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

Mathematics and Morphogenesis of the City: A Geometrical Approach

Cities are living organisms. They are out of equilibrium, open systems that never stop developing and sometimes die. The local geography can be compared to a shell constraining its development. In brief, a city's current layout is a step in a running morphogenesis process. Thus cities display a huge diversity of shapes and none of traditional models from random graphs, complex networks theory or stochastic geometry takes into account geometrical, functional and dynamical aspects of a city in the same framework. We present here a global mathematical model dedicated to cities that permits describing, manipulating and explaining cities' overall shape and layout of their street systems. This street-based framework conciliates the topological and geometrical sides of the problem. From the static analysis of several French towns (topology of first and second order, anisotropy, streets scaling) we make the hypothesis that the development of a city follows a logic of division / extension of space. We propose a dynamical model that mimics this logic and which from simple general rules and a few parameters succeeds in generating a large diversity of cities and in reproducing the general features the static analysis has pointed out.Comment: 13 pages, 13 figure

Pemodelan Dimensi Fraktal Multiskala untuk Mengenali Bentuk Daun

Penelitian ini membangun model untuk membedakan bentuk daun menggunakan dimensi fraktal multiskala. Identifikasi tumbuhan obat sangat penting mengingat keanekaragaman hayati di Indonesia dan peran pentingnya di Indonesia. Identifikasi tanaman dapat dilakukan menggunakan analisis bentuk dengan daun sebagai cirinya. Dimensi fraktal multiskala adalah salah satu metode analisis bentuk yang menganalisis bentuk melalui kompleksitasnya. Empat tipe bentuk daun dari spesies berbeda dimodelkan dalam penelitian ini. Analisis multiskala mampu memberikan informasi tambahan mengenai alur Perubahan luas bidang dilasi, namun tidak mencirikan bentuk daun yang diuji dalam penelitian ini

Pemodelan Dimensi Fraktal Multiskala untuk Mengenali Bentuk Daun

Penelitian ini membangun model untuk membedakan bentuk daun menggunakan dimensi fraktal multiskala. Identifikasi tumbuhan obat sangat penting mengingat keanekaragaman hayati di Indonesia dan peran pentingnya di Indonesia. Identifikasi tanaman dapat dilakukan menggunakan analisis bentuk dengan daun sebagai cirinya. Dimensi fraktal multiskala adalah salah satu metode analisis bentuk yang menganalisis bentuk melalui kompleksitasnya. Empat tipe bentuk daun dari spesies berbeda dimodelkan dalam penelitian ini. Analisis multiskala mampu memberikan informasi tambahan mengenai alur perubahan luas bidang dilasi, namun tidak mencirikan bentuk daun yang diuji dalam penelitian ini.Kata kunci: bentuk daun, dimensi fraktal multiskala, tanaman obat

Instabilite parametrique d'ondes de surface

SIGLECNRS T Bordereau / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Shapes and growth motions of leaves

Leaf shapes are very variable but restricted to some stereotyped families. Among one family of lobed leaves, this shape can be related to its folded growth within the bud. In general, this open the question of how much the final shape can be constrained by steric constrains during its development. Similarly, since most of the leaves do not first expand flat and straight, but commonly folded or rolled in different ways, there needs to be some regulations to reach the usually rather flat and straight state. This growth, from the primordial to the final leaf, presents several striking motions. On some examples we propose that these motions precisely help the regulation.Non UBCUnreviewedAuthor affiliation: CNRS / University Paris 7 Denis DiderotFacult

DYNAMIQUE DES AVALANCHES

PARIS7-Bibliothèque centrale (751132105) / SudocPARIS-BIUSJ-Physique recherche (751052113) / SudocSudocFranceF

Centrality analysis of metro network, a case study of Paris

International audienceMetro systems are playing an increasingly important role in the cities all around the world, due to the demand of reduction on traffic congestions and energy consumption. The purpose of the present study is to investigate the relationship between the entering traffic and a new conception of centrality Structuality on metro network. The centrality analysis is carried out for study the metro network in Paris. It is found that the coefficient of centrality could help indicate the potential traffic flow. The intersections on metro networks showed a relatively high centrality as well as entering traffic. An “effect of pump” could be observed around the intersections. This method could be applied to compare different network design in the planning phrase, as well as optimize the current metro networks

Morphogenesis of spatial networks through way analysis

International audienc