Isotropic cellular automaton for modelling excitable media

Markus, Mario; Hess, Benno

doi:10.1038/347056a0

Cited by 191 publications

(80 citation statements)

References 20 publications

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“…However, 'cellular automata' in a broader sense may be favourable tools for modelling complexity, self organisation and even nonlinear dynamics. [33][34][35] The examples presented here are not based on assumptions about the time scale and the molecular mechanisms underlying cell-to-cell communication. Therefore, they are open for further refinements in order to simulate observed events and concrete mechanisms.…”

Section: Discussionmentioning

confidence: 99%

Signal percolation through plants and the shape of the calcium signature

Plieth

2010

Plant Signaling & Behavior

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Section: Discussionmentioning

confidence: 99%

Signal percolation through plants and the shape of the calcium signature

Plieth

2010

Plant Signaling & Behavior

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“…Because this is an essentially discrete process, we employ a discrete coupled map lattice, or lattice Boltzmann model, with a square lattice of discrete space and time but continuous state variables, that puts nucleation and growth on an equal footing. The surface is divided into a randomized grid of cells, as introduced by Markus and Hess (16), to avoid anisotropic growth. Each cell has a growth height H(i, j), initially zero, updated at the end of each iteration of the growth.…”

Section: Liquid-crystal Layer Growth Model Of Nacrementioning

confidence: 99%

Spiral and target patterns in bivalve nacre manifest a natural excitable medium from layer growth of a biological liquid crystal

Cartwright

Checa

Escribano

et al. 2009

Proc. Natl. Acad. Sci. U.S.A.

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Nacre is an exquisitely structured biocomposite of the calcium carbonate mineral aragonite with small amounts of proteins and the polysaccharide chitin. For many years, it has been the subject of research, not just because of its beauty, but also to discover how nature can produce such a superior product with excellent mechanical properties from such relatively weak raw materials. Four decades ago, Wada [Wada K (1966) Spiral growth of nacre. Nature 211:1427] proposed that the spiral patterns in nacre could be explained by using the theory Frank [Frank F (1949) The influence of dislocations on crystal growth. Discuss Faraday Soc 5:48 -54] had put forward of the growth of crystals by means of screw dislocations. Frank's mechanism of crystal growth has been amply confirmed by experimental observations of screw dislocations in crystals, but it is a growth mechanism for a single crystal, with growth fronts of molecules. However, the growth fronts composed of many tablets of crystalline aragonite visible in micrographs of nacre are not a molecular-scale but a mesoscale phenomenon, so it has not been evident how the Frank mechanism might be of relevance. Here, we demonstrate that nacre growth is organized around a liquid-crystal core of chitin crystallites, a skeleton that the other components of nacre subsequently flesh out in a process of hierarchical self-assembly. We establish that spiral and target patterns can arise in a liquid crystal formed layer by layer through the Burton-Cabrera-Frank [Burton W, Cabrera N, Frank F (1951) The growth of crystals and the equilibrium structure of their surfaces. Philos Trans R Soc London Ser A 243:299 -358] dynamics, and furthermore that this layer growth mechanism is an instance of an important class of physical systems termed excitable media. Artificial liquid crystals grown in this way may have many technological applications.biomineralization ͉ chitin ͉ interlamellar membranes ͉ mollusc T he splendor of a pearl extends even to under a microscope; with magnification, one can see that the nacreous surfaces of bivalve mollusks-clams, mussels, oysters, scallops, and so onare made up of a striking arrangement of spiral, target, and labyrinthine patterns (1); see Fig. 1. Nacre, or mother of pearl, is the iridescent material that forms an inner layer of the shells of numerous species of mollusks as well as the pearls that many of those same species produce. The structure of nacre is often likened to a brick wall, and indeed, it is composed of bricks of aragonite tablets (Ϸ95%) and mortar of organic so-called interlamellar membranes (polysaccharide and protein, Ϸ5%), but it is a brick wall built in a peculiar fashion, because first, the mortar is put in place, and then the bricks grow within it. (See Fig. 2 for a sketch of bivalve molluscan anatomy and nacre structure.) From an examination of the extrapallial space of the bivalve mollusk, the narrow liquid-filled cavity between the soft tissues and the shell of the organism, it is seen that the first visible feature in nacre growth ...

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“…These latticegas automata are probabilistic cellular automata that employ a particle description of the dynamics and should be distinguished from other cellular automata that are designed to simulate reaction-diffusion equation dynamics. [13][14][15] While most of the phenomena of interest occur on sufficiently long space and time scales that a continuum description using reaction-diffusion equations is appropriate, the cellular automaton models have the advantage that they naturally incorporate fluctuations that are responsible for the nucleation events that play a role in the process and, as well, can be extended to smaller scales where continuum models are no longer appropriate. Cellular automaton models allow one to describe the system at a mesoscopic level which incorporates the essential mechanistic features of the reaction dynamics.…”

Section: Introductionmentioning

confidence: 99%

Surface structure and catalytic CO oxidation oscillations

Danielak

Perera²,

Moreau³

et al. 1996

Physica A: Statistical Mechanics and its Applications

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A cellular automaton model is used to describe the dynamics of the catalytic oxidation of CO on a P t(100) surface. The cellular automaton rules account for the structural phase transformations of the P t substrate, the reaction kinetics of the adsorbed phase and diffusion of adsorbed species. The model is used to explore the spatial structure that underlies the global oscillations observed in some parameter regimes. The spatiotemporal dynamics varies significantly within the oscillatory regime and depends on the harmonic or relaxational character of the global oscillations. Diffusion of adsorbed CO plays an important role in the synchronization of the patterns on the substrate and this effect is also studied.

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Isotropic cellular automaton for modelling excitable media

Cited by 191 publications

References 20 publications

Signal percolation through plants and the shape of the calcium signature

Signal percolation through plants and the shape of the calcium signature

Spiral and target patterns in bivalve nacre manifest a natural excitable medium from layer growth of a biological liquid crystal

Surface structure and catalytic CO oxidation oscillations

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