Related papers: Phyllotaxis: a framework for foam topological evol…
We stress the importance of stochastic geometry as a branch of mathematical statistics particularly suited to model and investigate nontrivial spatial patterns. One of its key concepts, Voronoi tessellations, represents a versatile and…
Cellular structures manifest their outstanding mechanical properties in many biological systems. One key challenge for designing and optimizing these geometrically complicated structures lies in devising an effective geometric…
The plant microtubule cortical array is a striking feature of all growing plant cells. It consists of a more or less homogeneously distributed array of highly aligned microtubules connected to the inner side of the plasma membrane and…
Blob-filaments (or simply 'blobs') are coherent structures formed by turbulence and sustained by nonlinear processes in the edge and scrape-off layer (SOL) of tokamaks and other magnetically confined plasmas. The dynamics of these…
Complex distribution networks are pervasive in biology. Examples include nutrient transport in the slime mold \emph{Physarum polycephalum} as well as mammalian and plant venation. Adaptive rules are believed to guide development of these…
Many physical systems can be studied as collections of particles embedded in space, evolving through deterministic evolution equations. Natural questions arise concerning how to characterize these arrangements - are they ordered or…
A holomorphic foliation is defined as an integrable coherent subsheaf of the tangent sheaf. The structure of the leaves around a singularity is read off from the structure of the stalks. This was done by Baum when the dimension of the…
Phyllotactic states are regular lattice-like structures on cylinders and are a botanical classification scheme. In this communication, we report a sequence of transitions between phyllotactic states for particles with a repulsive…
The shape of the cross section of a dense fiber bundle is related to the symmetry of its molecular packing. However, this statement might be belied by type I collagen fibrils which have a rounded section of high symmetry while structural…
The distribution of the deformations of elementary cells is studied in an abstract lattice constructed from the existence of the empty set. One combination rule determining oriented sequences with continuity of set-distance function in such…
Voronoi mosaics inspired by the seed points placed on the Archimedes Spirals are reported. Voronoi entropy was calculated for these patterns. Equidistant and non-equidistant patterns are treated. Voronoi mosaics built from cells of equal…
Plant morphogenesis relies on dynamic growth deformations at the cell and tissue scales driven by osmotic fluxes. A mechanistic understanding of this phenomenon demands a physical framework that integrates cell imbibition, tissue mechanics,…
Voronoi Tessellations form an attractive and versatile geometrical asymptotic model for the foamlike cosmic distribution of matter and galaxies. In the Voronoi model the vertices are identified with clusters of galaxies. For a substantial…
Proteins in photosynthetic membranes can organize into patterned arrays that span the membrane's lateral size. Attractions between proteins in different layers of a membrane stack can play a key role in this ordering, as was suggested by…
Geometrically, foams or covalent graphs can be decomposed into successive layers or strata. Disorder of the underlying structure imposes a characteristic roughening of the layers. Our main results are hysteresis and convergence in the layer…
Under hard-agar and nutrient-rich conditions, a cell of $Bacillus$ $subtilis$ grows as a single filament owing to the failure of cell separation after each growth and division cycle. The self-elongating filament of cells shows sequential…
A key process in the life of any multicellular organism is its development from a single egg into a full grown adult. The first step in this process often consists of forming a tissue layer out of randomly placed cells on the surface of the…
We derive a mesoscopic modeling and simulation technique that is very close to the technique known as dissipative particle dynamics. The model is derived from molecular dynamics by means of a systematic coarse-graining procedure. Thus the…
We use hydrodynamical simulations to investigate the response of geometrically thin, self-gravitating, singular isothermal disks of gas to imposed rigidly rotating spiral potentials. By minimizing reflection-induced feedback from…
Space-saving design is a requirement that is encountered in biological systems and the development of modern technological devices alike. Many living organisms dynamically pack their polymer chains, filaments or membranes inside of…