laboratoire de physique statistique
laboratoire de physique statistique


Measuring order in the isotropic packing of elastic rods - Bayart, E. and Deboeuf, S. and Corson, F. and Boudaoud, A. and Adda-Bedia, M.
EPL 95 (2011) 

Abstract : The packing of elastic bodies has emerged as a paradigm for the study of macroscopic disordered systems. However, progress is hampered by the lack of controlled experiments. Here we consider a model experiment for the isotropic two-dimensional confinement of a rod by a central force. We seek to measure how ordered is a folded configuration and we identify two key quantities. A geometrical characterization is given by the number of superposed layers in the configuration. Using temporal modulations of the confining force, we probe the mechanical properties of the configuration and we define and measure its effective susceptibility. These two quantities may be used to build a statistical framework for packed elastic systems. Copyright (C) EPLA, 2011
A model for hierarchical patterns under mechanical stresses - Corson, F. and Henry, H. and Adda-Bedia, M.

Abstract : We present a model for mechanically-induced pattern formation in growing biological tissues and discuss its application to the development of leaf venation networks. Drawing an analogy with phase transitions in solids, we use a phase field method to describe the transition between two states of the tissue, e.g. the differentiation of leaf veins, and consider a layered system where mechanical stresses are generated by differential growth. We present analytical and numerical results for one-dimensional systems, showing that a combination of growth and irreversibility gives rise to hierarchical patterns. Two-dimensional simulations suggest that such a mechanism could account for the hierarchical, reticulate structure of leaf venation networks, yet point to the need for a more detailed treatment of the coupling between growth and mechanical stresses.
Fluctuations and Redundancy in Optimal Transport Networks - Corson, Francis

Abstract : The structure of networks that provide optimal transport properties has been investigated in a variety of contexts. While many different formulations of this problem have been considered, it is recurrently found that optimal networks are trees. It is shown here that this result is contingent on the assumption of a stationary flow through the network. When time variations or fluctuations are allowed for, a different class of optimal structures is found, which share the hierarchical organization of trees yet contain loops. The transitions between different network topologies as the parameters of the problem vary are examined. These results may have strong implications for the structure and formation of natural networks, as is illustrated by the example of leaf venation networks.
Turning a plant tissue into a living cell froth through isotropic growth - Corson, Francis and Hamant, Olivier and Bohn, Steffen and Traas, Jan and Boudaoud, Arezki and Couder, Yves

Abstract : The forms resulting from growth processes are highly sensitive to the nature of the driving impetus, and to the local properties of the medium, in particular, its isotropy or anisotropy. In turn, these local properties can be organized by growth. Here, we consider a growing plant tissue, the shoot apical meristem of Arabidopsis thaliana. In plants, the resistance of the cell wall to the growing internal turgor pressure is the main factor shaping the cells and the tissues. It is well established that the physical properties of the walls depend on the oriented deposition of the cellulose microfibrils in the extracellular matrix or cell wall; this order is correlated to the highly oriented cortical array of microtubules attached to the inner side of the plasma membrane. We used oryzalin to depolymerize microtubules and analyzed its influence on the growing meristem. This had no short-term effect, but it had a profound impact on the cell anisotropy and the resulting tissue growth. The geometry of the cells became similar to that of bubbles in a soap froth. At a multicellular scale, this switch to a local isotropy induced growth into spherical structures. A theoretical model is presented in which a cellular structure grows through the plastic yielding of its walls under turgor pressure. The simulations reproduce the geometrical properties of a normal tissue if cell division is included. If not, a ``cell froth'' very similar to that observed experimentally is obtained. Our results suggest strong physical constraints on the mechanisms of growth regulation.
Thermal fracture as a framework for quasi-static crack propagation - Corson, F. and Adda-Bedia, M. and Henry, H. and Katzav, E.

Abstract : We address analytically and numerically the problem of crack path prediction in the model system of a crack propagating under thermal loading. We show that one can explain the instability from a straight to a wavy crack propagation by using only the principle of local symmetry and the Griffith criterion. We then argue that the calculations of the stress intensity factors can be combined with the standard crack propagation criteria to obtain the evolution equation for the crack tip within any loading configuration. The theoretical results of the thermal crack problem agree with the numerical simulations we performed using a phase field model. Moreover, it turns out that the phase-field model allows to clarify the nature of the transition between straight and oscillatory cracks which is shown to be supercritical.
Localization through Surface Folding in Solid Foams under Compression - Reis, P. M. and Corson, F. and Boudaoud, A. and Roman, B.

Abstract : We report a combined experimental and theoretical study of the compression of a solid foam coated with a thin elastic film. Past a critical compression threshold, a pattern of localized folds emerges with a characteristic size that is imposed by an instability of the thin surface film. We perform optical surface measurements of the statistical properties of these localization zones and find that they are characterized by robust exponential tails in the strain distributions. Following a hybrid continuum and statistical approach, we develop a theory that accurately describes the nucleation and length scale of these structures and predicts the characteristic strains associated with the localized regions.
In silico leaf venation networks: Growth and reorganization driven by mechanical forces - Corson, Francis and Adda-Bedia, Mokhtar and Boudaoud, Arezki

Abstract : Development commonly involves an interplay between signaling, genetic expression and biophysical forces. However, the relative importance of these mechanisms during the different stages of development is unclear. Leaf venation networks provide a fitting context for the examination of these questions. In mature leaves, venation patterns are extremely diverse, yet their local structure satisfies a universal property: at junctions between veins, angles and diameters are related by a vectorial equation analogous to a force balance. Using a cell proliferation model, were produce in silico the salient features of venation patterns. Provided that vein cells are given different mechanical properties, tensile forces develop along the veins during growth, causing the network to deform progressively. Our results suggest that the local structure of venation networks results from are organization driven by mechanical forces, independently of how veins form. This conclusion is supported by recent observations of vein development in young leaves and by the good quantitative agreement between our simulations and data from mature leaves. (C) 2009 Elsevier Ltd. All rights reserved.
Developmental Patterning by Mechanical Signals in Arabidopsis - Hamant, Olivier and Heisler, Marcus G. and Jonsson, Henrik and Krupinski, Pawel and Uyttewaal, Magalie and Bokov, Plamen and Corson, Francis and Sahlin, Patrik and Boudaoud, Arezki and Meyerowitz, Elliot M. and Couder, Yves and Traas, Jan
SCIENCE 3221650-1655 (2008) 

Abstract : A central question in developmental biology is whether and how mechanical forces serve as cues for cellular behavior and thereby regulate morphogenesis. We found that morphogenesis at the Arabidopsis shoot apex depends on the microtubule cytoskeleton, which in turn is regulated by mechanical stress. A combination of experiments and modeling shows that a feedback loop encompassing tissue morphology, stress patterns, and microtubule- mediated cellular properties is sufficient to account for the coordinated patterns of microtubule arrays observed in epidermal cells, as well as for patterns of apical morphogenesis.