69 research outputs found
Spatiotemporal intermittency and scaling laws in the coupled sine circle map lattice
We study spatio-temporal intermittency (STI) in a system of coupled sine
circle maps. The phase diagram of the system shows parameter regimes with STI
of both the directed percolation (DP) and non-DP class. STI with synchronized
laminar behaviour belongs to the DP class. The regimes of non-DP behaviour show
spatial intermittency (SI), where the temporal behaviour of both the laminar
and burst regions is regular, and the distribution of laminar lengths scales as
a power law. The regular temporal behaviour for the bursts seen in these
regimes of spatial intermittency can be periodic or quasi-periodic, but the
laminar length distributions scale with the same power-law, which is distinct
from the DP case. STI with traveling wave (TW) laminar states also appears in
the phase diagram. Soliton-like structures appear in this regime. These are
responsible for cross-overs with accompanying non-universal exponents. The
soliton lifetime distributions show power law scaling in regimes of long
average soliton life-times, but peak at characteristic scales with a power-law
tail in regimes of short average soliton life-times. The signatures of each
type of intermittent behaviour can be found in the dynamical characterisers of
the system viz. the eigenvalues of the stability matrix. We discuss the
implications of our results for behaviour seen in other systems which exhibit
spatio-temporal intermittency.Comment: 25 pages, 11 figures. Submitted to Phys. Rev.
Comment on ``Deterministic equations of motion and phase ordering dynamics''
Zheng [Phys. Rev. E {\bf 61}, 153 (2000), cond-mat/9909324] claims that phase
ordering dynamics in the microcanonical model displays unusual scaling
laws. We show here, performing more careful numerical investigations, that
Zheng only observed transient dynamics mostly due to the corrections to scaling
introduced by lattice effects, and that Ising-like (model A) phase ordering
actually takes place at late times. Moreover, we argue that energy conservation
manifests itself in different corrections to scaling.Comment: 5 pages, 4 figure
How does the market react to your order flow?
We present an empirical study of the intertwined behaviour of members in a
financial market. Exploiting a database where the broker that initiates an
order book event can be identified, we decompose the correlation and response
functions into contributions coming from different market participants and
study how their behaviour is interconnected. We find evidence that (1) brokers
are very heterogeneous in liquidity provision -- some are consistently
liquidity providers while others are consistently liquidity takers. (2) The
behaviour of brokers is strongly conditioned on the actions of {\it other}
brokers. In contrast brokers are only weakly influenced by the impact of their
own previous orders. (3) The total impact of market orders is the result of a
subtle compensation between the same broker pushing the price in one direction
and the liquidity provision of other brokers pushing it in the opposite
direction. These results enforce the picture of market dynamics being the
result of the competition between heterogeneous participants interacting to
form a complicated market ecology.Comment: 22 pages, 5+9 figure
Lyapunov exponents as a dynamical indicator of a phase transition
We study analytically the behavior of the largest Lyapunov exponent
for a one-dimensional chain of coupled nonlinear oscillators, by
combining the transfer integral method and a Riemannian geometry approach. We
apply the results to a simple model, proposed for the DNA denaturation, which
emphasizes a first order-like or second order phase transition depending on the
ratio of two length scales: this is an excellent model to characterize
as a dynamical indicator close to a phase transition.Comment: 8 Pages, 3 Figure
Absorbing Phase Transitions of Branching-Annihilating Random Walks
The phase transitions to absorbing states of the branching-annihilating
reaction-diffusion processes mA --> (m+k)A, nA --> (n-l)A are studied
systematically in one space dimension within a new family of models. Four
universality classes of non-trivial critical behavior are found. This provides,
in particular, the first evidence of universal scaling laws for pair and
triplet processes.Comment: 4 pages, 4 figure
Comment on ``Phase ordering in chaotic map lattices with conserved dynamics''
Angelini, Pellicoro, and Stramaglia [Phys. Rev. E {\bf 60}, R5021 (1999),
cond-mat/9907149] (APS) claim that the phase ordering of two-dimensional
systems of sequentially-updated chaotic maps with conserved ``order parameter''
does not belong, for large regions of parameter space, to the expected
universality class. We show here that these results are due to a slow crossover
and that a careful treatment of the data yields normal dynamical scaling.
Moreover, we construct better models, i.e. synchronously-updated coupled map
lattices, which are exempt from these crossover effects, and allow for the
first precise estimates of persistence exponents in this case.Comment: 3 pages, to be published in Phys. Rev.
Phase separation in coupled chaotic maps on fractal networks
The phase ordering dynamics of coupled chaotic maps on fractal networks are
investigated. The statistical properties of the systems are characterized by
means of the persistence probability of equivalent spin variables that define
the phases. The persistence saturates and phase domains freeze for all values
of the coupling parameter as a consequence of the fractal structure of the
networks, in contrast to the phase transition behavior previously observed in
regular Euclidean lattices. Several discontinuities and other features found in
the saturation persistence curve as a function of the coupling are explained in
terms of changes of stability of local phase configurations on the fractals.Comment: (4 pages, 4 Figs, Submitted to PRE
Universality in the pair contact process with diffusion
The pair contact process with diffusion is studied by means of multispin
Monte Carlo simulations and density matrix renormalization group calculations.
Effective critical exponents are found to behave nonmonotonically as functions
of time or of system length and extrapolate asymptotically towards values
consistent with the directed percolation universality class. We argue that an
intermediate regime exists where the effective critical dynamics resembles that
of a parity conserving process.Comment: 8 Pages, 9 figures, final version as publishe
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