1,235 research outputs found
Large-Scale Synchrony in Weakly Interacting Automata
We study the behavior of two spatially distributed (sandpile) models which
are weakly linked with one another. Using a Monte-Carlo implementation of the
renormalization group and algebraic methods, we describe how large-scale
correlations emerge between the two systems, leading to synchronized behavior.Comment: 6 pages, 3 figures; to appear PR
The Emergence of Correlations in Studies of Global Economic Inter-dependence and Contagion
We construct a simple firm-based automata model for global economic inter-dependence of countries using modern notions of self-organized criticality and recently developed dynamical-renormalization-group methods (e.g., L. Pietronero et al., Phys. Rev. Lett., 72(11):1690 (1994); J. Hasty and K. Wiesenfeld, Phys. Rev. Lett., 81(8):1722, (1998)). We demonstrate how extremely strong statistical correlations can naturally develop between two countries even if the financial interconnections between those countries remain very weak. Potential policy implications of this result are also discussed.
Binary neutron stars: Equilibrium models beyond spatial conformal flatness
Equilibria of binary neutron stars in close circular orbits are computed
numerically in a waveless formulation: The full Einstein-relativistic-Euler
system is solved on an initial hypersurface to obtain an asymptotically flat
form of the 4-metric and an extrinsic curvature whose time derivative vanishes
in a comoving frame. Two independent numerical codes are developed, and
solution sequences that model inspiraling binary neutron stars during the final
several orbits are successfully computed. The binding energy of the system near
its final orbit deviates from earlier results of third post-Newtonian and of
spatially conformally flat calculations. The new solutions may serve as initial
data for merger simulations and as members of quasiequilibrium sequences to
generate gravitational wave templates, and may improve estimates of the
gravitational-wave cutoff frequency set by the last inspiral orbit.Comment: 4 pages, 6 figures, revised version, PRL in pres
Nonlinear Dynamics in Combinatorial Games: Renormalizing Chomp
We develop a new approach to combinatorial games that reveals connections between such games and some of the central ideas of nonlinear dynamics: scaling behaviors, complex dynamics and chaos, universality, and aggregation processes. We take as our model system the combinatorial game Chomp, which is one of the simplest in a class of unsolved combinatorial games that includes Chess, Checkers, and Go. We discover that the game possesses an underlying geometric structure that grows (reminiscent of crystal growth), and show how this growth can be analyzed using a renormalization procedure adapted from physics. In effect, this methodology allows one to transform a combinatorial game like Chomp into a type of dynamical system. Not only does this provide powerful insights into the game of Chomp (yielding a complete probabilistic description of optimal play in Chomp and an answer to a longstanding question about the nature of the winning opening move), but more generally, it offers a mathematical framework for exploring this unexpected relationship between combinatorial games and modern dynamical systems theory
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