A mathematical formalization of the parallel replica dynamics

The purpose of this article is to lay the mathematical foundations of a well known numerical approach in computational statistical physics and molecular dynamics, namely the parallel replica dynamics introduced by A.F. Voter. The aim of the approach is to efficiently generate a coarse-grained evolution (in terms of state-to-state dynamics) of a given stochastic process. The approach formally consists in concurrently considering several realizations of the stochastic process, and tracking among the realizations that which, the soonest, undergoes an important transition. Using specific properties of the dynamics generated, a computational speed-up is obtained. In the best cases, this speed-up approaches the number of realizations considered. By drawing connections with the theory of Markov processes and, in particular, exploiting the notion of quasi-stationary distribution, we provide a mathematical setting appropriate for assessing theoretically the performance of the approach, and possibly improving it

Seasonality in coastal macrobenthic biomass and its implications for estimating secondary production using empirical models

Macrobenthic secondary production is widely used to assess the trophic capacity, health, and functioning of marine and freshwater ecosystems. Annual production estimates are often calculated using empirical models and based on data collected during a single period of the year. Yet, many ecosystems show seasonal variations. Although ignoring seasonality may lead to biased and inaccurate estimates of annual secondary production, it has never been tested at the community level. Using time series of macrobenthic data collected seasonally at three temperate marine coastal soft-bottom sites, we assessed seasonal variations in biomass of macrobenthic invertebrates at both population and community levels. We then investigated how these seasonal variations affect the accuracy of annual benthic production when assessed using an empirical model and data from a single sampling event. Significant and consistent seasonal variations in biomass at the three study sites were highlighted. Macrobenthic biomass was significantly lower in late winter and higher in summer/early fall for 18 of the 30 populations analyzed and for all three communities studied. Seasonality led to inaccurate and often biased estimates of annual secondary production at the community level when based on data from a single sampling event. Bias varied by site and sampling period, but reached similar to 50% if biomass was sampled at its annual minimum or maximum. Since monthly sampling is rarely possible, we suggest that ecologists account for uncertainty in annual production estimates caused by seasonality.Agência financiadora EDF French Ministry of Higher Education, Research and Innovation French Ministry for the Ecological and Inclusive Transition through the Marine Strategy Framework Directive Agreement French Biodiversity Agency (Agence francaise pour la biodiversite) as part of the CAPANOUR projectinfo:eu-repo/semantics/publishedVersio

Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients

In this paper we give an affirmative answer to an open question mentioned in [Le Bris and Lions, Comm. Partial Differential Equations 33 (2008), 1272--1317], that is, we prove the well-posedness of the Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients.Comment: 11 pages. The proof has been modifie

Animal community dynamics at senescent and active vents at the 9° N East Pacific Rise after a volcanic eruption

© The Author(s), 2020. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Gollner, S., Govenar, B., Arbizu, P. M., Mullineaux, L. S., Mills, S., Le Bris, N., Weinbauer, M., Shank, T. M., & Bright, M. Animal community dynamics at senescent and active vents at the 9° N East Pacific Rise after a volcanic eruption. Frontiers in Marine Science, 6, (2020): 832, doi:10.3389/fmars.2019.00832.In 2005/2006, a major volcanic eruption buried faunal communities over a large area of the 9°N East Pacific Rise (EPR) vent field. In late 2006, we initiated colonization studies at several types of post eruption vent communities including those that either survived the eruption, re-established after the eruption, or arisen at new sites. Some of these vents were active whereas others appeared senescent. Although the spatial scale of non-paved (surviving) vent communities was small (several m2 compared to several km2 of total paved area), the remnant individuals at surviving active and senescent vent sites may be important for recolonization. A total of 46 meio- and macrofauna species were encountered at non-paved areas with 33 of those species detected were also present at new sites in 2006. The animals living at non-paved areas represent refuge populations that could act as source populations for new vent sites directly after disturbance. Remnants may be especially important for the meiofauna, where many taxa have limited or no larval dispersal. Meiofauna may reach new vent sites predominantly via migration from local refuge areas, where a reproductive and abundant meiofauna is thriving. These findings are important to consider in any potential future deep-sea mining scenario at deep-sea hydrothermal vents. Within our 4-year study period, we regularly observed vent habitats with tubeworm assemblages that became senescent and died, as vent fluid emissions locally stopped at patches within active vent sites. Senescent vents harbored a species rich mix of typical vent species as well as rare yet undescribed species. The senescent vents contributed significantly to diversity at the 9°N EPR with 55 macrofaunal species (11 singletons) and 74 meiofaunal species (19 singletons). Of these 129 species associated with senescent vents, 60 have not been reported from active vents. Tubeworms and other vent megafauna not only act as foundation species when alive but provide habitat also when dead, sustaining abundant and diverse small sized fauna.We received funding from the Austrian FWF (GrantP20190-B17; MB), the U.S. National Science Foundation (OCE-0424953; to LM, D. McGillicuddy, A. Thurnherr, J. Ledwell, and W. Lavelle; and OCE-1356738 to LM), and the European Union Seventh Framework Programme (FP7/2007-2013) under the MIDAS project, Grant Agreement No. 603418. Ifremer and CNRS (France) supported NL cruise participation and sensor developments. BG was supported by a postdoctoral fellowship from the Deep Ocean Exploration Institute at WHOI (United States). TS was supported by the U.S. National Science Foundation (OCE-0327261 to TS and OCE-0937395 to TS and BG)

Analytic structure of solutions to multiconfiguration equations

We study the regularity at the positions of the (fixed) nuclei of solutions to (non-relativistic) multiconfiguration equations (including Hartree--Fock) of Coulomb systems. We prove the following: Let {phi_1,...,phi_M} be any solution to the rank--M multiconfiguration equations for a molecule with L fixed nuclei at R_1,...,R_L in R^3. Then, for any j in {1,...,M} and k in {1,...,L}, there exists a neighbourhood U_{j,k} in R^3 of R_k, and functions phi^{(1)}_{j,k}, phi^{(2)}_{j,k}, real analytic in U_{j,k}, such that phi_j(x) = phi^{(1)}_{j,k}(x) + |x - R_k| phi^{(2)}_{j,k}(x), x in U_{j,k} A similar result holds for the corresponding electron density. The proof uses the Kustaanheimo--Stiefel transformation, as applied earlier by the authors to the study of the eigenfunctions of the Schr"odinger operator of atoms and molecules near two-particle coalescence points.Comment: 15 page

Approximating a Wavefunction as an Unconstrained Sum of Slater Determinants

The wavefunction for the multiparticle Schr\"odinger equation is a function of many variables and satisfies an antisymmetry condition, so it is natural to approximate it as a sum of Slater determinants. Many current methods do so, but they impose additional structural constraints on the determinants, such as orthogonality between orbitals or an excitation pattern. We present a method without any such constraints, by which we hope to obtain much more efficient expansions, and insight into the inherent structure of the wavefunction. We use an integral formulation of the problem, a Green's function iteration, and a fitting procedure based on the computational paradigm of separated representations. The core procedure is the construction and solution of a matrix-integral system derived from antisymmetric inner products involving the potential operators. We show how to construct and solve this system with computational complexity competitive with current methods.Comment: 30 page

Migrations togolaises : bilan et perspectives

Cet ouvrage a pour objectif de faire le point sur les recherches concernant les migrations togolaises. Sans minimiser le poids des déterminations externes, les chercheurs se sont appliqués à analyser les réponses différenciées des sociétés face à ces phénomènes migratoires. Celà se traduit par une plus grande prise en compte des sociétés de départ et d'accueil, des mouvements migratoires, des stratégies des migrants et de l'évolution de leurs statuts sociaux. Les textes regroupés dans ce volume correspondent à trois approches différentes : l'approche de la mobilité en terme de stocks et de flux, en termes spatiaux (structure et articulations des espaces) et la subjectivisation de la mobilité (espaces de vie, de cycle familial et de systèmes résidentiels)