Related papers: First-order patterning transitions on a sphere as …
Smectic orders on curved substrates can be described by differential forms of rank one (1-forms), whose geometric meaning is the differential of the local phase field of density modulation. The exterior derivative of 1-form is the local…
The aim of the present paper is to elucidate the transition from collective to random behavior exhibited by various mathematical models of bird flocking. In particular, we compare Vicsek's model [Viscek et al., Phys. Rev. Lett. 75, 1226 --…
The set of all permutations, ordered by pattern containment, forms a poset. This paper presents the first explicit major results on the topology of intervals in this poset. We show that almost all (open) intervals in this poset have a…
We are surrounded by spatio-temporal patterns resulting from the interaction of the numerous basic units constituting natural or human-made systems. In presence of diffusive-like coupling, Turing theory has been largely applied to explain…
First-order separability of a spatio-temporal point process plays a fundamental role in the analysis of spatio-temporal point pattern data. While it is often a convenient assumption that simplifies the analysis greatly, existing…
We present a simple model based on a reaction-diffusion equation to explain pattern formation in a multicellular bacterium (Streptomyces). We assume competition for resources as the basic mechanism that leads to pattern formation; in…
A first-order percolation transition, called explosive percolation, was recently discovered in evolution networks with random edge selection under a certain restriction. However, the network percolation with more realistic evolution…
The structure and dynamics of tissue cultures depend strongly on the physical and chemical properties of the underlying substrate. Inspired by previous advances in the context of inorganic materials, the use of patterned culture surfaces…
Spatially ordered systems confined to surfaces such as spheres exhibit interesting topological structures because of curvature induced frustration in orientational as well as translational order. The study of these structures is important…
In certain biological contexts, such as the plumage patterns of birds and stripes on certain species of fishes, pattern formation takes place behind a so-called "wave of competency". Currently, the effects of a wave of competency on the…
The biopolymers actin and microtubules are often in an ongoing assembling/disassembling state far from thermal equilibrium. Above a critical density this leads to spatially periodic patterns, as shown by a scaling argument and in terms of a…
The microscopic model in which nodes interacting with each other are statistical systems is introduced. The nodes conditions are connected with a string of distinct microscopic configurations and depend on external parameters (pressure and…
The rheological properties of biological tissues are core to processes such as cancer metastasis, wound healing and embryo development. The emergence of tissue and organ structures during morphogenesis requires the precise formation of…
There are three fundamental physical processes that gives rise to the morphology of a surface: deposition, surface diffusion and desorption. The characteristics of the interfaces generated by the combination of deposition and surface…
In this first paper, we demonstrate a theorem that establishes a first step toward proving a necessary topological condition for the occurrence of first or second order phase transitions: we prove that the topology of certain submanifolds…
Patterns often appear in a variety of large, real-world networks, and interesting physical phenomena are often explained by network topology as in the case of the bow-tie structure of the World Wide Web, or the small world phenomenon in…
Control over the physical properties of materials is ubiquitously required in many fields. One means by which this can be achieved is controlling the internal structure of multi-component materials with an eye to enhancing mechanical…
Ordered phases on curved substrates experience a complex interplay of ordering and intrinsic curvature, commonly producing frustration and singularities. This is an especially important issue in crystals as ever-smaller scale materials are…
We consider here the morphogenesis (pattern formation) problem for some genetic network models. First, we show that any given spatio-temporal pattern can be generated by a genetic network involving a sufficiently large number of genes.…
The short-range attraction and long-range repulsion (SALR) between nanoparticles or macromolecules can lead to spontaneous pattern formation on solid surfaces, fluid interfaces or membranes. In order to study the self-assembly in such…