740 research outputs found
Public channel cryptography by synchronization of neural networks and chaotic maps
Two different kinds of synchronization have been applied to cryptography:
Synchronization of chaotic maps by one common external signal and
synchronization of neural networks by mutual learning. By combining these two
mechanisms, where the external signal to the chaotic maps is synchronized by
the nets, we construct a hybrid network which allows a secure generation of
secret encryption keys over a public channel. The security with respect to
attacks, recently proposed by Shamir et al, is increased by chaotic
synchronization.Comment: 4 page
Critical behavior for mixed site-bond directed percolation
We study mixed site-bond directed percolation on 2D and 3D lattices by using
time-dependent simulations. Our results are compared with rigorous bounds
recently obtained by Liggett and by Katori and Tsukahara. The critical
fractions and of sites and bonds are extremely well
approximated by a relationship reported earlier for isotropic percolation,
, where and are the critical fractions in
pure site and bond directed percolation.Comment: 10 pages, figures available on request from [email protected]
Active Width at a Slanted Active Boundary in Directed Percolation
The width W of the active region around an active moving wall in a directed
percolation process diverges at the percolation threshold p_c as W \simeq A
\epsilon^{-\nu_\parallel} \ln(\epsilon_0/\epsilon), with \epsilon=p_c-p,
\epsilon_0 a constant, and \nu_\parallel=1.734 the critical exponent of the
characteristic time needed to reach the stationary state \xi_\parallel \sim
\epsilon^{-\nu_\parallel}. The logarithmic factor arises from screening of
statistically independent needle shaped sub clusters in the active region.
Numerical data confirm this scaling behaviour.Comment: 5 pages, 5 figure
Compact parity conserving percolation in one-dimension
Compact directed percolation is known to appear at the endpoint of the
directed percolation critical line of the Domany-Kinzel cellular automaton in
1+1 dimension. Equivalently, such transition occurs at zero temperature in a
magnetic field H, upon changing the sign of H, in the one-dimensional
Glauber-Ising model with well known exponents characterising spin-cluster
growth. We have investigated here numerically these exponents in the
non-equilibrium generalization (NEKIM) of the Glauber model in the vicinity of
the parity-conserving phase transition point of the kinks. Critical
fluctuations on the level of kinks are found to affect drastically the
characteristic exponents of spreading of spins while the hyperscaling relation
holds in its form appropriate for compact clusters.Comment: 7 pages, 7 figures embedded in the latex, final form before J.Phys.A
publicatio
Numerical Diagonalisation Study of the Trimer Deposition-Evaporation Model in One Dimension
We study the model of deposition-evaporation of trimers on a line recently
introduced by Barma, Grynberg and Stinchcombe. The stochastic matrix of the
model can be written in the form of the Hamiltonian of a quantum spin-1/2 chain
with three-spin couplings given by H= \sum\displaylimits_i [(1 -
\sigma_i^-\sigma_{i+1}^-\sigma_{i+2}^-) \sigma_i^+\sigma_{i+1}^+\sigma_{i+2}^+
+ h.c]. We study by exact numerical diagonalization of the variation of
the gap in the eigenvalue spectrum with the system size for rings of size up to
30. For the sector corresponding to the initial condition in which all sites
are empty, we find that the gap vanishes as where the gap exponent
is approximately . This model is equivalent to an interfacial
roughening model where the dynamical variables at each site are matrices. From
our estimate for the gap exponent we conclude that the model belongs to a new
universality class, distinct from that studied by Kardar, Parisi and Zhang.Comment: 11 pages, 2 figures (included
Directed Percolation with a Wall or Edge
We examine the effects of introducing a wall or edge into a directed
percolation process. Scaling ansatzes are presented for the density and
survival probability of a cluster in these geometries, and we make the
connection to surface critical phenomena and field theory. The results of
previous numerical work for a wall can thus be interpreted in terms of surface
exponents satisfying scaling relations generalising those for ordinary directed
percolation. New exponents for edge directed percolation are also introduced.
They are calculated in mean-field theory and measured numerically in 2+1
dimensions.Comment: 14 pages, submitted to J. Phys.
Directed Fixed Energy Sandpile Model
We numerically study the directed version of the fixed energy sandpile. On a
closed square lattice, the dynamical evolution of a fixed density of sand
grains is studied. The activity of the system shows a continuous phase
transition around a critical density. While the deterministic version has the
set of nontrivial exponents, the stochastic model is characterized by mean
field like exponents.Comment: 5 pages, 6 figures, to be published in Phys. Rev.
Hyperscaling in the Domany-Kinzel Cellular Automaton
An apparent violation of hyperscaling at the endpoint of the critical line in
the Domany-Kinzel stochastic cellular automaton finds an elementary resolution
upon noting that the order parameter is discontinuous at this point. We derive
a hyperscaling relation for such transitions and discuss applications to
related examples.Comment: 8 pages, latex, no figure
Nature of phase transitions in a probabilistic cellular automaton with two absorbing states
We present a probabilistic cellular automaton with two absorbing states,
which can be considered a natural extension of the Domany-Kinzel model. Despite
its simplicity, it shows a very rich phase diagram, with two second-order and
one first-order transition lines that meet at a tricritical point. We study the
phase transitions and the critical behavior of the model using mean field
approximations, direct numerical simulations and field theory. A closed form
for the dynamics of the kinks between the two absorbing phases near the
tricritical point is obtained, providing an exact correspondence between the
presence of conserved quantities and the symmetry of absorbing states. The
second-order critical curves and the kink critical dynamics are found to be in
the directed percolation and parity conservation universality classes,
respectively. The first order phase transition is put in evidence by examining
the hysteresis cycle. We also study the "chaotic" phase, in which two replicas
evolving with the same noise diverge, using mean field and numerical
techniques. Finally, we show how the shape of the potential of the
field-theoretic formulation of the problem can be obtained by direct numerical
simulations.Comment: 19 pages with 7 figure
A simple model of epitaxial growth
A discrete solid-on-solid model of epitaxial growth is introduced which, in a
simple manner, takes into account the effect of an Ehrlich-Schwoebel barrier at
step edges as well as the local relaxation of incoming particles. Furthermore a
fast step edge diffusion is included in 2+1 dimensions. The model exhibits the
formation of pyramid-like structures with a well-defined constant inclination
angle. Two regimes can be distinguished clearly: in an initial phase (I) a
definite slope is selected while the number of pyramids remains unchanged. Then
a coarsening process (II) is observed which decreases the number of islands
according to a power law in time. Simulations support self-affine scaling of
the growing surface in both regimes. The roughness exponent is alpha =1 in all
cases. For growth in 1+1 dimensions we obtain dynamic exponents z = 2 (I) and z
= 3 (II). Simulations for d=2+1 seem to be consistent with z= 2 (I) and z= 2.3
(II) respectively.Comment: 8 pages Latex2e, 4 Postscript figures included, uses packages
a4wide,epsfig,psfig,amsfonts,latexsy
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