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Random cellular froths in spaces of any dimension and curvature

Aste, T; Rivier, N; (1995) Random cellular froths in spaces of any dimension and curvature. Journal of Physics A: Mathematical and General , 28 (5) 1381 - 1398. 10.1088/0305-4470/28/5/023.

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Abstract

Froth is a random partition of a D-dimensional space by cells. This assembly of cells obeys two fundamental laws: Euler's relation and the condition of maximum vertex figure, imposed by geometry and by topological stability, respectively. These two conditions generate a set of relations between the variables that fully characterize the system topologically. The number of degrees of freedom of the system and a set of useful independent variables, the 'even valences', have been found. The influence of the space dimension and curvature on the range of variability of these valences is discussed and, up to D=5, the regions in valence space corresponding to differently curved froths are calculated explicitly.

Type:Article
Title:Random cellular froths in spaces of any dimension and curvature
DOI:10.1088/0305-4470/28/5/023
UCL classification:UCL > School of BEAMS > Faculty of Engineering Science > Computer Science

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