5,971 research outputs found
Exact solution of the one-dimensional deterministic Fixed-Energy Sandpile
In reason of the strongly non-ergodic dynamical behavior, universality
properties of deterministic Fixed-Energy Sandpiles are still an open and
debated issue. We investigate the one-dimensional model, whose microscopical
dynamics can be solved exactly, and provide a deeper understanding of the
origin of the non-ergodicity. By means of exact arguments, we prove the
occurrence of orbits of well-defined periods and their dependence on the
conserved energy density. Further statistical estimates of the size of the
attraction's basins of the different periodic orbits lead to a complete
characterization of the activity vs. energy density phase diagram in the limit
of large system's size.Comment: 4 pages, accepted for publication in Phys. Rev. Let
Spatio-Temporal Patterns act as Computational Mechanisms governing Emergent behavior in Robotic Swarms
open access articleOur goal is to control a robotic swarm without removing its swarm-like nature. In other words, we aim to intrinsically control a robotic swarm emergent behavior. Past attempts at governing robotic swarms or their selfcoordinating emergent behavior, has proven ineffective, largely due to the swarm’s inherent randomness (making it difficult to predict) and utter simplicity (they lack a leader, any kind of centralized control, long-range communication, global knowledge, complex internal models and only operate on a couple of basic, reactive rules). The main problem is that emergent phenomena itself is not fully understood, despite being at the forefront of current research. Research into 1D and 2D Cellular Automata has uncovered a hidden computational layer which bridges the micromacro gap (i.e., how individual behaviors at the micro-level influence the global behaviors on the macro-level). We hypothesize that there also lie embedded computational mechanisms at the heart of a robotic swarm’s emergent behavior. To test this theory, we proceeded to simulate robotic swarms (represented as both particles and dynamic networks) and then designed local rules to induce various types of intelligent, emergent behaviors (as well as designing genetic algorithms to evolve robotic swarms with emergent behaviors). Finally, we analysed these robotic swarms and successfully confirmed our hypothesis; analyzing their developments and interactions over time revealed various forms of embedded spatiotemporal patterns which store, propagate and parallel process information across the swarm according to some internal, collision-based logic (solving the mystery of how simple robots are able to self-coordinate and allow global behaviors to emerge across the swarm)
Resonant nucleation of spatio-temporal order via parametric modal amplification
We investigate, analytically and numerically, the emergence of
spatio-temporal order in nonequilibrium scalar field theories. The onset of
order is triggered by destabilizing interactions (DIs), which instantaneously
change the interacting potential from a single to a double-well, tunable to be
either degenerate (SDW) or nondegenerate (ADW). For the SDW case, we observe
the emergence of spatio-temporal coherent structures known as oscillons. We
show that this emergence is initially synchronized, the result of parametric
amplification of the relevant oscillon modes. We also discuss how these ordered
structures act as bottlenecks for equipartition. For ADW potentials, we show
how the same parametric amplification mechanism may trigger the rapid decay of
a metastable state. For a range of temperatures, the decay rates associated
with this resonant nucleation can be orders of magnitude larger than those
computed by homogeneous nucleation, with time-scales given by a simple power
law, , where depends weakly on the
temperature and is the free-energy barrier of a critical
fluctuation.Comment: 38 pages, 20 figures now included within the tex
Damage spreading in the Bak-Sneppen model: Sensitivity to the initial conditions and equilibration dynamics
The short-time and long-time dynamics of the Bak-Sneppen model of biological
evolution are investigated using the damage spreading technique. By defining a
proper Hamming distance measure, we are able to make it exhibits an initial
power-law growth which, for finite size systems, is followed by a decay towards
equilibrium. In this sense, the dynamics of self-organized critical states is
shown to be similar to the one observed at the usual critical point of
continuous phase-transitions and at the onset of chaos of non-linear
low-dimensional dynamical maps. The transient, pre-asymptotic and asymptotic
exponential relaxation of the Hamming distance between two initially
uncorrelated equilibrium configurations is also shown to be fitted within a
single mathematical framework. A connection with nonextensive statistical
mechanics is exhibited.Comment: 6 pages, 4 figs, revised version, accepted for publication in
Int.J.Mod.Phys.C 14 (2003
Regularization of Vertical-Cavity Surface-Emitting Lasers emission by periodic non-Hermitian potentials
We propose a novel physical mechanism based on periodic non-Hermitian
potentials to efficiently control the complex spatial dynamics of broad-area
lasers, particularly in Vertical-Cavity Surface-Emitting Lasers (VCSELs),
achieving a stable emission of maximum brightness. Radially dephased periodic
refractive index and gain-loss modulations accumulate the generated light from
the entire active layer and concentrate it around the structure axis to emit
narrow, bright beams. The effect is due to asymmetric-inward radial coupling
between transverse modes, for particular phase differences of the refractive
index and gain-loss modulations. Light is confined into a central beam with
large intensity opening the path to design compact, bright and efficient
broad-area light sources. We perform a comprehensive analysis to explore the
maximum central intensity enhancement and concentration regimes. The study
reveals that the optimum schemes are those holding unidirectional inward
coupling but not fulfilling a perfect local PT-symmetry.Comment: 4 pages, 4 figure
Out of equilibrium dynamics of classical and quantum complex systems
Equilibrium is a rather ideal situation, the exception rather than the rule
in Nature. Whenever the external or internal parameters of a physical system
are varied its subsequent relaxation to equilibrium may be either impossible or
take very long times. From the point of view of fundamental physics no generic
principle such as the ones of thermodynamics allows us to fully understand
their behaviour. The alternative is to treat each case separately. It is
illusionary to attempt to give, at least at this stage, a complete description
of all non-equilibrium situations. Still, one can try to identify and
characterise some concrete but still general features of a class of out of
equilibrium problems - yet to be identified - and search for a unified
description of these. In this report I briefly describe the behaviour and
theory of a set of non-equilibrium systems and I try to highlight common
features and some general laws that have emerged in recent years.Comment: 36 pages, to be published in Compte Rendus de l'Academie de Sciences,
T. Giamarchi e
Asymptotic and effective coarsening exponents in surface growth models
We consider a class of unstable surface growth models, z_t = -\partial_x J,
developing a mound structure of size lambda and displaying a perpetual
coarsening process, i.e. an endless increase in time of lambda. The coarsening
exponents n, defined by the growth law of the mound size lambda with time,
lambda=t^n, were previously found by numerical integration of the growth
equations [A. Torcini and P. Politi, Eur. Phys. J. B 25, 519 (2002)]. Recent
analytical work now allows to interpret such findings as finite time effective
exponents. The asymptotic exponents are shown to appear at so large time that
cannot be reached by direct integration of the growth equations. The reason for
the appearance of effective exponents is clearly identified.Comment: 6 pages. Several parts and conclusions have been rewritten. (Addendum
to the article that can be found in
http://www.arxiv.org/abs/cond-mat/0110058
Coarsening process in one-dimensional surface growth models
Surface growth models may give rise to unstable growth with mound formation
whose tipical linear size L increases in time. In one dimensional systems
coarsening is generally driven by an attractive interaction between domain
walls or kinks. This picture applies to growth models for which the largest
surface slope remains constant in time (model B): coarsening is known to be
logarithmic in the absence of noise (L(t)=log t) and to follow a power law
(L(t)=t^{1/3}) when noise is present. If surface slope increases indefinitely,
the deterministic equation looks like a modified Cahn-Hilliard equation: here
we study the late stage of coarsening through a linear stability analysis of
the stationary periodic configurations and through a direct numerical
integration. Analytical and numerical results agree with regard to the
conclusion that steepening of mounds makes deterministic coarsening faster: if
alpha is the exponent describing the steepening of the maximal slope M of
mounds (M^alpha = L) we find that L(t)=t^n: n is equal to 1/4 for 1<alpha<2 and
it decreases from 1/4 to 1/5 for alpha>2, according to n=alpha/(5*alpha -2). On
the other side, the numerical solution of the corresponding stochastic equation
clearly shows that in the presence of shot noise steepening of mounds makes
coarsening slower than in model B: L(t)=t^{1/4}, irrespectively of alpha.
Finally, the presence of a symmetry breaking term is shown not to modify the
coarsening law of model alpha=1, both in the absence and in the presence of
noise.Comment: One figure and relative discussion changed. To be published in Eur.
Phys. J.
- …