Collective Behaviors in Spatially Extended Systems with Local Interactions and Synchronous Updating

Hierarchies of Spatially Extended Systems and Synchronous Concurrent Algorithms

First, we study the general idea of a spatially extended system (SES) and argue that many mathematical models of systems in computing and natural science are examples of SESs. We examine the computability and the equational deenability of SESs and show that, in the discrete case, there is a natural sense in which an SES is computable if, and only if, it is deenable by equations. We look at a si...

Broken symmetries and directed collective energy transport in spatially extended systems.

We study the appearance of directed energy current in homogeneous spatially extended systems coupled to a heat bath in the presence of an external ac field E(t). The systems are described by nonlinear field equations. By making use of a symmetry analysis, we predict the right choice of E(t) and obtain directed energy transport for systems with a nonzero topological charge Q. We demonstrate that...

Symmetry and control: spatially extended chaotic systems

In a recent paper [Phys. Rev. E 57 (1998) 1550] it was demonstrated that the symmetries of the evolution equation and the target state have a profound effect on controlling the chaotic behavior. In the present paper we extend these results to the cases of time-periodic target trajectories and inexact symmetries, and apply the developed formalism to the problem of controlling spatiotemporal chao...

Entropy Production in Driven Spatially Extended Systems

This is a short review of the statistical mechanical definition of entropy production for systems composed of a large number of interacting components. Emphasis is on open systems driven away from equilibrium where the entropy production can be identified with a logarithmic ratio of microstate multiplicities of the original macrostate with respect to the time-reversed state. A special role is t...

Finite Propagation Speeds in Spatially Extended Systems