laboratoire de physique statistique
 
 
laboratoire de physique statistique

Publications

Rechercher
Martine BEN AMAR 


PHYSICAL REVIEW LETTERS 


6
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 :



 
2011
Mutual Adaptation of a Faraday Instability Pattern with its Flexible Boundaries in Floating Fluid Drops - Pucci, G. and Fort, E. and Ben Amar, M. and Couder, Y.
PHYSICAL REVIEW LETTERS 106 (2011) 
LPS


Abstract : Hydrodynamic instabilities are usually investigated in confined geometries where the resulting spatiotemporal pattern is constrained by the boundary conditions. Here we study the Faraday instability in domains with flexible boundaries. This is implemented by triggering this instability in floating fluid drops. An interaction of Faraday waves with the shape of the drop is observed, the radiation pressure of the waves exerting a force on the surface tension held boundaries. Two regimes are observed. In the first one there is a coadaptation of the wave pattern with the shape of the domain so that a steady configuration is reached. In the second one the radiation pressure dominates and no steady regime is reached. The drop stretches and ultimately breaks into smaller domains that have a complex dynamics including spontaneous propagation.
Contour Instabilities in Early Tumor Growth Models - Ben Amar, M. and Chatelain, C. and Ciarletta, P.
PHYSICAL REVIEW LETTERS 106 (2011) 
LPS


Abstract : Recent tumor growth models are often based on the multiphase mixture framework. Using bifurcation theory techniques, we show that such models can give contour instabilities. Restricting to a simplified but realistic version of such models, with an elastic cell-to-cell interaction and a growth rate dependent on diffusing nutrients, we prove that the tumor cell concentration at the border acts as a control parameter inducing a bifurcation with loss of the circular symmetry. We show that the finite wavelength at threshold has the size of the proliferating peritumoral zone. We apply our predictions to melanoma growth since contour instabilities are crucial for early diagnosis. Given the generality of the equations, other relevant applications can be envisaged for solving problems of tissue growth and remodeling.
Shape Transition in Artificial Tumors: From Smooth Buckles to Singular Creases - Dervaux, Julien and Couder, Yves and Guedeau-Boudeville, Marie-Alice and Ben Amar, Martine
PHYSICAL REVIEW LETTERS 107 (2011) 
LPS


Abstract : Using swelling hydrogels, we study the evolution of a thin circular artificial tumor whose growth is confined at the periphery. When the volume of the outer proliferative ring increases, the tumor loses its initial symmetry and bifurcates towards an oscillatory shape. Depending on the geometrical and elastic parameters, we observe either a smooth large-wavelength undulation of the swelling layer or the formation of sharp creases at the free boundary. Our experimental results as well as previous observations from other studies are in very good agreement with a nonlinear poroelastic model.
 
2010
Self-Contact and Instabilities in the Anisotropic Growth of Elastic Membranes - Stoop, Norbert and Wittel, Falk K. and Ben Amar, Martine and Mueller, Martin Michael and Herrmann, Hans J.
PHYSICAL REVIEW LETTERS 105 (2010) 
LPS


Abstract : We investigate the morphology of thin discs and rings growing in the circumferential direction. Recent analytical results suggest that this growth produces symmetric excess cones ( e cones). We study the stability of such solutions considering self-contact and bending stress. We show that, contrary to what was assumed in previous analytical solutions, beyond a critical growth factor, no symmetric e cone solution is energetically minimal any more. Instead, we obtain skewed e cone solutions having lower energy, characterized by a skewness angle and repetitive spiral winding with increasing growth. These results are generalized to discs with varying thickness and rings with holes of different radii.
 
2008
Morphogenesis of growing soft tissues - Dervaux, Julien and Ben Amar, Martine
PHYSICAL REVIEW LETTERS 101 (2008) 
LPS


Abstract : Recently, much attention has been given to a noteworthy property of some soft tissues: their ability to grow. Many attempts have been made to model this behavior in biology, chemistry, and physics. Using the theory of finite elasticity, Rodriguez has postulated a multiplicative decomposition of the geometric deformation gradient into a growth-induced part and an elastic one needed to ensure compatibility of the body. In order to fully explore the consequences of this hypothesis, the equations describing thin elastic objects under finite growth are derived. Under appropriate scaling assumptions for the growth rates, the proposed model is of the Foppl-von Karman type. As an illustration, the circumferential growth of a free hyperelastic disk is studied.
Conical Defects in Growing Sheets - Mueller, Martin Michael and Ben Amar, Martine and Guven, Jemal
PHYSICAL REVIEW LETTERS 101 (2008) 
LPS


Abstract : A growing or shrinking disc will adopt a conical shape, its intrinsic geometry characterized by a surplus angle phi(e) at the apex. If growth is slow, the cone will find its equilibrium. Whereas this is trivial if phi(e)<= 0, the disc can fold into one of a discrete infinite number of states if phi(e)> 0. We construct these states in the regime where bending dominates and determine their energies and how stress is distributed in them. For each state a critical value of phi(e) is identified beyond which the cone touches itself. Before this occurs, all states are stable; the ground state has twofold symmetry.