Multiscale measures of equilibrium on finite dynamic systems
Type
Articles dans des revues avec comité de lectureDate
2004Journal
Chaos, Solitons & 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 MonteCarlo 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.

VAN GORP, Adrien; BIGERELLE, Maxence; GRELLIER, Alain; IOST, Alain; NAJJAR, Denis (ELSEVIER, 2007)This paper proposes a new multiscale 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 ...

BIGERELLE, Maxence; BOUNICHANE, Benaamer; HAGEGE, Benjamin; JOURANI, Abdeljalil; IOST, Alain (Inderscience Enterprises Ltd., 2010)This paper proposes a new simulation method of thermal transfers based on the concepts of Brownian motion via the theory of potential and the characteristics of materials. In our simulation the particles take their origins ...

BIGERELLE, Maxence; IOST, Alain (ELSEVIER, 2004)This paper comments upon some statistical aspects of the slit island method which is widely used to calculate the fractal dimension of fractured surfaces or of materials’ features like grain geometry. If a noise is introduced ...

FOURNIER, Benjamin; RUPIN, Nicolas; BIGERELLE, Maxence; NAJJAR, Denis; IOST, Alain; WILCOX, R (ELSEVIER, 2007)The method of moments is a popular technique for estimating the parameters of a generalized lambda distribution (GLD), but published results suggest that the percentile method gives superior results. However, the percentile ...

BIGERELLE, Maxence; VAN GORP, Adrien; IOST, Alain (Willey, 2008)The roughness of polymer surfaces is often investigated to guarantee both the surface integrity and the surface functionality. One of the major problems in roughness measurement analyses consists in determining both the ...