Related papers: Small cells in a Poisson hyperplane tessellation
We develop a simple computational model for cell boundary evolution in plastic deformation. We study the cell boundary size distribution and cell boundary misorientation distribution that experimentally have been found to have scaling forms…
The behaviour and fate of tissue cells is controlled by the rigidity and geometry of their adhesive environment, possibly through forces localized to sites of adhesion. We introduce a mechanical model that predicts cellular force…
Ordered polarity alignment of a cell population plays a vital role in biology, such as in hair follicle alignment and asymmetric cell division. Here, we propose a theoretical framework for the understanding of generic dynamical properties…
Let $\mathfrak{m}$ be a random tessellation in $\mathbf{R}^d$ observed in a bounded Borel subset $W$ and $f(\cdot)$ be a measurable function defined on the set of convex bodies. To each cell $C$ of $\mathfrak{m}$ we associate a point $z(C)$…
We consider a stationary face-to-face tessellation $X$ of $\mathbb{R}^d$ and introduce several percolation models by colouring some of the faces black in a consistent way. Our main model is cell percolation, where cells are declared black…
Consider a second-order elliptic operator $L$ in the half-plane $\mathbb R \times (0, \infty)$ with coefficients depending only on the second coordinate. The Poisson kernel for $L$ is used in the representation of positive $L$-harmonic…
Open cellular solids usually possess random microstructures that may contain a characteristic length scale, such as the cell size. This gives rise to size dependent mechanical properties where large systems behave differently from small…
Crawling cell motility is vital to many biological processes such as wound healing and the immune response. Using a minimal model we investigate the effects of patterned substrate adhesiveness and biophysical cell parameters on the…
The concept of splitting tessellations and splitting tessellation processes in spherical spaces of dimension $d\geq 2$ is introduced. Expectations, variances and covariances of spherical curvature measures induced by a splitting…
The space subdivision in cells resulting from a process of random nucleation and growth is a subject of interest in many scientific fields. In this paper, we deduce the expected value and variance of these distributions while assuming that…
In a previous work, two of the authors proposed a new proof of a well known convergence result for the scaled elementary connected vacant component in the high intensity Boolean model towards the Crofton cell of the Poisson hyperplane…
Results from molecular dynamics simulations of simple, structured particles capable of self-assembling into polyhedral shells are described. The analysis focuses on the growth histories of individual shells in the presence of an explicit…
We investigate the dynamics of a colony of crawling, proliferating cells with a minimal, mechanical cell model. The cells consist of two disks, modelling the cell body and a pseudopod, connected by a finite extensible spring. The cells…
Constrictions in blood vessels and microfluidic devices can dramatically change the spatial distribution of passing cells or particles and are commonly used in biomedical cell sorting applications. However, the three-dimensional nature of…
A series of simulations aimed at elucidating the self-assembly dynamics of spherical virus capsids is described. This little-understood phenomenon is a fascinating example of the complex processes that occur in the simplest of organisms.…
In this paper two new classes of stationary random simplicial tessellations, the so-called $\beta$- and $\beta'$-Delaunay tessellations, are introduced. Their construction is based on a space-time paraboloid hull process and generalizes…
Let $p$ be a large prime, and let $C$ be a hyperelliptic curve over $\mathbb{F}_p$. We study the distribution of the $x$-coordinates in short intervals when the $y$-coordinates lie in a prescribed interval, and the distribution of the…
We report here new electrical laws, derived from nonlinear electro-diffusion theory, about the effect of the local geometrical structure, such as curvature, on the electrical properties of a cell. We adopt the Poisson-Nernst-Planck (PNP)…
The paper deals with planar segment processes given by a density with respect to the Poisson process. Parametric models involve reference distributions of directions and/or lengths of segments. These distributions generally do not coincide…
We introduce a notion of a weak Poisson structure on a manifold $M$ modeled on a locally convex space. This is done by specifying a Poisson bracket on a subalgebra $\cA \subeq C^\infty(M)$ which has to satisfy a non-degeneracy condition…