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Stage M2 2016-2017: Uncovering shuffling mechanisms

During at least four centuries, cellular patterns ranging from foams to biological tissues have attracted scientists and artists. The fascination they exert lies in the balance between small-scale regularities and global disorder. Mathematical quantitative descriptions of these patterns have alternatively emphasised the cell size, curvatures and angles (geometry) or the cell number of sides and neighbour relationships (topology), trying to establish correlations.

We propose to use statistical physics to investigate physical mechanisms underlying the observed disorders. We will build upon our two recent successes. First, analytically, within a mean field approximation (top-down approach), we have reproduced without any adjusting parameter the correlation between cell size and number of sides in a shuffled foam [1]. Second, numerically, we have developed a computer simulation (bottom-up approach) of shuffled cellular patterns which is now both realistic (see Figure) and efficient [2]. By combining both approaches, we are now able to investigate in detail the correlations in such systems.

Mixing large and small cells. From left to right: an increasing ratio of large to small size yields an increasing disorder. Colors label the cell side numbers, with hexagons in yellow.

For an internship : At short term, the candidate will simulate shuffled patterns. She/he will quantify different variables such as size, number of sides, or positional and orientational order in 1, 2, or 3 dimensions. She/he will then quantify the correlations between cells at both small and large scales, first using existing characterisations, and then developing new ones.

For a PhD : At long term, the candidate will compare mechanical vs thermal shuffling methods. She/he will quantify both the shuffling dynamics and the final shuffled state. She/he will then investigate other shuffling mechanisms such as those acting within biological tissues in response to membrane activity as well as to cell division, birth or death. She/he will study how the correlations and the parameters investigated during the internship evolve, starting from a well ordered hexagonal pattern. Finally, she/he will simulate the mixture of two cell sizes, or the mixture of two cell types, which should display a rich variety of behaviours.

[1] Durand M. et al., ``Statistical mechanics of two-dimensional shuffled foams: Prediction of the correlation between geometry and topology’’, Physical Review Letters, 107, 168304 (2011).

[2] Durand M. and Guesnet E., ``An efficient cellular Potts model algorithm that forbids cell fragmentation’’, Computer Physics Communications 208, 54-63 (2016).

Profile: physicist or engineer; statistical physics, programming, cross-disciplinary research.

Contact: Marc.Durand (at) (room 710A, Condorcet building), Francois.Graner (at)

PDF - 252.8 kb


Materials and Soft Matter, Biofluidics, Foams, bubbles, drops, emulsions, Morphogenesis, embryogenesis, development, collective motion, self-organization, Out of equilibrium dynamic systems and nonlinear physics, DURAND Marc, Proposition de stage ou de thèse, GRANER François, Ancienne proposition

Contact : Published on / Publié le 26 October 2016