Related papers: Tessellations and Pattern Formation in Plant Growt…
We present a class of models based on extended gauged flavour symmetries that address the hierarchical structure of fermion masses in the Standard Model (SM) through the radiative mass generation mechanism. In these frameworks, only…
Growth patterns generated by filamentous organisms (e.g. actinomycetes and fungi) involve spatial and temporal dynamics at different length scales. Several mathematical models have been proposed in the last thirty years to address these…
Cell proliferation and cell movement are fundamentally stochastic processes which lead to variability in the growth and spatial structure of cell populations in many biological settings, such as cell invasion, wound healing, and tumour…
A one-dimensional cellular automaton with a probabilistic evolution rule can generate stochastic surface growth in $(1 + 1)$ dimensions. Two such discrete models of surface growth are constructed from a probabilistic cellular automaton…
Convergent extension of epithelial tissue is a key motif of animal morphogenesis. On a coarse scale, cell motion resembles laminar fluid flow; yet in contrast to a fluid, epithelial cells adhere to each other and maintain the tissue layer…
Voronoi tessellations have been used to model the geometric arrangement of cells in morphogenetic or cancerous tissues, however so far only with flat hypersurfaces as cell-cell contact borders. In order to reproduce the experimentally…
We apply the method of iterated inflations to show that the wreath product of a cellular algebra with a symmetric group is cellular, and obtain descriptions of the cell and simple modules together with a semisimplicity condition for such…
Voronoi mosaics inspired by the seed points placed on the Archimedes Spirals are reported. Voronoi entropy was calculated for these patterns. Equidistant and non-equidistant patterns are treated. Voronoi mosaics built from cells of equal…
Epithelial tissues play a fundamental role in various morphogenetic events during development and early embryogenesis. Although epithelial monolayers are often modeled as two-dimensional (2D) elastic surfaces, they distinguish themselves…
The paper studies a PDE model for the growth of a tree stem or a vine, having the form of a differential inclusion with state constraints. The equations describe the elongation due to cell growth, and the response to gravity and to external…
Proteins synthesized on membrane-bound ribosomes are sorted at the Golgi apparatus level for delivery to various cellular destinations: the plasma membrane or the extracellular space, and the lytic vacuole or lysosome. Sorting involves the…
Forest regeneration is a spatial multifaceted process with numerous unknown variables. The individual area or the area potentially available (APA) to an individual plant embodies an idea widely used in population ecology but it has fewer…
Voronoi tessellations of Poisson point processes are widely used for modeling many types of physical and biological systems. In this paper, we analyze simulated Poisson-Voronoi structures containing a total of 250,000,000 cells to provide…
Most of normal proliferative epithelia of plants and metazoans are topologically invariant and characterized by similar cell distributions according to the number of cell neighbors (DCNs). Here we study peculiarities of these distributions…
Cell growth in size is a complex process coordinated by intrinsic and environmental signals. In a recent work [Tzur et al., Science, 2009, 325:167-171], size distributions in an exponentially growing population of mammalian cells were used…
Combining experimental procedures and theoretical modeling, we studied patterns, shapes, and growth of a special type of SuperAbsorbent Polymers (SAP). At the initial stage, embed in water, we have a polygonal pattern over a spherical form,…
We rigorously prove a form of disorder-resistance for a class of one-dimensional cellular automaton rules, including some that arise as boundary dynamics of two-dimensional solidification rules. Specifically, when started from a random…
We simulate the dynamics of pelagic \emph{Sargassum} rafts as systems of finite-size floating particles, governed by a Maxey--Riley law with nonlinear elastic interactions. Using surface ocean currents and wind data from reanalysis systems…
Growth and shape formation in crowded multicellular assemblies arise from the interplay of chemical gradients, single-cell expansion and mechanical interactions, making it essential to understand how these processes jointly shape collective…
Ever since the ground breaking work of Trepat et al. in 2009, we know that cell colonies growing on a substrate can be under tensile mechanical stress. The origin of tension has so far been attributed to cellular motility forces being…