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Slow viscous gravity-driven interaction between a bubble and a free surfacewith unequal surface tensions
International audienceThe axisymmetric gravity-driven dynamics of a bubble rising toward a free surface isaddressed for gas-liquid interfaces having unequal surface tensions. The liquid flowis governed by the Stokes equations which are here solved using a boundary elementmethod in axisymmetric configuration. Within this framework, two dimensionlessnumbers arise: the Bond number Bo1 based on the surface tension of the bubbleinterface and the surface tension ratio ˆ γ comparing the free surface and bubble surfacetensions. Under a careful and discussed selection of the code key settings (numberof boundary elements, initial bubble location, and distance beyond which the freesurface is truncated), it has been possible to numerically and accurately track in timethe bubble and free surface shapes for several values of (Bo1, ˆ γ). The long-time shapesare found to deeply depend upon both Bo1 and ˆ γ and also to compare well withthe shapes predicted in Princen and Mason [“Shape of a fluid drop at a fluid-liquidinterface. II. Theory for three-phase systems,” J. Colloid. Sci. 20, 246–266 (1965)]using a hydrostatic model in which both surfaces are touching. Similarly, the drainagedynamics of the liquid film thickness between the bubble and the free surface dependson (Bo1, ˆ γ). The long-time film thickness exponentially decays in time and a so-calledthinning rate α for which the numerical behaviors and a simple model reveal twobasic behaviors: (i) at small Bond number, α behaves as 1/Bo1 and (ii) at largeBond number, α is nearly constant. In addition, it is found that in the entire rangeof the quantity χ = (1 + ˆ γ)Bo1/(2 ˆ γ), the thinning rate α is well approximated by thefunction 1/(18 χ) + α∞ with α∞ ≈ 0.158. Such a result also permits one to estimatethe typical drainage time versus the initial bubble radius a, the liquid density ρ andviscosity μ, the gravity and the free surface, and bubble surface tensions
Conservativity of embeddings in the lambda-Pi calculus modulo rewriting (long version)
The lambda-Pi calculus can be extended with rewrite rules to embed any other functional pure type system. The normalization and conserva-tivity properties of the embedding is an open problem. In this paper, we show that the embedding is conservative. We define an inverse translation into a pure type system completion and show that the completion is con-servative using the reducibility method. This result further justifies the use of the lambda-Pi calculus modulo rewriting as a logical framework
Production of non-gyrotropic and gyrotropic backstreaming ion distributions in the quasi-perpendicular ion foreshock region : Origin and acceleration mechanisms.
International audienc
Probabilistic representation of a class of non conservative nonlinear Partial Differential Equations
We introduce a new class of nonlinear Stochastic Differential Equations in the sense of McKean, related to non conservative nonlinear Partial Differential equations (PDEs). We discuss existence and uniqueness pathwise and in law under various assumptions. We propose an original interacting particle system for which we discuss the propagation of chaos. To this system, we associate a random function which is proved to converge to a solution of a regularized version of PDE
Comment expliquer la variabilité du climat à l'échelle régionale ? Utilisation de SIRTA-reOBS
International audienc
The Steady Boltzmann and Navier-Stokes Equations
55 pages, 4 multiple figuresInternational audienceThe paper discusses the similarities and the differences in the mathematical theories of the steady Boltzmann and incompressible Navier-Stokes equations posed in a bounded domain. First we discuss two different scaling limits in which solutions of the steady Boltzmann equation have an asymptotic behavior described by the steady Navier-Stokes Fourier system. Whether this system includes the viscous heating term depends on the ratio of the Froude number to the Mach number of the gas flow. While the steady Navier-Stokes equations with smooth divergence-free external force always have at least one smooth solutions, the Boltzmann equation with the same external force set in the torus, or in a bounded domain with specular reflection of gas molecules at the boundary may fail to have any solution, unless the force field is identically zero. Viscous heating seems to be of key importance in this situation. The nonexistence of any steady solution of the Boltzmann equation in this context seems related to the increase of temperature for the evolution problem, a phenomenon that we have established with the help of numerical simulations on the Boltzmann equation and the BGK model
Search for third-generation scalar leptoquarks in the t-tau channel in proton-proton collisions at 8 TeV
Submitted to JHEP ; see paper for full list of authorsInternational audienceA search for pair production of third-generation scalar leptoquarks decaying to top quark and tau lepton pairs is presented using proton-proton collision data at a center-of-mass energy of sqrt(s)=8 TeV collected with the CMS detector at the LHC and corresponding to an integrated luminosity of 19.7 inverse femtobarns. The search is performed using events that contain an electron or a muon, a hadronically decaying tau lepton, and two or more jets. The observations are found to be consistent with the standard model predictions. Assuming that all leptoquarks decay to a top quark and a tau lepton, the existence of pair produced, charge -1/3, third-generation leptoquarks up to a mass of 685 GeV is excluded at 95% confidence level. This result constitutes the first direct limit for leptoquarks decaying into a top quark and a tau lepton, and is also directly applicable to pair produced bottom squarks decaying via the R-parity violating coupling lambda'[333]
Méthodes géométriques et statistiques pour l'analyse et la prédiction des interactions structurales de biomolécules
The biological function of macromolecules, such as proteins and nucleic acids, relies heavily on their interactions with their partners. The prediction of how molecules interact and how they can create large assemblies acting as nanomachines is essential for our understanding of biology but also for therapeutics and nanotechnology design.Blind challenges in biology, such as the CAPRI worldwide experiment for docking, have shown that in silico studies and simulations, mainly using physics-based potentials and techniques, could give structural insights in atomic detail. They might however be of very limited accuracy, particularly in predicting the native molecular structure of proteins, RNAs and complexes.Resorting to simple geometric coarse-grained modelling and machine learning strategies, such as genetic algorithms and support vector machines, we have shown that scoring the putative complex structures can be very much improved to reach the accuracy needed for experiment design and analysis, at least in a semi-rigid body context. From that proof of concept studies, most of the prediction strategies for docking now use machine learning for scoring optimization.Being able to predict the structure and the way molecular partners deform upon binding is also key to obtain better predictions, in particular for non-coding RNAs that are essential to target oncogenes. Our efforts in RNA structure prediction techniques have shown that data based parameterization of energy functions and statistical techniques largely improve the accuracy of structure prediction.Reaching the large assemblies stage also requires to be able to assess the dynamics of molecules from partial experimental data. We developed an efficient sampling technique based on inverse kinematics that does not rely on constraint counting, and implicitly calculates the rigidity of the molecule. Paired with experimental data, it offers an integrative view of the dynamics of non-coding RNAs for biological processes. Combined with clustering techniques, it allows for efficient and flexible cross-docking analysis for protein-RNA complexes
Assessing the robustness of parsimonious predictions for gene neighborhoods from reconciled phylogenies
International audienceThe availability of a large number of assembled genomes opens the way to study the evolution of syntenic character within a phylogenetic context. The DeCo algorithm, recently introduced by Bérard et al. allows the computation of parsimonious evolutionary scenarios for gene adjacencies, from pairs of reconciled gene trees. Following the approach pioneered by Sturmfels and Pachter, we describe how to modify the DeCo dynamic programming algorithm to identify classes of cost schemes that generates similar parsimonious evolutionary scenarios for gene adjacencies, as well as the robustness to changes to the cost scheme of evolutionary events of the presence or absence of specific ancestral gene adjacencies. We apply our method to six thousands mammalian gene families, and show that computing the robustness to changes to cost schemes provides new and interesting insights on the evolution of gene adjacencies and the DeCo model
High-frequency viscosity of a dilute suspension of elongated particles in a linear shear flow between two walls
International audienceA general expression for the effective viscosity of a dilute suspension of arbitrary-shaped particles in linear shear flow between two parallel walls is derived in terms of the induced stresslets on particles. This formula is applied to N-bead rods and to prolate spheroids with the same length, aspect ratio and volume. The effective viscosity of non-Brownian particles in a periodic shear flow is considered here. The oscillating frequency is high enough for the particle orientation and centre-of-mass distribution to be practically frozen, yet small enough for the flow to be quasi-steady. It is known that for spheres, the intrinsic viscosity [μ] increases monotonically when the distance H between the walls is decreased. The dependence is more complex for both types of elongated particles. Three regimes are theoretically predicted here: (i) a ‘weakly confined’ regime (for H>l, where l is the particle length), where [μ] is slightly larger for smaller H; (ii) a ‘semi-confined’ regime, when H becomes smaller than l, where [μ] rapidly decreases since the geometric constraints eliminate particle orientations corresponding to the largest stresslets; (iii) a ‘strongly confined’ regime when H becomes smaller than 2–3 particle widths d, where [μ] rapidly increases owing to the strong hydrodynamic coupling with the walls. In addition, for sufficiently slender particles (with aspect ratio larger than 5–6) there is a domain of narrow gaps for which the intrinsic viscosity is smaller than that in unbounded fluid