laboratoire de physique statistique
laboratoire de physique statistique


Suction in Darcy and Stokes interfacial flows: Maximum growth rate versus minimum dissipation - Ben Amar, M. and Boudaoud, A.

Abstract : Two-dimensional flows with suction or mass loss are investigated within Darcy's or Stokes' framework. Examples include a Hele-Shaw cell with a lifted plate or extraction of lipids from a lipid bilayer. An initially circular patch ret-racts due to the suction and might undergo an instability whereby it becomes undulating. The selection of the wavelength of undulations is investigated with the help of an extremum principle, the minimization of the generalized dissipation, from which derive the flow equations.
Morphogenesis of thin hyperelastic plates: A constitutive theory of biological growth in the Foppl-von Karman limit - Dervaux, Julien and Ciarletta, Pasquale and Ben Amar, Martine

Abstract : The shape of plants and other living organisms is a crucial element of their biological functioning. Morphogenesis is the result of complex growth processes involving biological, chemical and physical factors at different temporal and spatial scales. This study aims at describing stresses and strains induced by the production and reorganization of the material. The mechanical properties of soft tissues are modeled within the framework of continuum mechanics in finite elasticity. The kinematical description is based on the multiplicative decomposition of the deformation gradient tensor into an elastic and a growth term. Using this formalism, the authors have studied the growth of thin hyperelastic samples. Under appropriate assumptions, the dimensionality of the problem can be reduced, and the behavior of the plate is described by a two-dimensional surface. The results of this theory demonstrate that the corresponding equilibrium equations are of the Foppl-von Karman type where growth acts as a source of mean and Gaussian curvatures. Finally, the cockling of paper and the rippling of a grass blade are considered as two examples of growth-induced pattern formation. (C) 2008 Published by Elsevier Ltd.
Local Membrane Mechanics of Pore-Spanning Bilayers - Mey, Ingo and Stephan, Milena and Schmitt, Eva K. and Mueller, Martin Michael and Ben Amar, Martine and Steinem, Claudia and Janshoff, Andreas

Abstract : The mechanical behavior of lipid bilayers; spanning the pores of highly ordered porous silicon substrates was scrutinized by local indentation experiments as a function of surface functionalization, lipid composition, solvent content, indentation velocity, and pore radius. Solvent-containing nano black lipid membranes (nano-BLMs) as well as solvent-free pore-spanning bilayers were imaged by fluorescence and atomic force microscopy prior to force curve acquisition, which allows distinguishing between membrane-covered and uncovered pores. Force indentation curves on pore-spanning bilayers attached to functionalized hydrophobic porous silicon substrates reveal a predominately linear response that is mainly attributed to prestress in the membranes. This is in agreement with the observation that indentation leads to membrane lysis well below 5\% area dilatation. However, membrane bending and lateral tension dominate over prestress and stretching if solvent-free supported membranes obtained from spreading giant liposomes on hydrophilic porous silicon are indented. An elastic regime diagram is presented that readily allows determining the dominant contribution to the mechanical response upon indentation as a function of load and pore radius.
Continuum model of epithelial morphogenesis during Caenorhabditis elegans embryonic elongation - Ciarletta, P. and Ben Amar, M. and Labouesse, M.

Abstract : The purpose of this work is to provide a biomechanical model to investigate the interplay between cellular structures and the mechanical force distribution during the elongation process of Caenorhabditis elegans embryos. Epithelial morphogenesis drives the elongation process of an ovoid embryo to become a worm-shaped embryo about four times longer and three times thinner. The overall anatomy of the embryo is modelled in the continuum mechanics framework from the structural organization of the subcellular filaments within epithelial cells. The constitutive relationships consider embryonic cells as homogeneous materials with an active behaviour, determined by the non-muscle myosin II molecular motor, and a passive viscoelastic response, related to the directional properties of the filament network inside cells. The axisymmetric elastic solution at equilibrium is derived by means of the incompressibility conditions, the continuity conditions for the overall embryo deformation and the balance principles for the embryonic cells. A particular analytical solution is proposed from a simplified geometry, demonstrating the mechanical role of the microtubule network within epithelial cells in redistributing the stress from a differential contraction of circumferentially oriented actin filaments. The theoretical predictions of the biomechanical model are discussed within the biological scenario proposed through genetic analysis and pharmacological experiments.
Hamiltonian formulation of surfaces with constant Gaussian curvature - Trejo, Miguel and Ben Amar, Martine and Mueller, Martin Michael

Abstract : Dirac's method for constrained Hamiltonian systems is used to describe surfaces of constant Gaussian curvature. A geometrical free energy, for which these surfaces are equilibrium states, is introduced and interpreted as an action. An equilibrium surface can then be generated by the evolution of a closed space curve. Since the underlying action depends on second derivatives, the velocity of the curve and its conjugate momentum must be included in the set of phase-space variables. Furthermore, the action is linear in the acceleration of the curve and possesses a local symmetry-reparametrization invariance-which implies primary constraints in the canonical formalism. These constraints are incorporated into the Hamiltonian through Lagrange multiplier functions that are identified as the components of the acceleration of the curve. The formulation leads to four first-order partial differential equations, one for each canonical variable. With the appropriate choice of parametrization, only one of these equations has to be solved to obtain the surface which is swept out by the evolving space curve. To illustrate the formalism, several evolutions of pseudospherical surfaces are discussed.