Biomedical subjects

Y Couder

Publications and source records attributed to Y Couder.

At least 19 recordsLinked to original sources

PubMed2006

Spiral patterns in the packing of flexible structures.

Spiral patterns are found to be a generic feature in close-packed elastic structures. We describe model experiments of compaction of quasi-1D sheets into quasi-2D containers that allow simultaneous quantitative measurements of mechanical forces and observation of folded configurations. Our theoretical approach shows how the interplay between elasticity and geometry leads to a succession of bifurcations responsible for the emergence of such patterns. Both experimental forces and shapes are also reproduced without any adjustable parameters.

Elasticity↗

PubMed2005

Dynamical phenomena: walking and orbiting droplets.

Small drops can bounce indefinitely on a bath of the same liquid if the container is oscillated vertically at a sufficiently high acceleration. Here we show that bouncing droplets can be made to 'walk' at constant horizontal velocity on the liquid surface by increasing this acceleration. This transition yields a new type of localized state with particle-wave duality: surface capillary waves emanate from a bouncing drop, which self-propels by interaction with its own wave and becomes a walker. When two walkers come close, they interact through their waves and this 'collision' may cause the two walkers to orbit around each other.

Journal Article↗

PubMed2005

From bouncing to floating: noncoalescence of drops on a fluid bath.

When a drop of a viscous fluid is deposited on a bath of the same fluid, it is shown that its coalescence with this substrate is inhibited if the system oscillates vertically. Small drops lift off when the peak acceleration of the surface is larger than g. This leads to a steady regime where a drop can be kept bouncing for any length of time. It is possible to inject more fluid into the drop to increase its diameter up to several centimeters. Such a drop remains at the surface, forming a large sunk hemisphere. When the oscillation is stopped, the two fluids remain separated by a very thin air film, which drains very slowly (approximately 30 min). An analysis using lubrication theory accounts for most of the observations.

Journal Article↗

PubMed2005

Side-branch growth in two-dimensional dendrites. II. Phase-field model.

The development of side-branching in solidifying dendrites in a regime of large values of the Peclet number is studied by means of a phase-field model. We have compared our numerical results with experiments of the preceding paper and we obtain good qualitative agreement. The growth rate of each side branch shows a power-law behavior from the early stages of its life. From their birth, branches which finally succeed in the competition process of side-branching development have a greater growth exponent than branches which are stopped. Coarsening of branches is entirely defined by their geometrical position relative to their dominant neighbors. The winner branches escape from the diffusive field of the main dendrite and become independent dendrites.

Journal Article↗

PubMed2005

Hierarchical crack pattern as formed by successive domain divisions. I. Temporal and geometrical hierarchy.

Crack patterns, as they can be observed in the glaze of ceramics or in desiccated mud layers, are formed by successive fractures and divide the two-dimensional plane into distinct domains. On the basis of experimental observation, we develop a description of the geometrical structure of these hierarchical networks. In particular, we show that the essential feature of such a structure can be represented by a genealogical tree of successive domain divisions. This approach allows for a detailed discussion of the relationship between the formation process and the geometric result. We show that--with some restraints--it is possible to reconstruct the history of the system from the geometry of the final pattern.

Journal Article↗

PubMed2005

Hierarchical crack pattern as formed by successive domain divisions. II. From disordered to deterministic behavior.

Hierarchical crack patterns, such as those formed in the glaze of ceramics or in desiccated layers of mud or gel, can be understood as a successive division of two-dimensional domains. We present an experimental study of the division of a single rectangular domain in drying starch and show that the dividing fracture essentially depends on the domain size, rescaled by the thickness of the cracking layer e. Utilizing basic assumptions regarding the conditions of crack nucleation, we show that the experimental results can be directly inferred from the equations of linear elasticity. Finally, we discuss the impact of these results on hierarchical crack patterns, and in particular the existence of a transition from disordered cracks at large scales--the first ones--to a deterministic behavior at small scales--the last cracks.

Journal Article↗

PubMed2005

Side-branch growth in two-dimensional dendrites. I. Experiments.

The dynamics of growth of dendrites' side branches is investigated experimentally during the crystallization of solutions of ammonium bromide in a quasi-two-dimensional cell. Two regimes are observed. At small values of the Peclet number a self-affine fractal forms. In this regime it is known that the mean lateral front grows as t(0.5). Here the length of each individual branch is shown to grow (before being screened off) with a power-law behavior t (alpha(n)). The value of the exponent alpha(n) (0.5< or = alpha(n) < or =1) is determined from the start by the strength of the initial disturbance. Coarsening then takes place, when the branches of small alpha(n) are screened off by their neighbors. The corresponding decay of the growth of a weak branch is exponential and defined by its geometrical position relative to its dominant neighbors. These results show that the branch structure results from a deterministic growth of initially random disturbances. At large values of the Peclet number, the faster of the side branches escape and become independent dendrites. The global structure then covers a finite fraction of the two-dimensional space. The crossover between the two regimes and the spacing of these independent branches are characterized.

Journal Article↗

PubMed2005

Four sided domains in hierarchical space dividing patterns.

The cracks observed in the glaze of ceramics form networks, which divide the 2D plane into domains. It is shown that, on the average, the number of sides of these domains is four. This contrasts with the usual 2D space divisions observed in Voronoi tessellation or 2D soap froths. In the latter networks, the number of sides of a domain coincides with the number of its neighbors, which, according to Euler's theorem, has to be six on average. The four sided property observed in cracks is the result of a formation process which can be understood as the successive divisions of domains with no later reorganization. It is generic for all networks having such hierarchical construction rules. We introduce a "geometrical charge," analogous to Euler's topological charge, as the difference from four of the number of sides of a domain. It is preserved during the pattern formation of the crack pattern.

Journal Article↗

PubMed2003

Morphologies resulting from the directional propagation of fractures.

When growing in a stress gradient, cracks have a directional growth. We investigate here this type of instability in the case of a colloidal gel deposited on a substrate and left to dry. The use of various materials reveals the existence of two distinct types of dynamics. When the crack nucleation is easy a well known situation is reached: an array of periodic fractures forms, which grow parallel to each other and move quasistatically with the stressed region. In contrast, in materials where the crack nucleation is difficult, a subcritical process is observed with the retarded formation of isolated cracks which move faster and which display an arch shaped trajectory. This type of process appears to be generic in all cases where there is delayed nucleation. This is confirmed by experiments on the directional propagation of cracks in thermally stressed glass.

Journal Article↗

PubMed2002

Constitutive property of the local organization of leaf venation networks.

The leaf venation of dicotyledons forms complex patterns. In spite of their large variety of morphologies these patterns have common features. They are formed of a hierarchy of structures, which are connected to form a reticulum. Excellent images of these patterns can be obtained from leaves from which the soft tissues have been removed. A numerical image processing has been developed, specially designed for a quantitative analysis of this type of network. It provides a precise characterization of its geometry. The resulting data reveals a surprising property of reticula's nodes: the angles between vein segments are very well defined and it is shown that they are directly related by the radii of the segments. The relation between radii and angles can be expressed very simply using a phenomenological analogy to mechanics. This local organization principle is universal; all leaf venation patterns studied show the same behavior. The results are compared with physical networks such as fracture arrays or soap froth in terms of hierarchy and reorganization.

Biophysical Phenomena↗

PubMed2000

Dynamics of singularities in a constrained elastic plate.

Large deformations of thin elastic plates usually lead to the formation of singular structures which are either linear (ridges) or pointlike (developable cones). These structures are thought to be generic for crumpled plates, although they have been investigated quantitatively only in simplified geometries. Previous studies have also shown that a large number of singularities are generated by successive instabilities. Here we study, experimentally and numerically, a generic situation in which a plate is initially bent in one direction into a cylindrical arch, then deformed in the other direction by a load applied at its centre. This induces the generation of pairs of singularities; we study their position, their dynamics and the corresponding resistance of the plate to deformation. We solve numerically the equations describing large deformations of plates; developable cones are predicted, in quantitative agreement with the experiments. We use geometrical arguments to predict the observed patterns, assuming that the energy of the plate is given by the energy of the singularities.

Journal Article↗

PubMed1993