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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Statistical mechanics of two-dimensional shuffled foams: prediction of the correlation between geometry and topology

## Statistical mechanics of two-dimensional shuffled foams: prediction of the correlation between geometry and topologyAdd to your list(s) Download to your calendar using vCal - Durand, M (Universit Paris Diderot)
- Tuesday 25 February 2014, 11:45-12:05
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact Mustapha Amrani. Foams and Minimal Surfaces Co-authors: S. Ataei Talebi (Universit Grenoble 1), S. Cox (Aberystwyth University), F. Graner (Universit Paris Diderot), J. Kfer (Universit Lyon 1), C. Quilliet (Universit Grenoble 1) Two-dimensional foams are characterised by their number of bubbles, $N_{}$, area distribution, $p(A)$, and number-of-sides distribution, $p(n)$. When the liquid fraction is very low (``dry’’ foams), their bubbles are polygonal, with shapes that are locally governed by the laws of Laplace and Plateau. Bubble size distribution and packing (or ``topology”) are crucial in determining extit{e.g.} rheological properties or coarsening rate. When a foam is shuffled (either mechanically or thermally), $N_{}$ and $p(A)$ remain fixed, but bubbles undergo ``T1’’ neighbour changes, which induce a random exploration of the foam configurations. We explore the relation between the distributions of bubble number-of-sides (topology) and bubble areas (geometry). We develop a statistical model which takes into account physical ingredients and space-filling constraintes. The model predicts that the mean number of sides of a bubble with area $A$ within a foam sample with moderate size dispersity is given by: $$ar{n}(A) = 3left(1+dfrac{ qrt{A}}{langle qrt{A}
angle}
ight),$$ where $langle .
angle$ denotes the average over all bubbles in the foam. The model also relates the extit{topological disorder} $ Delta n / langle n
angle = qrt{langle n At the other extreme, when approaching the perfectly regular honeycomb pattern, we identify and quantitatively discuss a crystallisation mechanism whereby topological disorder vanishes. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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