laboratoire de physique statistique
 
 
laboratoire de physique statistique

Publications

Rechercher
 
2009
DOI
41
Continuum model of epithelial morphogenesis during Caenorhabditis elegans embryonic elongation - Ciarletta, P. and Ben Amar, M. and Labouesse, M.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 3673379-3400 (2009) 
LPS


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.
DOI
42
Hamiltonian formulation of surfaces with constant Gaussian curvature - Trejo, Miguel and Ben Amar, Martine and Mueller, Martin Michael
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 42 (2009) 
LPS


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.
 
2008
DOI
43
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.
DOI
44
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.
 
2007
DOI
45
Periodic lipidic membrane tubes - Campelo, F. and Allain, J. -M. and Ben Amar, M.
EPL 77 (2007) 
LPS


Abstract : We investigate the formation of two-phase lipidic tubes of membrane in the framework of the Canham-Helfrich model. The two phases have different elastic moduli (bending and Gaussian rigidity), different tensions and a line tension prevents the mixing. For a set of parameters close to experimental values, periodic patterns with arbitrary wavelength can be found numerically. A wavelength selection is detected via the existence of an energy minimum. When the chemical composition induces an important enough size disequilibrium between both phases, a segregation into two half infinite tubes is preferred to a periodic structure. Copyright (C) EPLA, 2007.
DOI
46
On the definition and modeling of incremental, cumulative, and continuous growth laws in morphoelasticity - Goriely, Alain and Ben Amar, Martine
BIOMECHANICS AND MODELING IN MECHANOBIOLOGY 6289-296 (2007) 
LPS


Abstract : In the theory of elastic growth, a growth process is modeled by a sequence of growth itself followed by an elastic relaxation ensuring integrity and compatibility of the body. The description of this process is local in time and only corresponds to an incremental step in the total growth process. As time evolves, these incremental growth steps are compounded and a natural question is the description of the overall cumulative growth and whether a continuous description of this process is possible. These ideas are discussed and further studied in the case of incompressible shells.
DOI
47
Roughness of moving elastic lines: Crack and wetting fronts - Katzav, E. and Adda-Bedia, M. and Ben Amar, M. and Boudaoud, A.
PHYSICAL REVIEW E 76 (2007) 
LPS


Abstract : We investigate propagating fronts in disordered media that belong to the universality class of wetting contact lines and planar tensile crack fronts. We derive from first principles their nonlinear equations of motion, using the generalized Griffith criterion for crack fronts and three standard mobility laws for contact lines. Then we study their roughness using the self-consistent expansion. When neglecting the irreversibility of fracture and wetting processes, we find a possible dynamic rough phase with a roughness exponent of zeta=1/2 and a dynamic exponent of z=2. When including the irreversibility, we conclude that the front propagation can become history dependent, and thus we consider the value zeta=1/2 as a lower bound for the roughness exponent. Interestingly, for propagating contact line in wetting, where irreversibility is weaker than in fracture, the experimental results are close to 0.5, while for fracture the reported values of 0.55-0.65 are higher.