Multiscale measures of equilibrium on finite dynamic systems
Article dans une revue avec comité de lecture
Date
2004Journal
Chaos, Solitons and FractalsAbstract
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.
Files in this item
Related items
Showing items related by title, author, creator and subject.
-
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 ...
-
Communication avec acteVAN GORP, Adrien; BIGERELLE, Maxence; IOST, Alain (Université de Poitiers, 2007)L’analyse de la rugosité des surfaces consiste à séparer les défauts à différents ordres ou types correspondant à la forme, l’ondulation et la rugosité. La norme appliquée aux cas courants utilise un filtrage gaussien pour ...
-
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 lectureBIGERELLE, Maxence; NAJJAR, Denis; MATHIA, Thomas; IOST, Alain; COOREVITS, Thierry; ANSELME, Karine (Elsevier, 2013)Knowing that a surface or profile can be characterized by numerous roughness parameters, the objective of this investigation was to present a methodology which aims to determine quantitatively and without preconceived ...
-
Article dans une revue avec comité de lectureBIGERELLE, Maxence; IOST, Alain (Elsevier, 2007)A numerical technique was proposed to plot the Abbott curve and to compute its associated parameters defined by the DIN 4776 and ISO 13565 norms. These parameters were then extended and applied to non-sigmoid Abbott curves. ...