menos formal, a una lógica utilitarista. Sin embargo, algunos hechos significativos no se pueden explicar dentro de esta lógica. Estos hechos son analizados a partir de la teoría del Don en unos casos de ayuda espontánea y de dispositivos de apoyo con estudiantes, docentes en prácticas y formadores. El análisis muestra que la naturaleza de los lazos de confianza o de desconfianza que se generan entre formadores y formados podría influir en la formación docente. Estos lazos permiten la realización de ciclos de don o de venganza que autorizan o no la transferencia de conocimientos en los docentes recién llegados