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Maximum Entropy and Equations of State for Random Cellular Structures

  • N. Rivier
Part of the Fundamental Theories of Physics book series (FTPH, volume 39)

Abstract

Random, space-filling cellular structures (biological tissues, metallurgical grain aggregates, foams, etc) are investigated. Maximum entropy inference under a few constraints yields structural equations of state, relating the size of cells to their topological shape. These relations are known empirically as Lewis’s law in Botany, or Desch’s relation in Metallurgy. Here, the functional form of the constraints is not known a priori, and one takes advantage of this arbitrariness to increase the entropy further. The resulting structural equations of state are independent of priors, they are measurable experimentally and constitute therefore a direct test for the applicability of MaxEnt inference (given that the structure is in statistical equilibrium, a fact which can be tested by another simple relation (Aboav’s law)).

Keywords

Cellular Network Detailed Balance Microscopic Parameter Human Amnion Topological Shape 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • N. Rivier
    • 1
  1. 1.Materials Science DivisionArgonne National LaboratoryArgonneUSA

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