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We analyze the leading Lyapunov exponents of SU(2) Yang-Mills field configurations on the lattice which are initialized by quantum Monte Carlo simulations. We find that configurations in the strong coupling phase at finite temperature are substantially more chaotic than in deconfinement.
A coupled map model for cloud dynamics is proposed, which consists of the successive operations of the physical processes; buoyancy, diffusion, viscosity, adiabatic expansion, fall of a droplet by gravity, descent flow dragged by the falling droplet, and advection. Through extensive simulations, the phases corresponding to stratus, cumulus, stratocumulus and cumulonimbus are found, with the change of the ground temperature and the moisture of the air. They are characterized by order parameters such as the cluster number, perimeter-to-area ratio of a cloud, and Kolmogorov-Sinai entropy.
Dissipative Euler and Navier Stokes equations are discussed with the aim of proposing several experiments apt to test the equivalence of dynamical ensembles and the chaotic hypothesis.
Computational mechanics, an approach to structural complexity, defines a process's causal states and gives a procedure for finding them. We show that the causal-state representation--an $ε$-machine--is the minimal one consistent with accurate prediction. We establish several results on $ε$-machine optimality and uniqueness and on how $ε$-machines compare to alternative representations. Further results relate measures of randomness and structural complexity obtained from $ε$-machines to those from ergodic and information theories.
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Cosma Rohilla Shalizi contributes to research discovery and scholarly infrastructure.
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Kunihiko Kaneko contributes to research discovery and scholarly infrastructure.
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Giovanni Gallavotti contributes to research discovery and scholarly infrastructure.
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Tatsuo Yanagita contributes to research discovery and scholarly infrastructure.
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James P. Crutchfield contributes to research discovery and scholarly infrastructure.
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Tamas S. Biro contributes to research discovery and scholarly infrastructure.
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Harald Markum contributes to research discovery and scholarly infrastructure.
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Markus Feurstein contributes to research discovery and scholarly infrastructure.
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