57,199 research outputs found
A framework for the local information dynamics of distributed computation in complex systems
The nature of distributed computation has often been described in terms of
the component operations of universal computation: information storage,
transfer and modification. We review the first complete framework that
quantifies each of these individual information dynamics on a local scale
within a system, and describes the manner in which they interact to create
non-trivial computation where "the whole is greater than the sum of the parts".
We describe the application of the framework to cellular automata, a simple yet
powerful model of distributed computation. This is an important application,
because the framework is the first to provide quantitative evidence for several
important conjectures about distributed computation in cellular automata: that
blinkers embody information storage, particles are information transfer agents,
and particle collisions are information modification events. The framework is
also shown to contrast the computations conducted by several well-known
cellular automata, highlighting the importance of information coherence in
complex computation. The results reviewed here provide important quantitative
insights into the fundamental nature of distributed computation and the
dynamics of complex systems, as well as impetus for the framework to be applied
to the analysis and design of other systems.Comment: 44 pages, 8 figure
On the shapes of elementary domains or why Mandelbrot Set is made from almost ideal circles?
Direct look at the celebrated "chaotic" Mandelbrot Set in Fig..\ref{Mand2}
immediately reveals that it is a collection of almost ideal circles and
cardioids, unified in a specific {\it forest} structure. In /hep-th/9501235 a
systematic algebro-geometric approach was developed to the study of generic
Mandelbrot sets, but emergency of nearly ideal circles in the special case of
the family was not fully explained. In the present paper the shape of
the elementary constituents of Mandelbrot Set is explicitly {\it calculated},
and difference between the shapes of {\it root} and {\it descendant} domains
(cardioids and circles respectively) is explained. Such qualitative difference
persists for all other Mandelbrot sets: descendant domains always have one less
cusp than the root ones. Details of the phase transition between different
Mandelbrot sets are explicitly demonstrated, including overlaps between
elementary domains and dynamics of attraction/repulsion regions. Explicit
examples of 3-dimensional sections of Universal Mandelbrot Set are given. Also
a systematic small-size approximation is developed for evaluation of various
Feigenbaum indices.Comment: 65 pages, 30 figure
Observations of spatiotemporal instabilities in the strong-driving regime of an AC-driven nonlinear Schr\"odinger system
Localized dissipative structures (LDS) have been predicted to display a rich
array of instabilities, yet systematic experimental studies have remained
scarce. We have used a synchronously-driven optical fiber ring resonator to
experimentally study LDS instabilities in the strong-driving regime of the
AC-driven nonlinear Schr\"odinger equation (also known as the Lugiato-Lefever
model). Through continuous variation of a single control parameter, we have
observed a string of theoretically predicted instability modes, including
irregular oscillations and chaotic collapses. Beyond a critical point, we
observe behaviour reminiscent of a phase transition: LDSs trigger localized
domains of spatiotemporal chaos that invade the surrounding homogeneous state.
Our findings directly confirm a number of theoretical predictions, and they
highlight that complex LDS instabilities can play a role in experimental
systems.Comment: 6 pages, 4 figure
Dynamics and Thermodynamics of Systems with Long Range Interactions: an Introduction
We review theoretical results obtained recently in the framework of
statistical mechanics to study systems with long range forces. This fundamental
and methodological study leads us to consider the different domains of
applications in a trans-disciplinary perspective (astrophysics, nuclear
physics, plasmas physics, metallic clusters, hydrodynamics,...) with a special
emphasis on Bose-Einstein condensates.Comment: Chapter of the forthcoming "Lecture Notes in Physics" volume:
``Dynamics and Thermodynamics of Systems with Long Range Interactions'', T.
Dauxois, S. Ruffo, E. Arimondo, M. Wilkens Eds., Lecture Notes in Physics
Vol. 602, Springer (2002). (see http://link.springer.de/series/lnpp/
Kinetics, Hydrodynamics and Stochastodynamics of Cellular Structure Coarsening
For the first time the phenomenon of cellular structure coarsening are
consistently analysed from the positions of kinetic, hydrodynamic and
stochastodynamic theories of nonequilibrium statistical systems. Thereby
micro-, meso- and macroscopic levels of approach are distinguished. At the
microscopic level the cellular structure is describe by a probability
distribution function in a phase space of cell coordinates and of cell sizes. A
kinetic equation for the function is written and a development to a
hydrodynamic equation of a mesoscopic cell medium is realised. It has the form
of a diffusion-reaction equation with a negative "diffusion" coefficient and
with a cell interface density playing the role of concentration. Its analysis
reveals a new effect of macroscopic patterning in the cell medium: existence of
space-correlated stochastic fluctuations of the cell interface density.Comment: 12 pages, Latex, 3 eps figures. Submitted for publication in Modern
Physics Letters B on 11/04/97, accepted on 18/09/97 . Revision was made to
include the PS figures in the body of the pape
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