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Mistral and Tramontane wind speed and wind direction patterns in regional climate simulations
No full textInternational audienceThe Mistral and Tramontane are important wind phenomena that occur over southern France and the northwestern Mediterranean Sea. Both winds travel through constricting valleys before flowing out towards the Mediterranean Sea. The Mistral and Tramontane are thus interesting phenomena, and represent an opportunity to study channeling effects, as well as the interactions between the atmosphere and land/ocean surfaces. This study investigates Mistral and Tramontane simulations using five regional climate models with grid spacing of about 50 km and smaller. All simulations are driven by ERA-Interim reanalysis data. Spatial patterns of surface wind, as well as wind development and error propagation along the wind tracks from inland France to offshore during Mistral and Tramontane events, are presented and discussed. To disentangle the results from large-scale error sources in Mistral and Tramontane simulations, only days with well simulated large-scale sea level pressure field patterns are evaluated. Comparisons with the observations show that the large-scale pressure patterns are well simulated by the considered models, but the orographic modifications to the wind systems are not well simulated by the coarse-grid simulations (with a grid spacing of about 50 km), and are reproduced slightly better by the higher resolution simulations. On days with Mistral and/or Tramontane events, most simulations underestimate (by 13 % on average) the wind speed over the Mediterranean Sea. This effect is strongest at the lateral borders of the main flow—the flow width is underestimated. All simulations of this study show a clockwise wind direction bias over the sea during Mistral and Tramontane events. Simulations with smaller grid spacing show smaller biases than their coarse-grid counterparts
Expressing Additives Using Multiplicatives and Subexponentials
No full textInternational audienceSubexponential logic is a variant of linear logic with a family of exponential connectives—called subex-ponentials—that are indexed and arranged in a pre-order. Each subexponential has or lacks associated structural properties of weakening and contraction. We show that a classical propositional multiplicative subexponential logic (MSEL) with one unrestricted and two linear subexponentials can encode the halting problem for two register Minsky machines, and is hence undecidable. We then show how the additive con-nectives can be directly simulated by giving an encoding of propositional multiplicative additive linear logic (MALL) in an MSEL with one unrestricted and four linear subexponentials
Collision of almost parallel vortex filaments
No full textInternational audienceWe investigate the occurrence of collisions in the evolution of vortex filaments through a system introduced by Klein, Majda and Damodaran [KMD95] and Zakharov [Z88, Z99]. We first establish rigorously the existence of a pair of almost parallel vortex filaments, with opposite circulation, colliding at some point in finite time. The collision mechanism is based on the one of the self-similar solutions of the model, described in [BFM14]. In the second part of this paper we extend this construction to the case of an arbitrary number of filaments, with poly-gonial symmetry, that are perturbations of a configuration of parallel vortex filaments forming a polygon, with or without its center, rotating with constant angular velocity
Vérifier la positivité stricte d'une application de Kraus est NP-dur
No full textAlso preprint arXiv:1402.1429International audienceBasic properties in Perron-Frobenius theory are positivity,primitivity, and irreducibility. Whereas these properties can bechecked in polynomial time for stochastic matrices, we show that forKraus maps - the noncommutative generalization of stochastic matrices- checking positivity is NP-hard. This is in contrast withirreducibility and primitivity, which we show to be checkable instrongly polynomial time for completely positive maps - thenoncommutative generalization of nonpositive matrices. As anintermediate result, we get that the bilinear feasibility problem over is NP-hard
Dependence of tropical eigenspaces
No full textAlso arXiv:1504.07986 (2015)International audienceWe study the pathology that causes tropical eigenspaces of distinct su-pertropical eigenvalues of a non-singular matrix A, to be dependent. We show that in lower dimensions the eigenvectors of distinct eigenvalues are independent, as desired. The index set that differentiates between subsequent essential monomials of the characteristic polynomial, yields an eigenvalue λ, and corresponds to the columns of adj(A + λI) from which the eigenvectors are taken. We ascertain the cause for failure in higher dimensions, and prove that independence of the eigenvectors is recovered in case the " difference criterion " holds, defined in terms of disjoint differences between index sets of subsequent coefficients. We conclude by considering the eigenvectors of the matrix A ∇ := 1 det(A) adj(A) and the connection of the independence question to generalized eigenvectors
Simply generated non-crossing partitions
No full textDiffers slightly from the published version.International audienceWe introduce and study the model of simply generated non-crossing partitions, which are, roughly speaking, chosen at random according to a sequence of weights. This framework encompasses the particular case of uniform non-crossing partitions with constraints on their block sizes. Our main tool is a bijection between non-crossing partitions and plane trees, which maps such simply generated non-crossing partitions into simply generated trees so that blocks of size are in correspondence with vertices of out-degree . This allows us to obtain limit theorems concerning the block structure of simply generated non-crossing partitions. We apply our results in free probability by giving a simple formula relating the maximum of the support of a compactly supported probability measure on the real line in terms of its free cumulants
Regularity for the optimal compliance problem with length penalization
No full textInternational audienceWe prove some regularity results for a connected set S in the planar domain O, which minimizes the compliance of its complement O\S, plus its length. This problem, interpreted as to find the best location for attaching a membrane subject to a given external force f so as to minimize the compliance, can be seen as an elliptic PDE version of the average distance problem/irrigation problem (in a penalized version rather than a constrained one), which has been extensively studied in the literature. We prove that minimizers consist of a finite number of smooth curves meeting only by three at 120 degree angles, containing no loop, and possibly touching the boundary of the domain only tangentially. Several new technical tools together with the classical ones are developed for this purpose
Persistently damped transport on a network of circles
No full textInternational audienceIn this paper we address the exponential stability of a system of transport equations with intermittent damping on a network of circles intersecting at a single point . The equations are coupled through a linear mixing of their values at , described by a matrix . The activity of the intermittent damping is determined by persistently exciting signals, all belonging to a fixed class. The main result is that, under suitable hypotheses on and on the rationality of the ratios between the lengths of the circles, such a system is exponentially stable, uniformly with respect to the persistently exciting signals. The proof relies on an explicit formula for the solutions of this system, which allows one to track down the effects of the intermittent damping
Optimal Rationing within a Heterogeneous Population
No full textInternational audienceA government agency delegates to a provider (hospital, medical gatekeeper, school, social worker) the decision to supply a service or treatment to individual recipients. The agency does not perfectly know the distribution of individual treatment costs in the population. The single-crossing property is not satisfied when the uncertainty pertains to the dispersion of the distribution. We find that the provision of service should be distorted upwards when the first-best efficient number of recipients is sufficiently high
Ion transport through deformable porous media:derivation of the macroscopic equations using upscaling
No full textInternational audienceWe study the homogenization (or upscaling) of the transport of a multicomponentelectrolyte in a dilute Newtonian solvent through a deformable porous medium. The porescale interaction between the flow and the structure deformation (modeled by linearizedelasticity equations) is taken into account. After a careful adimensionalization process, we first consider so-called equilibrium solutions, in the absence of external forces, for which thevelocity and diffusive fluxes vanish and the electrostatic potential is the solution of a Poisson–Boltzmann equation. When the motion is governed by a small static electric field and smallhydrodynamic and elastic forces, we use O’Brien’s argument to deduce a linearized model.Then we perform the homogenization of these linearized equations for a suitable choice oftime scale. It turns out that the deformation of the porous medium is weakly coupled tothe electrokinetics system in the sense that it does not influence electrokinetics although thelatter one yields an osmotic pressure term in the mechanical equations. As a consequence,the effective tensor satisfies Onsager properties, namely is symmetric positive definite