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Crystal growth processes produce a diverse array of surface formations, primarily distinguished by their geometric shapes. While some structures strictly adhere to the underlying crystal symmetry, others exhibit universal circular or oval…
We propose a continuum model for pattern formation, based on the multiphase model framework, to explore in vitro cell patterning within an extracellular matrix. We demonstrate that, within this framework, chemotaxis-driven cell migration…
Layered Cellular Automata (LCA) extends the concept of traditional cellular automata (CA) to model complex systems and phenomena. In LCA, each cell's next state is determined by the interaction of two layers of computation, allowing for…
Neural Cellular Automata (NCA) are a powerful combination of machine learning and mechanistic modelling. We train NCA to learn complex dynamics from time series of images and PDE trajectories. Our method is designed to identify underlying…
The effects of a surfactant on two-dimensional pattern formation in epitaxial growth are explored theoretically using a simple model, in which an adatom becomes immobile only after overcoming a large energy barrier as it exchanges positions…
One technique for creating semiconductor crystals with new, desired properties involves replacing some atoms in the crystal lattice with additives - atoms of a different type. This substitution not only alters the bulk properties of the…
In the article a transition from pattern evolution equation of reaction-diffusion type to a cellular automaton (CA) is described. The applicability of CA is demonstrated by generating patterns of complex irregular structure on a hexagonal…
Mechanochemical processes on surfaces such as the cellular cortex or epithelial sheets, play a key role in determining patterns and shape changes of biological systems. To understand the complex interplay of hydrodynamics and material flows…
We investigate a continuum mechanical model for an adherent cell on two dimensional adhesive micropatterned substrates. The cell is modeled as an isotropic and homogeneous elastic material subject to uniform internal contractile stresses.…
A Cellular Automata (CA) rule is presented that can generate "loop patterns" in a 2D grid under fixed boundary conditions. A loop is a cyclically closed path represented by one-cells enclosed by zero-cells. A loop pattern can contain…
This paper studies complexity of recognition of classes of bounded configurations by a generalization of conventional cellular automata (CA) -- finite dynamic cellular automata (FDCA). Inspired by the CA-based models of biological and…
Recent biological experiments have shown that certain types of cells are able to move in structured and confined environment even without the activation of focal adhesion. Focusing on this particular phenomenon and based on previous works,…
We propose a two-scale model to resolve essential features of developmental tissue deformations. The model couples individual cellular behavior to the mechanics at tissue scale. This is realized by a multiphase-field model addressing the…
Recent extensions of Cellular Automata (CA) have incorporated key ideas from modern deep learning, dramatically extending their capabilities and catalyzing a new family of Neural Cellular Automata (NCA) techniques. Inspired by…
We relate structurally dynamic cellular networks, a class of models we developed in fundamental space-time physics, to SDCA, introduced some time ago by Ilachinski and Halpern. We emphasize the crucial property of a non-linear interaction…
Surfaces are at the frontier of every known solid. They provide versatile supports for functional nanostructures and mediate essential physicochemical processes. Being intimately related with 2D materials, interfaces and atomically thin…
We present a stochastic CA modelling approach of corrosion based on spatially separated electrochemical half-reactions, diffusion, acido-basic neutralization in solution and passive properties of the oxide layers. Starting from different…
Cells exert traction forces on compliant substrates and can induce surface instabilities that appear as characteristic wrinkling patterns. Here, we develop a mechanical description of cell-induced wrinkling on soft substrates using a thin…
We study the generalized diffusion-limited aggregates (DLA), with two seeds placed at distance d lattice units and investigate the probability p(d) that the patterns generated from those seeds get connected. In this model, one can vary the…
Shells, when confined, can deform in a broad assortment of shapes and patterns, often quite dissimilar to what is produced by their flat counterparts (plates). In this work we discuss the morphological landscape of shells deposited on a…