laboratoire de physique statistique
 
 
laboratoire de physique statistique

Publications

Rechercher
Martine BEN AMAR 


NEW JOURNAL OF PHYSICS 


2
P U B L I C A T I O N S

S E L E C T I O N N E R
P A R M I :



 
2012
Petal shapes of sympetalous flowers: the interplay between growth, geometry and elasticity - Ben Amar, Martine and Mueller, Martin Michael and Trejo, Miguel
NEW JOURNAL OF PHYSICS 14 (2012) 
LPS


Abstract : The growth of a thin elastic sheet imposes constraints on its geometry such as its Gaussian curvature KG. In this paper, we construct the shapes of sympetalous bell-shaped flowers with a constant Gaussian curvature. Minimizing the bending energies of both the petal and the veins, we are able to predict quantitatively the global shape of these flowers. We discuss two toy problems where the Gaussian curvature is either negative or positive. In the former case, the axisymmetric pseudosphere turns out to mimic the correct shape before edge curling; in the latter case, singularities of the mathematical surface coincide with strong veins. Using a variational minimization of the elastic energy, we find that the optimal number for the veins is either four, five or six, a number that is deceptively close to the statistics on real flowers in nature.
 
2011
Emergence of microstructural patterns in skin cancer: a phase separation analysis in a binary mixture - Chatelain, C. and Balois, T. and Ciarletta, P. and Ben Amar, M.
NEW JOURNAL OF PHYSICS 13 (2011) 
LPS


Abstract : Clinical diagnosis of skin cancers is based on several morphological criteria, among which is the presence of microstructures (e.g. dots and nests) sparsely distributed within the tumour lesion. In this study, we demonstrate that these patterns might originate from a phase separation process. In the absence of cellular proliferation, in fact, a binary mixture model, which is used to represent the mechanical behaviour of skin cancers, contains a cell-cell adhesion parameter that leads to a governing equation of the Cahn-Hilliard type. Taking into account a reaction-diffusion coupling between nutrient consumption and cellular proliferation, we show, with both analytical and numerical investigations, that two-phase models may undergo a spinodal decomposition even when considering mass exchanges between the phases. The cell-nutrient interaction defines a typical diffusive length in the problem, which is found to control the saturation of a growing separated domain, thus stabilizing the microstructural pattern. The distribution and evolution of such emerging cluster morphologies, as predicted by our model, are successfully compared to the clinical observation of microstructural patterns in tumour lesions.