Amplitude equations for weakly nonlinear surface waves in variational problems

Among hyperbolic Initial Boundary Value Problems (IBVP), those coming from a variational principle 'generically' admit linear surface waves, as was shown by Serre [J. Funct. Anal. 2006]. At the weakly nonlinear level, the behavior of surface waves is expected to be governed by an amplitude equation that can be derived by means of a formal asymptotic expansion. Amplitude equations for weakly nonlinear surface waves were introduced by Lardner [Int. J. Engng Sci. 1983], Parker and co-workers [J. Elasticity 1985] in the framework of elasticity, and by Hunter [Contemp. Math. 1989] for abstract hyperbolic problems. They consist of nonlocal evolution equations involving a complicated, bilinear Fourier multiplier in the direction of propagation along the boundary. It was shown by the authors in an earlier work [Arch. Ration. Mech. Anal. 2012] that this multiplier, or kernel, inherits some algebraic properties from the original IBVP. These properties are crucial for the (local) well-posedness of the amplitude equation, as shown together with Tzvetkov [Adv. Math., 2011]. Properties of amplitude equations are revisited here in a somehow simpler way, for surface waves in a variational setting. Applications include various physical models, from elasticity of course to the director-field system for liquid crystals introduced by Saxton [Contemp. Math. 1989] and studied by Austria and Hunter [Commun. Inf. Syst. 2013]. Similar properties are eventually shown for the amplitude equation associated with surface waves at reversible phase boundaries in compressible fluids, thus completing a work initiated by Benzoni-Gavage and Rosini [Comput. Math. Appl. 2009]

Financial Constraints on New Firms:Looking for Regional Disparities

Financial constraints affecting new firms are some of the factors most cited forimpeding entrepreneurial dynamics from flourishing. This article introduces the problem ofregional patterns of financial constraints. The research is conducted with regard to the Frenchregions and the new French firms being tracked at the firm level. It refers to entrepreneurialprojects that are concretized in new firms. General entrepreneurial intentions in the Frenchpopulation that are aborted due to financial constraints are not reported. The point is ofimportance as the firm financing conditions are considered. First, an assessment of theregional banking activity leads to the conclusion of a relatively homogeneous situation, theactivity in the core-region Île-de-France appearing however more contrasted. Second, thefinancial constraints affecting new firms are distinguished according to a four-case typologyof credit rationing. It appears, inter alia, that a majority of firms is not facing credit rationing,but also that a non-negligible share is “self-constrained”. The classification is, third andfinally, differentiated according to the regions. Despite the relatively homogeneous bankingsupply, some differences may still be at work. The explanations are hypothetical at this stage butevidence suggests that the regional dimension should definitely deserve further attention.Financial constraints; Credit rationing; New Firms; Regional Disparities

Does the regional dimension matter as regards finance and entrepreneurship?

This article investigates the interrelationships between finance and entrepreneurship by exploring regional discrepancies in France. The focus is (1) on regional differences in financial relationships, (2) on the way these relations influence financial constraints on new firms and (3) on the complementary/substitutable effects between funds. No path of exclusion is identified. Rather, firms that are self-constraining or suffer from a weak credit rationing are the ones that later on develop intensive relationships with banks. Substitution exists in almost all the French regions. Results suggest the departure point of an original pecking order theory according to the entrepreneurial intensity of regions.financial constraints, credit rationing, financial relationships, new firms, regional development, regional disparities

L’évaluation régionale de la politique de la santé et du bien-être. Quand une nouvelle perspective s’impose

Cinq ans après le dévoilement de la Politique de la santé et du bien-être (PSBE), quel était le chemin parcouru? Quels étaient les ajustements à faire? Voilà les questions de départ de notre évaluation. Les approches habituellement employées pour l'évaluation de politiques ne s'avérant d'aucun secours pour y répondre, il fallait trouver une méthode de remplacement. Il a donc été nécessaire de faire preuve de créativité pour réaliser une étude qui soit rigoureuse tout en permettant aux décideurs d'ajuster le tir avant la date d'expiration du délai pour réaliser les objectifs, soit 2002. Le présent article fait le point sur les considérations méthodologiques relatives à la démarche élaborée pour l'évaluation formative de la PSBE en Montérégie.Five years after the appearance of the Policy on Health and Well-Being, what has been achieved? What adjustments are required? These were the preliminary questions our evaluation had to address. But traditional methods used to evaluate policies were of no help in answering them. Therefore, we had to be innovative as our study had to be both rigorous and easy to use by decision-makers who have to make adjustments before the deadline for the attainment of the objectives (i.e. 2002). This paper addresses the methodological issues related to the formative evaluation of the policy in Montérégie

Shell structure and few-nucleon removal in intranuclear cascade

It is well known that intranuclear-cascade models generally overestimate the cross sections for one-proton removal from heavy, stable nuclei by a high-energy proton beam, but they yield reasonable predictions for one-neutron removal from the same nuclei and for one-nucleon removal from light targets. We use simple shell-model calculations to investigate the reasons of this deficiency. We find that a correct description of the neutron skin and of the energy density in the nuclear surface is crucial for the aforementioned observables. Neither ingredient is sufficient if taken separately.Comment: Presented at the 11th International Spring Seminar on Nuclear Physics. To be published in Journal of Physics: Conference Serie

Trusting Computations: a Mechanized Proof from Partial Differential Equations to Actual Program

Computer programs may go wrong due to exceptional behaviors, out-of-bound array accesses, or simply coding errors. Thus, they cannot be blindly trusted. Scientific computing programs make no exception in that respect, and even bring specific accuracy issues due to their massive use of floating-point computations. Yet, it is uncommon to guarantee their correctness. Indeed, we had to extend existing methods and tools for proving the correct behavior of programs to verify an existing numerical analysis program. This C program implements the second-order centered finite difference explicit scheme for solving the 1D wave equation. In fact, we have gone much further as we have mechanically verified the convergence of the numerical scheme in order to get a complete formal proof covering all aspects from partial differential equations to actual numerical results. To the best of our knowledge, this is the first time such a comprehensive proof is achieved.Comment: N° RR-8197 (2012). arXiv admin note: text overlap with arXiv:1112.179