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
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Journal ArticleDOI
Cellular automata and Riccati equation models for diffusion of innovations
Renato Guseo,Mariangela Guidolin +1 more
TL;DR: A link is presented between a particular kind of CA and a separable non autonomous Riccati equation and a new aggregate model, which simultaneously considers birth and death processes within the diffusion, which is both of theoretical and empirical interest.
Dissertation
Effects of dynamic vegetation and topography on hydrological processes in semi-arid areas
Abstract: Ecosystems of dry climates represent a particularly interesting object for ecohydrological studies, as water is generally considered to be the key limiting resource. This work focuses on vegetation-water-energy dynamics occurring in the complex terrain of a semi-arid area characteristic of central New Mexico. The study constructs a dynamic model of coupled interactions, [tRIBS+VEGGIE], that considers essential water and energy processes over the river basin and links them to the basic plant life regulatory processes. After model calibration, a set of numerical experiments is carried out for two small-scale synthetic domains that exhibit characteristic hillslope curvatures. A weather generator is used to create the long-term series of meteorological forcing. The linkages between terrain attributes and patterns of C4 grass productivity and water balance components are examined for three generic soil types: sand, loam, and clay. It is argued that in conditions of negligible moisture exchange, site aspect and slope are the key determinants of both the hydrologic behavior and the degree of "favorability" to vegetation. As shown, certain topographic locations are more favorable to vegetation development, as compared to a flat horizontal surface not affected by lateral effects such as radiative shading or water transfer. These locations are associated with sites of northerly aspect with surface slopes within a narrow range of magnitudes. Contributions from both the rainfall and radiation forcings are discussed to explain the existence of these niches. The sensitivity of results is investigated relative to modifications in the meteorological forcing and the dominant mechanism of lateral water transfer. The analysis unequivocally demonstrates the critical role of soil texture type in regulating the spatio-temporal aspects of coupling between vegetation-hydrology processes. Two additional controlling topographic features are suggested, corresponding to the local and global terrain convergence levels. Furthermore, it is argued that grass productivity and water fluxes of a site can be characterized as a function combining local and global terrain properties. Thesis Supervisor: Rafael L. Bras Title: Edward Abdun-Nur Professor of Civil and Environmental Engineering
Journal ArticleDOI
Classification of triangular and honeycomb cellular automata
TL;DR: Cellular automata on a two-dimensional triangular and honeycomb lattice are classified according to their fixed points and periods and the results are compared with other lattices in one of three dimensions.
Journal ArticleDOI
Cellular automata-based built-in self-test structures for VLSI systems
TL;DR: The great advantage of HACA over linear feedback shift registers (LFSR), as their size increases, is the fact that HACA display locality and topological regularity, important attributes for VLSI implementation.
Journal ArticleDOI
Stochastic coupling of two random Boolean networks
TL;DR: The dynamics of two coupled random Boolean networks are studied using the stochastic coupling techniques and the density evolution of networks is precisely described by two deterministic coupled polynomial maps.
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.
Journal ArticleDOI
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”.
Journal ArticleDOI
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