A Hamilton–Jacobi method to describe the evolutionary equilibria in heterogeneous environments and with non-vanishing effects of mutations

In this note, we characterize the solution to a system of elliptic integro-differential equations describing a phenotypically structured population subject to mutation, selection, and migration. Generalizing an approach based on the Hamilton–Jacobi equations, we identify the dominant terms of the solution when the mutation term is small (but nonzero). This method was initially used, for different problems arisen from evolutionary biology, to identify the asymptotic solutions, while the mutations vanish, as a sum of Dirac masses. A key point is a uniqueness property related to the weak KAM theory. This method allows us to go further than the Gaussian approximation commonly used by biologists, and is an attempt to fill the gap between the theories of adaptive dynamics and quantitative genetics.     

A sufficient condition for a rational differential operator to generate an integrable system

For a rational differential operator \({L=AB^{-1}}\), the Lenard–Magri scheme of integrability is a sequence of functions \({F_n, n \geq 0}\), such that (1) \({B(F_{n+1})=A(F_n)}\) for all \({n \geq 0}\) and (2) the functions \({B(F_n)}\) pairwise commute. We show that, assuming that property (1) holds and that the set of differential orders of \({B(F_n)}\) is unbounded, property (2) holds if and only if L belongs to a class of rational operators that we call integrable. If we assume moreover that the rational operator L is weakly non-local and preserves a certain splitting of the algebra of functions into even and odd parts, we show that one can always find such a sequence (F _n ) starting from any function in Ker B. This result gives some insight in the mechanism of recursion operators, which encode the hierarchies of the corresponding integrable equations.     

Identification of the scatter in high cycle fatigue from temperature measurementsIdentification de la dispersion des limites d'endurance à l'aide d'un essai d'échauffement.

It is proposed to determine the scatter in a Wöhler diagram by analyzing temperature changes induced by microplasticity. A unified framework is introduced to study both phenomena. The identification procedure is applied to a dual-phase steel. To cite this article: C. Doudard et al., C. R. Mecanique 332 (2004).     

A homogenised vibratory model for predicting the acoustic properties of hollow brick walls

The prediction and the physical understanding of sound transmission through masonry walls made of hollow bricks remain an open question. To solve this problem a semi-analytical approach is proposed. The inhomogeneous structures of the brick wall are homogenised and a simplified analytical model is established to calculate the transmission loss of an equivalent finite and multilayered anisotropic plate. An efficient numerical homogenisation technique is derived to define the equivalent anisotropic brick. This process only needs the knowledge of the elastic tensor of the brick material that has been determined using ultrasonic measurements. The features of the simplified brick wall have been then investigated through Lamb waves dispersion curves. Finally, the model has been used to explain the transmission loss curve of a wall and a good agreement between predictions and test data is obtained.     

Controlled synthesis of polyepichlorohydrin with pendant cyclic carbonate functions for isocyanate‐free polyurethane networks

Poly(allyl glycidyl ether) and poly(allyl glycidyl ether‐co‐epichlorohydrin) were prepared by monomer‐activated anionic polymerization. Quantitative and controlled polymerization of allyl glycidyl ether (AGE) giving high molar mass polyether was achieved in a few hours at room temperature in toluene using tetraoctylammonium salt as initiator in presence of an excess of triisobutylaluminum ([i‐Bu₃Al]/[NOct₄Br] = 2?4). Following the same polymerization route, the copolymerization of AGE and epichlorohydrin yields in a living‐like manner gradient‐type copolymers with controlled molar masses. Chemical modification of the pendant allyl group into cyclic carbonate was then investigated and the corresponding polymers were used as precursors for the isocyanate‐free synthesis of polyurethane networks in presence of a diamine. Formation of crosslinked materials was followed and characterized by infrared and differential scanning calorimetry. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Finiteness theorems for the Picard objects of an algebraic stack

We prove some finiteness theorems for the Picard functor of an algebraic stack, in the spirit of SGA 6, exp. XII and XIII. In particular, we give a stacky version of Raynaud?s relative representability theorem, we give sufficient conditions for the existence of the torsion component of the Picard functor, and for the finite generation of the Néron–Severi groups or of the Picard group itself. We give some examples and applications. In Appendix A, we prove the semicontinuity theorem for a (non-necessarily tame) algebraic stack.     

A GRASP-based approach for technicians and interventions scheduling for telecommunications

The Technicians and Interventions Scheduling Problem for Telecommunications embeds the scheduling of interventions, the assignment of teams to interventions and the assignment of technicians to teams. Every intervention is characterized, among other attributes, by a priority. The objective of this problem is to schedule interventions such that the interventions with the highest priority are scheduled at the earliest time possible while satisfying a set of constraints like the precedence between some interventions and the minimum number of technicians needed with the required skill levels for the intervention. We present a Greedy Randomized Adaptive Search Procedure (GRASP) for solving this problem. In the proposed implementation, we integrate learning to the GRASP framework in order to generate good-quality solutions using information brought by previous ones. We also compute lower bounds and present experimental results that validate the effectiveness of this approach.