Related papers: Eden model for Pentagons
The Eden cell growth model is a simple discrete stochastic process which produces a "blob" in $\mathbb{R}^d$: start with one cube in the regular grid, and at each time step add a neighboring cube uniformly at random. This process has been…
The stochastic Eden model of charged particles aggregation in two-dimensional systems is presented. This model is governed by two parameters: screening length of electrostatic interaction, $\lambda $, and short range attraction energy, $E$.…
We consider a pentagon chain described by a Hubbard type of model considered under periodic boundary conditions. The system i) is placed in an external magnetic field perpendicular to the plane of the cells, and ii) is in a site selective…
We consider a free boundary problem for a system of PDEs, modeling the growth of a biological tissue. A morphogen, controlling volume growth, is produced by specific cells and then diffused and absorbed throughout the domain. The geometric…
We introduce a formalism for the geometry of eukaryotic cells and organisms.Cells are taken to be star-convex with good biological reason. This allows for a convenient description of their extent in space as well as all manner of cell…
Spatial agent-based models are increasingly used to investigate the evolution of solid tumours subject to localised cell-cell interactions and microenvironmental heterogeneity. Here we present a non-technical step by step guide to…
The process of programmed cell death, namely apoptosis, is a natural mechanism that regulates healthy tissue, multicellular structures, and homeostasis. An improved understanding of apoptosis can significantly enhance our knowledge of…
In contrast to many known results concerning periodic tilings of the Euclidean plane with pentagons, here tilings with rotational symmetry are investigated. A certain class of convex pentagons is introduced. It can be shown that for any…
We consider the asymptotic shape of clusters in the Eden model on a d-dimensional hypercubical lattice. We discuss two improvements for the well-known upper bound to the growth velocity in different directions by that of the independent…
Epigenetic Tracking (ET) is an Artificial Embryology system which allows for the evolution and development of large complex structures built from artificial cells. In terms of the number of cells, the complexity of the bodies generated with…
Inspired by the concept of evolutoids of planar curves, we present the concept of evolutoids for regular surfaces as an envelope of a two-parameter family of lines in Euclidean 3-space. We give an explicit parametrization for such…
The majority of solid tumours arise in epithelia and therefore much research effort has gone into investigating the growth, renewal and regulation of these tissues. Here we review different mathematical and computational approaches that…
Stem cell regeneration is a crucial biological process for most self-renewing tissues during the development and maintenance of tissue homeostasis. In developing the mathematical models of stem cell regeneration and tissue development, cell…
We propose a physical model for developmental process at cellular level to discuss the mechanism of epigenetic landscape. In our simplified model, a minimal model, the network of the interaction among cells generates the landscape…
In order to describe two-dimensionally packed cells in epithelial tissues both mathematically and physically, there have been developed several sorts of geometrical models, such as the vertex model, the finite element model, the…
A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell.…
This article describes a natural piecewise Euclidean bi-simplicial cell structure for the space of $n$-element multisets in a fixed Euclidean rectangle. In particular, we highlight some connections with spaces of complex polynomials and…
We construct model sets arising from cut and project schemes in Euclidean spaces whose associated Delone dynamical systems have positive toplogical entropy. The construction works both with windows that are proper and with windows that have…
Rapid advance of experimental techniques provides an unprecedented in-depth view into complex developmental processes. Still, little is known on how the complexity of multicellular organisms evolved by elaborating developmental programs and…
We investigate a class of stochastic growth models involving competition between two phases in which one of the phases has a competitive advantage. The equilibrium populations of the competing phases are calculated using a mean field…