Paul Sabatier University

About: Paul Sabatier University is a education organization based out in Toulouse, France. It is known for research contribution in the topics: Population & Adipose tissue. The organization has 15431 authors who have published 23386 publications receiving 858364 citations.

On the breakdown of boundary layer streaks

Abstract: A scenario of transition to turbulence likely to occur during the development of natural disturbances in a flat-plate boundary layer is studied. The perturbations at the leading edge of the flat plate that show the highest potential for transient energy amplication consist of streamwise aligned vortices. Due to the lift-up mechanism these optimal disturbances lead to elongated streamwise streaks downstream, with signicant spanwise modulation. Direct numerical simulations are used to follow the nonlinear evolution of these streaks and to verify secondary instability calculations. The theory is based on a linear Floquet expansion and focuses on the temporal, inviscid instability of these flow structures. The procedure requires integration in the complex plane, in the coordinate direction normal to the wall, to properly identify neutral modes belonging to the discrete spectrum. The streak critical amplitude, beyond which streamwise travelling waves are excited, is about 26% of the free-stream velocity. The sinuous instability mode (either the fundamental or the subharmonic, depending on the streak amplitude) represents the most dangerous disturbance. Varicose waves are more stable, and are characterized by a critical amplitude of about 37%. Stability calculations of streamwise streaks employing the shape assumption, carried out in a parallel investigation, are compared to the results obtained here using the nonlinearly modied mean elds; the need to consider a base flow which includes mean flow modication and harmonics of the fundamental streak is clearly demonstrated.

Possibility Theory, Probability Theory and Multiple-Valued Logics: A Clarification

Abstract: There has been a long-lasting misunderstanding in the literature of artificial intelligence and uncertainty modeling, regarding the role of fuzzy set theory and many-valued logics. The recurring question is that of the mathematical and pragmatic meaningfulness of a compositional calculus and the validity of the excluded middle law. This confusion pervades the early developments of probabilistic logic, despite early warnings of some philosophers of probability. This paper tries to clarify this situation. It emphasizes three main points. First, it suggests that the root of the controversies lies in the unfortunate confusion between degrees of belief and what logicians call “degrees of truth”. The latter are usually compositional, while the former cannot be so. This claim is first illustrated by laying bare the non-compositional belief representation embedded in the standard propositional calculus. It turns out to be an all-or-nothing version of possibility theory. This framework is then extended to discuss the case of fuzzy logic versus graded possibility theory. Next, it is demonstrated that any belief representation where compositionality is taken for granted is bound to at worst collapse to a Boolean truth assignment and at best to a poorly expressive tool. Lastly, some claims pertaining to an alleged compositionality of possibility theory are refuted, thus clarifying a pervasive confusion between possibility theory axioms and fuzzy set basic connectives.

Generalized Hessian matrix and second-order optimality conditions for problems with C 1,1 data

Abstract: In this paper, we present a generalization of the Hessian matrix toC 1,1 functions, i.e., to functions whose gradient mapping is locally Lipschitz. This type of function arises quite naturally in nonlinear analysis and optimization. First the properties of the generalized Hessian matrix are investigated and then some calculus rules are given. In particular, a second-order Taylor expansion of aC 1,1 function is derived. This allows us to get second-order optimality conditions for nonlinearly constrained mathematical programming problems withC 1,1 data.

Physics and chemistry in a glow dielectric barrier discharge at atmospheric pressure: diagnostics and modelling

Abstract: Glow dielectric barrier discharge (GDBD) appears as an attractive solution to realise an atmospheric pressure cold plasma process suitable for all the surface treatments including thin film coatings. Such a development requires a large understanding of the GDBD physics and chemistry. The objective of this work is to contribute to that understanding. From the analysis of electrical measurements, time resolved emission spectroscopy, short exposure time pictures and numerical model results, it is shown that GDBD which are discharges due to a Townsend initiation and not to a streamer coupling, transit from Townsend to subnormal glow discharge during the current increase. Depending on the maximum current density, they can be considered as a glow or a Townsend discharge. In a glow discharge, the memory effect from one discharge to the following one is based on electrons and ions trapped in the positive column while in a Townsend discharge, it is metastables which stay in the gas and create electrons through cathode secondary emission. In all the cases, the ionisation has to be slowed down by a significant contribution of Penning ionisation.