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Hierarchical structures are very common in Nature, but only recently have they been systematically studied in materials physics, in order to understand the specific effects they can have on the mechanical properties of various systems.…
A discrete version of deposition-diffusion equations appropriate for description of step flow on a vicinal surface is analyzed for a two-dimensional grid of adsorption sites representing the stepped surface and explicitly incorporating…
Cellular automata (CA) have been utilized for decades as discrete models of many physical, mathematical, chemical, biological, and computing systems. The most widely known form of CA, the elementary cellular automaton (ECA), has been…
Neural Cellular Automata (NCA) models are trainable variations of traditional Cellular Automata (CA). Emergent motion in the patterns created by NCA has been successfully applied to synthesize dynamic textures. However, the conditions…
The friction force observed at macroscale is the result of interactions at various lower length scales that are difficult to model in a combined manner. For this reason, simplified approaches are required, depending on the specific aspect…
One of the most important problems in contemporary science, and especially in biology, is to reveal mechanisms of pattern formation. On the level of biological tissues, patterns form due to interactions between cells. These interactions can…
Fracture in quasi-statically driven systems is studied by means of a discrete spring-block model. Developed from close comparison with desiccation experiments, it describes crack formation induced by friction on a substrate. The model…
The phase field fracture method has emerged as a promising computational tool for modelling a variety of problems including, since recently, hydrogen embrittlement and stress corrosion cracking. In this work, we demonstrate the potential of…
We investigate the morphology and mechanics of a naturally curved elastic arch loaded at its center and frictionally supported at both ends on a flat, rigid substrate. Through systematic numerical simulations, we classify the observed…
In order to optimize a self-assembly reaction, it is essential to understand the factors that govern its pathway. Here, we examine the influence of nucleation pathways in a model system for addressable, multicomponent self-assembly based on…
While crack nucleation and propagation in the brittle or quasi-brittle regime can be predicted via variational or material-force-based phase field fracture models, these models often assume that the underlying elastic response of the…
A variety of studies have modeled the physics of material deformation and damage as examples of generalized phase transitions, involving either critical phenomena or spinodal nucleation. Here we study a model for frictional sliding with…
Morphogenesis, tissue regeneration and cancer invasion involve transitions in tissue morphology. These transitions, caused by collective cell migration (CCM), have been interpreted as active wetting/de-wetting transitions. This phenomenon…
State-of-the-art review of cellular automata, cellular automata for partial differential equations, differential equations for cellular automata and pattern formation in biology and engineering.
We present a weakly coupled map lattice model for patterning that explores the effects exerted by weakening the local dynamic rules on model biological and artificial networks composed of two-state building blocks (cells). To this end, we…
Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its detailed curvature. Topology…
Cell-cell adhesion is one the most fundamental mechanisms regulating collective cell migration during tissue development, homeostasis and repair, allowing cell populations to self-organize and eventually form and maintain complex tissue…
We present a diagrammatic method to build up sophisticated cellular automata (CAs) as models of complex physical systems. The diagrams complement the mathematical approach to CA modeling, whose details are also presented here, and allow CAs…
Cellular automata (CA), originally developed as computational models of natural processes, have become a central subject in the study of complex systems and generative visual forms. Among them, the Ulam-Warburton Cellular Automaton (UWCA)…
Cracks in thin layers are influenced by what lies beneath them. From buried craters to crocodile skin, crack patterns are found over an enormous range of length scales. Regardless of absolute size, their substrates can dramatically…