Steric Constraints as a Global Regulation of Growing Leaf Shape

Shape is one of the important characteristics for the structures observed in living organisms. Whereas biologists have proposed models where the shape is controlled on a molecular level [1], physicists, following Turing [2] and d'Arcy Thomson [3], have developed theories where patterns arise spontaneously [4]. Here, we propose a volume constraint that restricts the possible shapes of leaves. Focusing on palmate leaves, the central observation is that developing leaves first grow folded inside a bud, limited by the previous and subsequent leaves. We show that growing folded in this small volume controls globally the leaf development. This induces a direct relationship between the way it was folded and the final unfolded shape of the leaf. These dependencies can be approximated as simple geometrical relationships that we confirm on both folded embryonic and unfolded mature leaves. We find that independently of their position in the phylogenetic tree, these relationships work for folded species, but do not work for non-folded species. This steric constraint is a simple way to impose a global regulation for the leaf growth. Such steric regulation should be more general and considered as a new simple means of global regulation.Comment: 6 pages 4 figures, Supplementary materials (8 pages, 7 figures

Fluid interfaces with very sharp tips in viscous flow

When a fluid interface is subjected to a strong viscous flow, it tends to develop near-conical ends with pointed tips so sharp that their radius of curvature is undetectable. In microfluidic applications, tips can be made to eject fine jets, from which micrometer-sized drops can be produced. Here we show theoretically that the opening angle of the conical interface varies on a logarithmic scale as a function of the distance from the tip, owing to nonlocal coupling between the tip and the external flow. Using this insight we are able to show that the tip curvature grows like the exponential of the square of the strength of the external flow and to calculate the universal shape of the interface near the tip. Our experiments confirm the scaling of the tip curvature as well as of the interface’s universal shape. Our analytical technique, based on an integral over the surface, may also have far wider applications, for example treating problems with electric fields, such as electrosprays

Spatial structuring and size selection as collective behaviours in an agent-based model for barchan fields.

International audienceIn order to test parameters of the peculiar dynamics occurring in barchan fields, and compute statistical analysis over large numbers of dunes, we build and study an agent-based model, which includes the well-known physics of an isolated barchan, and observations of interactions between dunes. We showed in a previous study that such a model, where barchans interact through short-range sand recapture and collisions, reproduces the peculiar behaviours of real fields, namely its spatial structuring along the wind direction, and the size selection by the local density. In this paper we focus on the mechanisms that drives these features. In particular, we show that eolian remote sand transfer between dunes ensures that a dense field structures itself into a very heterogeneous pattern, which alternates dense and diluted stripes in the wind direction. In these very dense clusters of dunes, the accumulation of collisions leads to the local emergence of a new size for the dunes

Tl-rich pyrite and Sb-rich melnikovite in Montlouis pyrite veins (central armorican domain, Janze, Ille-et-Vilaine; France)

International audienceLower Ordovician sandstones of the «Grès Armoricain» formation in the Montlouis quarry near Janzé (Ille-et-Vilaine, France) display rare Fe-sulfide veins filled with a low-T (<300 °C) assemblage of pyrite, marcasite, « melnikovite », with trace amount of galena and sphalerite. Pyrite occur as contorted cm-scale veins of columnar pyrite invading sandstones and as larger idiomorphic crystals coating vugs. It is usually overgrown by fibroradiated marcasite outer layer. Concentrically-2 layered spheroids of « melnikovite » separate pyrite from marcasite. This mineral sequence is consistent with crystallization from near-neutral, moderately reducing, H 2 S-rich hydrothermal fluids evolving toward acidic conditions. Vug-hosted cm-sized pyrite cubes may be partly covered by a millimeter-thick fine-grained pyrite film. Unlike the other sulfide ores of the Central Armorican domain that carry Sb and Pb indices, trace element analyses identify As, Tl, Sb and Pb anomalies all distributed between Fe-sulfides, i.e. columnar vein pyrite (up to 1.0 wt.% As), « melnikovite » (up to 5 wt.% Sb), marcasite (up to 7600 ppm Pb) and fibrous pyrite overgrowths (up to 2060 ppm Tl). It is the first time that a Tl anomaly is reported in sulfide ores from the Armorican massif. A potential reservoir for Tl could be the altered dolerite body observed in the quarry