Related papers: Eden model for Pentagons
The architecture has its basis in a dialectic search of new choices of representation. We deal with the form on the contemporary architecture under two approaches: expression and content. We examine how mathematical principles based on…
This article presents new hexagonal and pentagonal PEM fuel cell models. The models have been optimized after achieving improved cell performance. The input parameters of the multi-objective optimization algorithm were pressure and…
Great computational effort is invested in generating equilibrium states for molecular systems using, for example, Markov chain Monte Carlo. We present a probabilistic model that generates statistically independent samples for molecules from…
Given a homogenous Poisson point process in the plane, we prove that it is possible to partition the plane into bounded connected cells of equal volume, in a translation-invariant way, with each point of the process contained in exactly one…
We present a general approach to study a class of random growth models in $n$-dimensional Euclidean space. These models are designed to capture basic growth features which are expected to manifest at the mesoscopic level for several…
A random planar quadrangulation process is introduced as an approximation for certain cellular automata in terms of random growth of rays from a given set of points. This model turns out to be a particular (rectangular) case of the…
We consider the Eden model on the d-dimensional hypercubical unoriented lattice , for large d. Initially, every lattice point is healthy, except the origin which is infected. Then, each infected lattice point contaminates any of its…
The growth rates of seeded QED cascades in counter propagating lasers are calculated with first principles 2D/3D QED-PIC simulations. The dependence of the growth rate on laser polarization and intensity are compared with analytical models…
Understanding how growth induces form is a longstanding biological question. Many studies concentrated on the shapes of plant cells, fungi or bacteria. Some others have shown the importance of the mechanical properties of bacterial walls…
Tumor angiogenesis concerns the development of new blood vessels supplying the necessary nutrients for the further development of existing tumor cells. The entire process is complex, involving the production and consumption of chemicals,…
We propose a PDE-ODE model for tissue regeneration, obtained by parabolic upscaling from kinetic transport equations written for the mesoscopic densities of mesenchymal stem cells and chondrocytes which evolve in an artificial scaffold…
A continuum model of epithelial tissue mechanics was formulated using cellular-level mechanical ingredients and cell morphogenetic processes, including cellular shape changes and cellular rearrangements. This model can include finite…
We investigate morphologies of proliferating cellular tissue using a newly developed numerical simulation model for mechanical cell division. The model reproduces structures of simple multi-cellular organisms via simple rules for selective…
We describe our optical and electron-microscopy observations of pearlite structures in eutectoid steels which seem to imply that the mechanisms of formation of pearlite colonies in these steels differ from those observed earlier for…
This contribution belongs to a combinatorial approach to hyperbolic geometry and it is aimed at possible applications to computer simulations. It is based on the splitting method which was introduced by the author and which is reminded in…
A contemporary procedure to grow artificial tissue is to seed cells onto a porous biomaterial scaffold and culture it within a perfusion bioreactor to facilitate the transport of nutrients to growing cells. Typical models of cell growth for…
The investigation of dynamical processes on networks has been one focus for the study of contagion processes. It has been demonstrated that contagions can be used to obtain information about the embedding of nodes in a Euclidean space.…
Cell layers eliminate unwanted cells through the extrusion process, which underlines healthy versus flawed tissue behaviors. Although several biochemical pathways have been identified, the underlying mechanical basis including the forces…
Pulsed laser deposition (PLD) is a popular growth method, which has been successfully used for fabricating thin films. Compared to continuous deposition (like molecular beam epitaxy) the pulse intensity can be used as an additional…
We perform a mass constrained phase-field approximation for a model that describes the epitaxial growth of a two-dimensional thin film on a substrate in the context of linearised elasticity. The approximated model encodes a variable on the…