• français
    • English
    français
  • Login
Help
View Item 
  •   Home
  • Laboratoire Mechanics, Surfaces and Materials Processing (MSMP)
  • View Item
  • Home
  • Laboratoire Mechanics, Surfaces and Materials Processing (MSMP)
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Analyses of the Instabilities in the Discretized Diffusion Equations via Information Theory

Article dans une revue avec comité de lecture
Author
BIGERELLE, Maxence
NACEUR, Hakim
1303 Laboratoire d'Automatique, de Mécanique et d'Informatique industrielles et Humaines - UMR 8201 [LAMIH]
IOST, Alain
211915 Mechanics surfaces and materials processing [MSMP]

URI
http://hdl.handle.net/10985/10901
DOI
10.3390/e18040155
Date
2016
Journal
Entropy

Abstract

In a previous investigation (Bigerelle and Iost, 2004), the authors have proposed a physical interpretation of the instability λ = Δt/Δx2 > 1/2 of the parabolic partial differential equations when solved by finite differences. However, our results were obtained using integration techniques based on erf functions meaning that no statistical fluctuation was introduced in the mathematical background. In this paper, we showed that the diffusive system can be divided into sub-systems onto which a Brownian motion is applied. Monte Carlo simulations are carried out to reproduce the macroscopic diffusive system. It is shown that the amount of information characterized by the compression ratio of information of the system is pertinent to quantify the entropy of the system according to some concepts introduced by the authors (Bigerelle and Iost, 2007). Thanks to this mesoscopic discretization, it is proved that information on each sub-cell of the diffusion map decreases with time before the unstable equality λ = 1/2 and increases after this threshold involving an increase in negentropy, i.e., a decrease in entropy contrarily to the second principle of thermodynamics.

Files in this item

Name:
MSMP_ENTROPY_2016_IOST
Size:
1.770Mb
Format:
PDF
View/Open

Collections

  • Laboratoire Mechanics, Surfaces and Materials Processing (MSMP)

Related items

Showing items related by title, author, creator and subject.

  • A multi-scale approach of roughness measurements: Evaluation of the relevant scale 
    Article dans une revue avec comité de lecture
    VAN 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 ...
  • Scratch tests to contribute designing performance maps of multilayer polymeric coatings 
    Article dans une revue avec comité de lecture
    RUDERMANN, Yann; IOST, Alain; BIGERELLE, Maxence (Elsevier, 2011)
    The scratching technique has gained interest in recent times because of the numerous inherent properties implied (adherence, hardness, elasticity, visco-elasticity, cohesion, etc.) during tests. Some singular mechanical ...
  • Relation between entropy, free energy and computational energy 
    Article dans une revue avec comité de lecture
    BIGERELLE, Maxence; ABDEL-AAL, Hisham; IOST, Alain (Inderscience, 2010)
    This paper proposes an isomorphism between the number of accessible states of the system including statistical fluctuation and the optimised size of a computer program set-up by combining the Huffman and R.L.E algebrae. ...
  • Analyse de la rugosité obtenue par un nouveau procédé de tribofinition 
    Article dans une revue avec comité de lecture
    BIGERELLE, Maxence; IOST, Alain; ROCHER, Philippe (Elsevier, 2007)
    Nous proposons dans cet article d'analyser un nouveau procédé de polissage automatique : Ecoclean, qui est développé principalement pour la préparation de prothèses dentaires. En faisant varier les conditions expérimentales ...
  • A new model of the heat transfer in materials: the surfacic potential algorithm 
    Article dans une revue avec comité de lecture
    BIGERELLE, Maxence; BOUNICHANE, Benaamer; HAGEGE, Benjamin; JOURANI, Abdeljalil; IOST, Alain (Inderscience, 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 ...

Browse

All SAMCommunities & CollectionsAuthorsIssue DateCenter / InstitutionThis CollectionAuthorsIssue DateCenter / Institution

Newsletter

Latest newsletterPrevious newsletters

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors

ÉCOLE NATIONALE SUPERIEURE D'ARTS ET METIERS

  • Contact
  • Mentions légales

ÉCOLE NATIONALE SUPERIEURE D'ARTS ET METIERS

  • Contact
  • Mentions légales