Maximum entropy and equations of state for random cellular structures

Conference · Sun Jan 01 04:00:00 EST 1989

DOI:https://doi.org/10.1007/978-94-009-0683-9_18· OSTI ID:5490331

Rivier, N

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 now known as 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)). 23 refs., 2 figs., 1 tab.

• Research Organization: Argonne National Lab., IL (USA)
• Sponsoring Organization: DOE/ER
• DOE Contract Number: W-31109-ENG-38
• OSTI ID: 5490331
• Report Number(s): CONF-8908179-2; ON: DE90002840
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
360102 -- Metals & Alloys-- Structure & Phase Studies
360602* -- Other Materials-- Structure & Phase Studies
99 GENERAL AND MISCELLANEOUS
990230 -- Mathematics & Mathematical Models-- (1987-1989)
BODY
COLLOIDS
CRYSTALLOGRAPHY
DISPERSIONS
ELEMENTS
ENTROPY
EQUATIONS
EQUATIONS OF STATE
FOAMS
MATHEMATICS
METALS
PHYSICAL PROPERTIES
STATISTICS
THERMODYNAMIC PROPERTIES
THERMODYNAMICS
TISSUES