Related papers: Eden model for Pentagons
"Epigenetic Tracking" is the name of a model of cellular development that, coupled with an evolutionary technique, becomes an evo-devo (or "artificial embryology", or "computational development") method to generate 2d or 3d sets of…
In this article, we propose a general framework to study the dynamics and topology of cellular networks that capture the geometry of cell packings in two-dimensional tissues. Such epithelia undergo large-scale deformation during…
The technique presented here identifies tethered mould designs, optimised for growing cultured tissue with very highly-aligned cells. It is based on a microscopic biophysical model for polarised cellular hydrogels. There is an unmet need…
We produce examples of codimension one foliations of the Euclidean and hyperbolic planes with bounded geometry which are topologically products, but for which leaves are non-recursively distorted. That is, the function which compares…
This paper uses a recent explanation for the fundamental haploid-diploid lifecycle of eukaryotic organisms to present a new memetic algorithm that differs from all previous known work using diploid representations. A form of the Baldwin…
Unlike other tissue types, like epithelial tissue, which consist of cells with a much more homogeneous structure and function, the nervous tissue spans in a complex multilayer environment whose topographical features display a large…
We analyze the performance of a reduced-order simulation of geometric meta-materials based on zigzag patterns using a simplified representation. As geometric meta-materials we denote planar cellular structures which can be fabricated in 2d…
In proliferating epithelia of mammalian skin, cells of irregular polygonal-like shapes pack into complex nearly flat two-dimensional structures that are pliable to deformations. In this work, we employ various sensitive correlation…
Topological physics opens up a plethora of exciting phenomena allowing to engineer disorder-robust unidirectional flows of light. Recent advances in topological protection of electromagnetic waves suggest that even richer functionalities…
The biphenylene network (BPN) has a unique two-dimensional atomic structure, where hexagonal unit cells are arranged on a square lattice. Inspired by such a BPN structure, we design a counterpart in the fashion of photonic crystals (PhCs),…
The positioning of new cellular walls during cell division plays a key role in shaping plant tissue organization. The influence of cell geometry on the positioning of division planes has been previously captured into various geometrical…
We establish some characterizations of elliptic hyperboloids (resp., ellipsoids) in the $(n+1)$-dimensional Euclidean space ${\Bbb E}^{n+1}$, using the $n$-dimensional area of the sections cut off by hyperplanes and the $(n+1)$-dimensional…
The colonization of unoccupied territory by invading species, known as range expansion, is a spatially heterogeneous non-equilibrium growth process. We introduce a two-species Eden growth model to analyze the interplay between…
A phase eld approach is developed to model wetting and heterogeneous crystal nucleation of an undercooled pure liquid in contact with a sharp wall. We discuss various choices for the boundary condition at the wall and determine the…
We study a new family of models of the sine-Gordon type, starting from the sine-Gordon model, including the double sine-Gordon, the triple one, and so on. The models appears as deformations of the starting model, with the deformation…
Tissue growth can be modeled in two dimension by only using circular granular cells, which can grow and produce child. Linear spring-dashpot model is used to bind the cells with a cut-off interaction range of 1.1 times sum of radii of…
From each point of a Poisson point process start growing a balloon at rate 1. When two balloons touch, they pop and disappear. Is every point contained in balloons infinitely often or not? We answer this for the Euclidean space, the…
In this paper, we propose to study a new geometric optimization problem called "geometric prototype" in Euclidean space. Given a set of patterns, where each pattern is represented by a (weighted or unweighted) point set, the geometric…
In this paper we investigate the metric properties of quadrics and cones of the $n$-dimensional Euclidean space. As applications of our formulas we give a more detailed description of the construction of Chasles and the wire model of…
We investigate the topological structure of entangled qudits under unitary local operations. Different sectors are identified in the evolution, and their geometrical and topological aspects are analyzed. The geometric phase is explicitly…