Related papers: Two-dimension tissue growth model based on circula…
Hybrid modeling provides an effective solution to cope with multiple time scales dynamics in systems biology. Among the applications of this method, one of the most important is the cell cycle regulation. The machinery of the cell cycle,…
Tuning cell rearrangements is essential in collective cell movement that underlies cancer progression, wound repair, and embryonic development. A key question is how tissue material properties and morphology emerge from cellular factors…
Growth-elasticity is a powerful model framework for understanding complex shape development in soft biological tissues. At each instant, by mapping how continuum building blocks have grown geometrically and how they respond elastically to…
We propose two toy-models to describe, predict, and interpret the wrinkles appearing on the surface of skin when it is sheared. With the first model, we account for the lines of greatest tension present in human skin by subjecting a layer…
The article addresses the mathematical modeling of the folding of a thin elastic sheet along a prescribed curved arc. A rigorous model reduction from a general hyperelastic material description is carried out under appropriate scaling…
A cutting-plane model for a nonsmooth function is the maximum of several first-order expansions centered at different points. Using such a model in a bundle method leads to linear convergence (of serious steps) to a minimum. In smooth…
We present a model for mechanically-induced pattern formation in growing biological tissues and discuss its application to the development of leaf venation networks. Drawing an analogy with phase transitions in solids, we use a phase field…
We present a novel computational method to simulate accurately a wide range of interfacial patterns whose growth is limited by a large scale diffusion field. To illustrate the computational power of this method, we demonstrate that it can…
The Cahn-Hilliard model with reaction terms can lead to situations in which no coarsening is taking place and, in contrast, growth and division of droplets occur which all do not grow larger than a certain size. This phenomenon has been…
Nowadays, multiscale modelling is recognized as the most suitable way to study biological processes. Indeed, almost every phenomenon in nature exhibits a multiscale behaviour, i.e., it is the outcome of interactions that occur at different…
We systematically study the boundaries of one-dimensional, 2-color cellular automata depending on 4 cells, begun from simple initial conditions. We determine the exact growth rates of the boundaries that appear to be reducible. Morphic…
Spatial self-organization emerges in distributed systems exhibiting local interactions when nonlinearities and the appropriate propagation of signals are at work. These kinds of phenomena can be modeled with different frameworks, typically…
The quintessential property of neuronal systems is their intensive patterns of selective synaptic connections. The current work describes a physics-based approach to neuronal shape modeling and synthesis and its consideration for the…
Despite significant advances in understanding neuronal development, a fully quantitative framework that integrates intracellular mechanisms with environmental cues during axonal growth remains incomplete. Here, we present a unified…
A mutualism is an interaction where the involved species benefit from each other. We study a two-dimensional hexagonal three-state cellular automaton model of a two-species mutualistic system. The simple model is characterized by four…
We propose a three dimensional mechanical model of embryonic tissue dynamics. Mechanically coupled adherent cells are represented as particles interconnected with elastic beams which can exert non-central forces and torques. Tissue…
A simple two dimensional model of a phase growing on a substrate is introduced. The model is characterized by an adsorption rate q, and a desorption rate p. It exhibits a wetting transition which may be viewed as an unbinding transition of…
I show that the evolution of a two dimensional surface in a Laplacian field can be described by Hamiltonian dynamics. First the growing region is mapped conformally to the interior of the unit circle, creating in the process a set of…
The evolution of human intelligence led to the huge amount of data in the information space. Accessing and processing this data helps in finding solutions to applied problems based on finite-dimensional models. We argue, that formally, such…
Monolayer cluster growth in far-from-equilibrium systems is investigated by applying simulation and analytic techniques to minimal hard core particle (exclusion) models. The first model (I), for post-deposition coarsening dynamics, contains…