Journal ArticleDOI
Statistical mechanics of cellular automata
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Analysis is given of ''elementary'' cellular automata consisting of a sequence of sites with values 0 or 1 on a line, with each site evolving deterministically in discrete time steps according to p definite rules involving the values of its nearest neighbors.Abstract:
Cellular automata are used as simple mathematical models to investigate self-organization in statistical mechanics. A detailed analysis is given of "elementary" cellular automata consisting of a sequence of sites with values 0 or 1 on a line, with each site evolving deterministically in discrete time steps according to definite rules involving the values of its nearest neighbors. With simple initial configurations, the cellular automata either tend to homogeneous states, or generate self-similar patterns with fractal dimensions \ensuremath{\simeq} 1.59 or \ensuremath{\simeq} 1.69. With "random" initial configurations, the irreversible character of the cellular automaton evolution leads to several self-organization phenomena. Statistical properties of the structures generated are found to lie in two universality classes, independent of the details of the initial state or the cellular automaton rules. More complicated cellular automata are briefly considered, and connections with dynamical systems theory and the formal theory of computation are discussed.read more
Citations
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Statistical Agent-Based Models for Discrete Spatio-Temporal Systems
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Robot Guided Crowd Evacuation
TL;DR: The proposed robot guided evacuation model is an accurate Cellular Automaton simulation model capable of assessing the human behavior during emergency situations and takes advantage of the simulation output to provide sufficient information to the mobile robotic guide, which in turn approaches and redirects a group of people towards a less congestive exit at a time.
Journal ArticleDOI
The Fermi–Pasta–Ulam 'numerical experiment': history and pedagogical perspectives
TL;DR: The pioneering Fermi-Pasta-Ulam (FPU) numerical experiment played a major role in the history of computer simulation because it introduced this concept for the first time.
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The complexity of small universal Turing machines: A survey
Damien Woods,Turlough Neary +1 more
TL;DR: In this paper, it was shown that the smallest known universal Turing machines of Minsky, Rogozhin, Baiocchi and Kudlek are efficient simulators of Turing machines.
Journal ArticleDOI
Accelerating geoscience and engineering system simulations on graphics hardware
TL;DR: GPU implementations of three example applications from computational fluid dynamics, seismic wave propagation, and rock magnetism are discussed, demonstrating the power of GPU implementations for these types of simulations and, more generally, their associated computing classes.
References
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Book
Introduction to Automata Theory, Languages, and Computation
TL;DR: This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity, appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.
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The Chemical Basis of Morphogenesis
TL;DR: In this article, it is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis.
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On Computable Numbers, with an Application to the Entscheidungsproblem
TL;DR: This chapter discusses the application of the diagonal process of the universal computing machine, which automates the calculation of circle and circle-free numbers.
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Metabolic stability and epigenesis in randomly constructed genetic nets
TL;DR: The hypothesis that contemporary organisms are also randomly constructed molecular automata is examined by modeling the gene as a binary (on-off) device and studying the behavior of large, randomly constructed nets of these binary “genes”.
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Diffusion-limited aggregation, a kinetic critical phenomenon
Abstract: A model for random aggregates is studied by computer simulation The model is applicable to a metal-particle aggregation process whose correlations have been measured previously Density correlations within the model aggregates fall off with distance with a fractional power law, like those of the metal aggregates The radius of gyration of the model aggregates has power-law behavior The model is a limit of a model of dendritic growth