Long-time averaging for integrable Hamiltonian dynamics

International audienceGiven a Hamiltonian dynamics, we address the question of computing the space-average (referred as the ensemble average in the field of molecular simulation) of an observable through the limit of its time-average. For a completely integrable system, it is known that ergodicity can be characterized by a diophantine condition on its frequencies and that the two averages then coincide. In this paper, we show that we can improve the rate of convergence upon using a filter function in the time-averages. We then show that this convergence persists when a numerical symplectic scheme is applied to the system, up to the order of the integrator

High-order averaging schemes with error bounds for thermodynamical properties calculations by MD simulations

We introduce high-order averaging formulae for the computation of statistical averages on the basis of the numerical simulation of long-time molecular dynamics trajectories. Using these formulae, we improve the convergence rate of the time average with respect to the computational effort. We provide some numerical examples that show the efficiency of our scheme. When trajectories are approximated using symplectic integration schemes (such as velocity Verlet), we give error bounds that provide guidelines to choose the parameters of the computation in order to reach a given desired accuracy in the most efficient manner

La modélisation mécaniste pour analyser des dynamiques especes-habitats ; exemple des diptères syrphides de forets fragmentées du cortège de quercus pubescens

La biologie de la conservation est un thème émergent des sciences de la biodiversité. Ce thème confronte les approches de l'écologie des populations et des communautés, des sciences économiques, de l'éthique, du droit et de la gestion de l'environnement autour des problèmes de préservation de la biodiversité. Une conception biologique de la conservation implique que les politiques de gestion du milieu naturel soient attentives au maintien du potentiel évolutif du vivant en créant les conditions de viabilité des populations et d'entretien de leur diversité génétique. Elles doivent aussi veiller au maintien de la richesse spécifique et de la diversité biologique et fonctionnelle des communautés. De telles politiques de gestion relèvent du concept de développement durable qui associe sciences économiques et juridiques pour définir des modes de développement respectueux de la qualité de l'environnement. La biodiversité représente à cet égard à la fois un indicateur et un enjeu pour la persistance de ressources potentielles et le maintien de la fonctionnalité des écosystèmes. Si ce champ interdisciplinaire est bien développé outre-atlantique, son émergence est plus récente en Europe, et plus particulièrement dans les régions francophones. Néanmoins de nombreuses opérations de conservation biologique réalisées dans ces régions sont accompagnées de programmes de recherche comme en atteste la multiplication des thèses de doctorats soutenues dans ce domaine. Le développement de ce champ interdisciplinaire a motivé l'idée d'organiser une réunion qui donnerait aux chercheurs impliqués dans ces thèmes émergents la possibilité de présenter leurs travaux. Les gestionnaires d'espaces naturels ou les administrations en charge de la préservation de la biodiversité pourraient trouver dans cette réunion une opportunité d'exprimer et de confronter leurs attentes aux derniers progrès méthodologiques et conceptuels. Ce colloque a permis de faire le point sur la discipline dans les contrées francophones et de faire le lien entre la communauté francophone et la section européenne de la Society for Conservation Biology

Modelling and simulating change in reforesting mountain landscapes using a social-ecological framework

Natural reforestation of European mountain landscapes raises major environmental and societal issues. With local stakeholders in the Pyrenees National Park area (France), we studied agricultural landscape colonisation by ash (Fraxinus excelsior) to enlighten its impacts on biodiversity and other landscape functions of importance for the valley socio-economics. The study comprised an integrated assessment of land-use and land-cover change (LUCC) since the 1950s, and a scenario analysis of alternative future policy. We combined knowledge and methods from landscape ecology, land change and agricultural sciences, and a set of coordinated field studies to capture interactions and feedback in the local landscape/land-use system. Our results elicited the hierarchically-nested relationships between social and ecological processes. Agricultural change played a preeminent role in the spatial and temporal patterns of LUCC. Landscape colonisation by ash at the parcel level of organisation was merely controlled by grassland management, and in fact depended on the farmer's land management at the whole-farm level. LUCC patterns at the landscape level depended to a great extent on interactions between farm household behaviours and the spatial arrangement of landholdings within the landscape mosaic. Our results stressed the need to represent the local SES function at a fine scale to adequately capture scenarios of change in landscape functions. These findings orientated our modelling choices in the building an agent-based model for LUCC simulation (SMASH - Spatialized Multi-Agent System of landscape colonization by ASH). We discuss our method and results with reference to topical issues in interdisciplinary research into the sustainability of multifunctional landscapes

High energy resolution measurements of the radiative decay of double K-shell vacancies in 20 ≤ Z ≤ 29 elements bombarded by fast C and Ne ions

We report on high energy resolution measurements of the Kα hypersatellite x-ray spectra of Ca, V, Fe and Cu induced by impact with 144 MeV C and 180 MeV Ne ions

Setting and analysis of the multi-configuration time-dependent Hartree-Fock equations

In this paper we motivate, formulate and analyze the Multi-Configuration Time-Dependent Hartree-Fock (MCTDHF) equations for molecular systems under Coulomb interaction. They consist in approximating the N-particle Schrodinger wavefunction by a (time-dependent) linear combination of (time-dependent) Slater determinants. The equations of motion express as a system of ordinary differential equations for the expansion coefficients coupled to nonlinear Schrodinger-type equations for mono-electronic wavefunctions. The invertibility of the one-body density matrix (full-rank hypothesis) plays a crucial role in the analysis. Under the full-rank assumption a fiber bundle structure shows up and produces unitary equivalence between convenient representations of the equations. We discuss and establish existence and uniqueness of maximal solutions to the Cauchy problem in the energy space as long as the density matrix is not singular. A sufficient condition in terms of the energy of the initial data ensuring the global-in-time invertibility is provided (first result in this direction). Regularizing the density matrix breaks down energy conservation, however a global well-posedness for this system in L^2 is obtained with Strichartz estimates. Eventually solutions to this regularized system are shown to converge to the original one on the time interval when the density matrix is invertible.Comment: 48 pages, 1 figur

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