465 research outputs found
Synchronization and directed percolation in coupled map lattices
We study a synchronization mechanism, based on one-way coupling of
all-or-nothing type, applied to coupled map lattices with several different
local rules. By analyzing the metric and the topological distance between the
two systems, we found two different regimes: a strong chaos phase in which the
transition has a directed percolation character and a weak chaos phase in which
the synchronization transition occurs abruptly. We are able to derive some
analytical approximations for the location of the transition point and the
critical properties of the system.
We propose to use the characteristics of this transition as indicators of the
spatial propagation of chaoticity.Comment: 12 pages + 12 figure
Secure exchange of information by synchronization of neural networks
A connection between the theory of neural networks and cryptography is
presented. A new phenomenon, namely synchronization of neural networks is
leading to a new method of exchange of secret messages. Numerical simulations
show that two artificial networks being trained by Hebbian learning rule on
their mutual outputs develop an antiparallel state of their synaptic weights.
The synchronized weights are used to construct an ephemeral key exchange
protocol for a secure transmission of secret data. It is shown that an opponent
who knows the protocol and all details of any transmission of the data has no
chance to decrypt the secret message, since tracking the weights is a hard
problem compared to synchronization. The complexity of the generation of the
secure channel is linear with the size of the network.Comment: 11 pages, 5 figure
On the Use of Finite-Size Scaling to Measure Spin-Glass Exponents
Finite-size scaling (FSS) is a standard technique for measuring scaling
exponents in spin glasses. Here we present a critique of this approach,
emphasizing the need for all length scales to be large compared to microscopic
scales. In particular we show that the replacement, in FSS analyses, of the
correlation length by its asymptotic scaling form can lead to apparently good
scaling collapses with the wrong values of the scaling exponents.Comment: RevTeX, 5 page
A lattice gas model of II-VI(001) semiconductor surfaces
We introduce an anisotropic two-dimensional lattice gas model of metal
terminated II-IV(001) seminconductor surfaces. Important properties of this
class of materials are represented by effective NN and NNN interactions, which
result in the competition of two vacancy structures on the surface. We
demonstrate that the experimentally observed c(2x2)-(2x1) transition of the
CdTe(001) surface can be understood as a phase transition in thermal
equilbrium. The model is studied by means of transfer matrix and Monte Carlo
techniques. The analysis shows that the small energy difference of the
competing reconstructions determines to a large extent the nature of the
different phases. Possible implications for further experimental research are
discussed.Comment: 7 pages, 2 figure
Surface Shape and Local Critical Behaviour in Two-Dimensional Directed Percolation
Two-dimensional directed site percolation is studied in systems directed
along the x-axis and limited by a free surface at y=\pm Cx^k. Scaling
considerations show that the surface is a relevant perturbation to the local
critical behaviour when k<1/z where z=\nu_\parallel/\nu is the dynamical
exponent. The tip-to-bulk order parameter correlation function is calculated in
the mean-field approximation. The tip percolation probability and the fractal
dimensions of critical clusters are obtained through Monte-Carlo simulations.
The tip order parameter has a nonuniversal, C-dependent, scaling dimension in
the marginal case, k=1/z, and displays a stretched exponential behaviour when
the perturbation is relevant. The k-dependence of the fractal dimensions in the
relevant case is in agreement with the results of a blob picture approach.Comment: 13 pages, Plain TeX file, epsf, 6 postscript-figures, minor
correction
Towards Classification of Phase Transitions in Reaction--Diffusion Models
Equilibrium phase transitions are associated with rearrangements of minima of
a (Lagrangian) potential. Treatment of non-equilibrium systems requires
doubling of degrees of freedom, which may be often interpreted as a transition
from the ``coordinate'' to the ``phase'' space representation. As a result, one
has to deal with the Hamiltonian formulation of the field theory instead of the
Lagrangian one. We suggest a classification scheme of phase transitions in
reaction-diffusion models based on the topology of the phase portraits of
corresponding Hamiltonians. In models with an absorbing state such a topology
is fully determined by intersecting curves of zero ``energy''. We identify four
families of topologically distinct classes of phase portraits stable upon RG
transformations.Comment: 14 pages, 9 figure
Crossover Scaling Functions in One Dimensional Dynamic Growth Models
The crossover from Edwards-Wilkinson () to KPZ () type growth is
studied for the BCSOS model. We calculate the exact numerical values for the
and massgap for using the master equation. We predict
the structure of the crossover scaling function and confirm numerically that
and , with . KPZ type growth is
equivalent to a phase transition in meso-scopic metallic rings where attractive
interactions destroy the persistent current; and to endpoints of facet-ridges
in equilibrium crystal shapes.Comment: 11 pages, TeX, figures upon reques
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