Multiscale measures of equilibrium on finite dynamic systems
Article dans une revue avec comité de lecture
Date
2004Journal
Chaos, Solitons and FractalsRésumé
This article presents a new method for the study of the evolution of dynamic systems based on the notion of quantity of information. The system is divided into elementary cells and the quantity of information is studied with respect to the cell size. We have introduced an analogy between quantity of information and entropy, and defined the intrinsic entropy as the entropy of the whole system independent of the size of the cells. It is shown that the intrinsic entropy follows a Gaussian probability density function (PDF) and thereafter, the time needed by the system to reach equilibrium is a random variable. For a finite system, statistical analyses show that this entropy converges to a state of equilibrium and an algorithmic method is proposed to quantify the time needed to reach equilibrium for a given confidence interval level. A Monte-Carlo simulation of diffusion of A* atoms in A is then provided to illustrate the proposed simulation. It follows that the time to reach equilibrium for a constant error probability, te, depends on the number, n, of elementary cells as: te∝n2.22±0.06. For an infinite system size (n infinite), the intrinsic entropy obtained by statistical modelling is a pertinent characteristic number of the system at the equilibrium.
Fichier(s) constituant cette publication
Cette publication figure dans le(s) laboratoire(s) suivant(s)
Documents liés
Visualiser des documents liés par titre, auteur, créateur et sujet.
-
Article dans une revue avec comité de lectureVAN GORP, Adrien; BIGERELLE, Maxence; GRELLIER, Alain; IOST, Alain; NAJJAR, Denis (Elsevier, 2007)This paper proposes a new multi-scale measurement approach performed to compare the surface roughness and the visual aspect of polished surfaces. In this investigation, five specimens of glass moulds presenting different ...
-
Article dans une revue avec comité de lectureMARTEAU, Julie; BIGERELLE, Maxence; BOUVIER, Salima; IOST, Alain (Wiley-Blackwell: No OnlineOpen, 2014)The goal of this paper is to study the main uses of the residual imprint of the indentation test. It also discusses the different technologies and methods employed in this context. The difficulties encountered when trying ...
-
Article dans une revue avec comité de lectureXIA, Yang; BIGERELLE, Maxence; MARTEAU, Julie; MAZERAN, Pierre-Emmanuel; BOUVIER, Salima; IOST, Alain (Wiley-Blackwell: No OnlineOpen, 2014)A quantitative model is proposed for the estimation of macro-hardness using nanoindentation tests. It decreases the effect of errors related to the non-reproducibility of the nanoindentation test on calculations of ...
-
Article dans une revue avec comité de lectureIOST, Alain; RUDERMAN, Y.; BIGERELLE, Maxence (EDP Sciences, 2005)La caractérisation des propriétés mécaniques des revêtements, et plus particulièrement de leur dureté est d'une grande importance dans le milieu industriel et fait l'objet de nombreuses études. Le plus souvent, la mesure ...
-
Article dans une revue avec comité de lectureNAJJAR, Denis; BIGERELLE, Maxence; MIGAUD, Henri; IOST, Alain (Elsevier, 2005)The degradation of the femoral head roughness caused by scratching is known to increase the wear rate of the polyethylene counterface of the Charnley total hip prostheses and therefore to have an impact on osteolysis. The ...