Polydispersity and optimal relaxation in the hard sphere fluid

We consider the mass heterogeneity in a gas of polydisperse hard particles as a key to optimizing a dynamical property: the kinetic relaxation rate. Using the framework of the Boltzmann equation, we study the long time approach of a perturbed velocity distribution toward the equilibrium Maxwellian solution. We work out the cases of discrete as well as continuous distributions of masses, as found in dilute fluids of mesoscopic particles such as granular matter and colloids. On the basis of analytical and numerical evidence, we formulate a dynamical equipartition principle that leads to the result that no such continuous dispersion in fact minimizes the relaxation time, as the global optimum is characterized by a finite number of species. This optimal mixture is found to depend on the dimension d of space, ranging from five species for d=1 to a single one for d>=4. The role of the collisional kernel is also discussed, and extensions to dissipative systems are shown to be possible.Comment: 20 pages, 8 figures, 3 table

Microscopic origin of self-similarity in granular blast waves

The self-similar expansion of a blast wave, well-studied in air, has peculiar counterparts in dense and dissipative media such as granular gases. Recent results have shown that, while the traditional Taylor-von Neumann-Sedov (TvNS) derivation is not applicable to such granular blasts, they can nevertheless be well understood via a combination of microscopic and hydrodynamic insights. In this article, we provide a detailed analysis of these methods associating Molecular Dynamics simulations and continuum equations, which successfully predict hydrodynamic profiles, scaling properties and the instability of the self-similar solution. We also present new results for the energy conserving case, including the particle-level analysis of the classic TvNS solution and its breakdown at higher densities.Comment: 47 pages, 9 figures Supplementary Materials: 2 appendices, 3 figure

Collective dynamical regimes predict invasion success and impacts in microbial communities

The outcomes of ecological invasions may depend on either characteristics of the invading species or attributes of the resident community. Here we use a combination of experiments and theory to show that the interplay between dynamics, interaction strength and diversity determine the invasion outcome in microbial communities. We find that the communities with fluctuating species abundances are more invasible and diverse than stable communities, leading to a positive diversity–invasibility relationship among communities assembled in the same environment. As predicted by theory, increasing interspecies interaction strength and species pool size leads to a decrease of invasion probability in our experiment. Our results show a positive correspondence between invasibility and survival fraction of resident species across all conditions. Communities composed of strongly interacting species can exhibit an emergent priority effect in which invader species are less likely to colonize than species in the original pool. However, if an invasion is successful, its ecological effects on the resident community are greater when interspecies interactions are strong. Our findings provide a unified perspective on the diversity–invasibility debate by showing that invasibility and invasion effect are emergent properties of interacting species, which can be predicted by simple community-level features

Field induced stationary state for an accelerated tracer in a bath

Our interest goes to the behavior of a tracer particle, accelerated by a constant and uniform external field, when the energy injected by the field is redistributed through collision to a bath of unaccelerated particles. A non equilibrium steady state is thereby reached. Solutions of a generalized Boltzmann-Lorentz equation are analyzed analytically, in a versatile framework that embeds the majority of tracer-bath interactions discussed in the literature. These results --mostly derived for a one dimensional system-- are successfully confronted to those of three independent numerical simulation methods: a direct iterative solution, Gillespie algorithm, and the Direct Simulation Monte Carlo technique. We work out the diffusion properties as well as the velocity tails: large v, and either large -v, or v in the vicinity of its lower cutoff whenever the velocity distribution is bounded from below. Particular emphasis is put on the cold bath limit, with scatterers at rest, which plays a special role in our model.Comment: 20 pages, 6 figures v3:minor corrections in sec.III and added reference

Instrumentation numérique de la rédaction incrémentale : leçons tirées de la mise à l’épreuve du carnet numérique de l’élève chercheur

We studied how the introduction of the CNEC, a learning environment whose function is to foster iterative writing, affected the interactions between pupils and teachers in a sample of elementary and middle schools. Based on class observations and focus groups and through the lens of activity theory, we study the difficulties associated with the implementation of iterative writing, before and after the introduction of the CNEC. Our results corroborate the hypothesis that digital artifacts can improve the regulation of class activity in the context of inquiry-learning, compared to their paper equivalents. Parallelly, our results suggested that the perception students had of their own mistakes seems to change in a context of iterative writing, since the remarks of the teacher on such mistakes are less considered as a punishment. Observations also suggested that new contradictions could arise of the will of teachers to use both paper-based and digital artifacts to perform iterative writing, and due to the increased time the formulation of feedbacks requires. Keywords: iterative writing, evaluation, virtual learning environmentDans une perspective d’évaluation d’EIAH (environnements informatiques pour l’apprentissage humain), nous étudions dans cette recherche les changements de pratiques d’enseignement liés à l’utilisation, en contexte scolaire, du CNEC (carnet numérique de l’élève chercheur), une application numérique instrumentant la rédaction incrémentale entre l’enseignant et les élèves. Au prisme du concept de contradiction développé dans la théorie de l’activité d’Engeström, nous cherchons à appréhender les difficultés associées à la rédaction incrémentale. Pour cela, nous avons mené des groupes de discussion et des observations en classe, avant et après l’introduction de l’application. Nos résultats corroborent l’hypothèse selon laquelle, dans un contexte de démarche d’investigation, l’instrumentation numérique de cette approche permet de mieux réguler l’activité des élèves que l’instrumentation papier. Par ailleurs, les entretiens collectifs révèlent que le rapport que les élèves entretiennent aux erreurs s’en trouve modifié, la correction de celles-ci étant moins considérée comme une sanction. La nécessité pour l’enseignant d’investir davantage de temps dans la formulation des retours ainsi que la multiplication des instruments, avec une redondance partielle entre instruments papier et instruments numériques, permettent de croire que de nouvelles contradictions pourraient émerger avec l’utilisation d’un tel EIAH. Mots-clés : rédaction incrémentale, EIAH, évaluation, numériqu

Linking intrinsic scales of ecological processes to characteristic scales of biodiversity and functioning patterns

Ecology is a science of scale, which guides our description of both ecological processes and patterns, but we lack a systematic understanding of how process scale and pattern scale are connected. Recent calls for synthesis between population ecology, community ecology, and ecosystem ecology motivate the integration of phenomena at multiple organizational levels. Furthermore, many studies leave out the scaling of a critical process: species interactions, which may be non-local through movement or foraging and must be distinguished from dispersal scales. Here, we use simulations to explore the consequences of three different process scales (species interactions, dispersal, and the environment) on emergent patterns of biodiversity, ecosystem functioning, and their relationship, in a spatially-explicit landscape and stable equilibrium setting. A major result of our study is that the spatial scales of dispersal and species interactions have opposite effects: a larger dispersal scale homogenizes spatial biomass patterns, while a larger interaction scale amplifies their heterogeneity. Interestingly, the specific scale at which dispersal and interaction scales begin to influence landscape patterns depends on the scale of environmental heterogeneity – in other words, the scale of one process allows important scales to emerge in other processes. This interplay between process scales, i.e. a situation where no single process dominates, can only occur when the environment is heterogeneous and the scale of dispersal small. Finally, contrary to our expectations, we observe that the spatial scale of ecological processes is more clearly reflected in landscape patterns (i.e. distribution of local outcomes) than in global patterns such as species–area relationships (SARs) or large-scale biodiversity–functioning relationships. Overall we conclude that long-range interactions often act differently and even in opposite ways to dispersal, and that the landscape patterns that emerge from the interplay of long-ranged interactions, dispersal and environmental heterogeneity are not well captured by often-used metrics like the SAR

Rapport scientifique de synthèse de la recherche Cahier numérique de l'élève chercheur (CNEC)

Le texte qui suit est fondé sur un travail collectif mené pendant 3 années au sein du projet EFRAN Les savanturiers du numérique