An elasto-visco-plastic model for immortal foams or emulsions

A variety of complex fluids consist in soft, round objects (foams, emulsions, assemblies of copolymer micelles or of multilamellar vesicles -- also known as onions). Their dense packing induces a slight deviation from their prefered circular or spherical shape. As a frustrated assembly of interacting bodies, such a material evolves from one conformation to another through a succession of discrete, topological events driven by finite external forces. As a result, the material exhibits a finite yield threshold. The individual objects usually evolve spontaneously (colloidal diffusion, object coalescence, molecular diffusion), and the material properties under low or vanishing stress may alter with time, a phenomenon known as aging. We neglect such effects to address the simpler behaviour of (uncommon) immortal fluids: we construct a minimal, fully tensorial, rheological model, equivalent to the (scalar) Bingham model. Importantly, the model consistently describes the ability of such soft materials to deform substantially in the elastic regime (be it compressible or not) before they undergo (incompressible) plastic creep -- or viscous flow under even higher stresses.Comment: 69 pages, 29 figure

Colloquium: Mechanical formalisms for tissue dynamics

The understanding of morphogenesis in living organisms has been renewed by tremendous progressin experimental techniques that provide access to cell-scale, quantitative information both on theshapes of cells within tissues and on the genes being expressed. This information suggests that ourunderstanding of the respective contributions of gene expression and mechanics, and of their crucialentanglement, will soon leap forward. Biomechanics increasingly benefits from models, which assistthe design and interpretation of experiments, point out the main ingredients and assumptions, andultimately lead to predictions. The newly accessible local information thus calls for a reflectionon how to select suitable classes of mechanical models. We review both mechanical ingredientssuggested by the current knowledge of tissue behaviour, and modelling methods that can helpgenerate a rheological diagram or a constitutive equation. We distinguish cell scale ("intra-cell")and tissue scale ("inter-cell") contributions. We recall the mathematical framework developpedfor continuum materials and explain how to transform a constitutive equation into a set of partialdifferential equations amenable to numerical resolution. We show that when plastic behaviour isrelevant, the dissipation function formalism appears appropriate to generate constitutive equations;its variational nature facilitates numerical implementation, and we discuss adaptations needed in thecase of large deformations. The present article gathers theoretical methods that can readily enhancethe significance of the data to be extracted from recent or future high throughput biomechanicalexperiments.Comment: 33 pages, 20 figures. This version (26 Sept. 2015) contains a few corrections to the published version, all in Appendix D.2 devoted to large deformation

Morphology and genetics reveal an intriguing pattern of differentiation at a very small geographic scale in a bird species, the forest thrush Turdus lherminieri.

12 pagesInternational audienceMobile organisms are expected to show population differentiation only over fairly large geographical distances. However, there is growing evidence of discrepancy between dispersal potential and realized gene flow. Here we report an intriguing pattern of differentiation at a very small spatial scale in the forest thrush (Turdus lherminieri), a bird species endemic to the Lesser Antilles. Analysis of 331 individuals from 17 sampling sites distributed over three islands revealed a clear morphological and genetic differentiation between these islands isolated by 40-50 km. More surprisingly, we found that the phenotypic divergence between the two geographic zones of the island of Guadeloupe was associated with a very strong genetic differentiation (Fst from 0.073-0.153), making this pattern a remarkable case in birds given the very small spatial scale considered. Molecular data (mitochondrial control region sequences and microsatellite genotypes) suggest that this strong differentiation could have occurred in situ, although alternative hypotheses cannot be fully discarded. This study suggests that the ongoing habitat fragmentation, especially in tropical forests, may have a deeper impact than previously thought on avian populations