937 research outputs found
Critical behavior of a cellular automaton highway traffic model
We derive the critical behavior of a CA traffic flow model using an order
parameter breaking the symmetry of the jam-free phase. Random braking appears
to be the symmetry-breaking field conjugate to the order parameter. For
, we determine the values of the critical exponents ,
and using an order-3 cluster approximation and computer
simulations. These critical exponents satisfy a scaling relation, which can be
derived assuming that the order parameter is a generalized homogeneous function
of and p in the vicinity of the phase transition point.Comment: 6 pages, 12 figure
Conservation Laws in Cellular Automata
If X is a discrete abelian group and B a finite set, then a cellular
automaton (CA) is a continuous map F:B^X-->B^X that commutes with all X-shifts.
If g is a real-valued function on B, then, for any b in B^X, we define G(b) to
be the sum over all x in X of g(b_x) (if finite). We say g is `conserved' by F
if G is constant under the action of F. We characterize such `conservation
laws' in several ways, deriving both theoretical consequences and practical
tests, and provide a method for constructing all one-dimensional CA exhibiting
a given conservation law.Comment: 19 pages, LaTeX 2E with one (1) Encapsulated PostScript figure. To
appear in Nonlinearity. (v2) minor changes/corrections; new references added
to bibliograph
Probabilistic cellular automata with conserved quantities
We demonstrate that the concept of a conservation law can be naturally
extended from deterministic to probabilistic cellular automata (PCA) rules. The
local function for conservative PCA must satisfy conditions analogous to
conservation conditions for deterministic cellular automata. Conservation
condition for PCA can also be written in the form of a current conservation
law. For deterministic nearest-neighbour CA the current can be computed
exactly. Local structure approximation can partially predict the equilibrium
current for non-deterministic cases. For linear segments of the fundamental
diagram it actually produces exact results.Comment: 17 pages, 2 figure
Non-deterministic density classification with diffusive probabilistic cellular automata
We present a probabilistic cellular automaton (CA) with two absorbing states
which performs classification of binary strings in a non-deterministic sense.
In a system evolving under this CA rule, empty sites become occupied with a
probability proportional to the number of occupied sites in the neighborhood,
while occupied sites become empty with a probability proportional to the number
of empty sites in the neighborhood. The probability that all sites become
eventually occupied is equal to the density of occupied sites in the initial
string.Comment: 4 pages, 4 figure
Persistence, extinction and spatio-temporal synchronization of SIRS cellular automata models
Spatially explicit models have been widely used in today's mathematical
ecology and epidemiology to study persistence and extinction of populations as
well as their spatial patterns. Here we extend the earlier work--static
dispersal between neighbouring individuals to mobility of individuals as well
as multi-patches environment. As is commonly found, the basic reproductive
ratio is maximized for the evolutionary stable strategy (ESS) on diseases'
persistence in mean-field theory. This has important implications, as it
implies that for a wide range of parameters that infection rate will tend
maximum. This is opposite with present results obtained in spatial explicit
models that infection rate is limited by upper bound. We observe the emergence
of trade-offs of extinction and persistence on the parameters of the infection
period and infection rate and show the extinction time having a linear
relationship with respect to system size. We further find that the higher
mobility can pronouncedly promote the persistence of spread of epidemics, i.e.,
the phase transition occurs from extinction domain to persistence domain, and
the spirals' wavelength increases as the mobility increasing and ultimately, it
will saturate at a certain value. Furthermore, for multi-patches case, we find
that the lower coupling strength leads to anti-phase oscillation of infected
fraction, while higher coupling strength corresponds to in-phase oscillation.Comment: 12page
Universal behavior at discontinuous quantum phase transitions
Discontinuous quantum phase transitions besides their general interest are
clearly relevant to the study of heavy fermions and magnetic transition metal
compounds. Recent results show that in many systems belonging to these classes
of materials, the magnetic transition changes from second order to first order
as they approach the quantum critical point (QCP). We investigate here some
mechanisms that may be responsible for this change. Specifically the coupling
of the order parameter to soft modes and the competition between different
types of order near the QCP. For weak first order quantum phase transitions
general results are obtained. In particular we describe the thermodynamic
behavior at this transition when it is approached from finite temperatures.
This is the discontinuous equivalent of the non-Fermi liquid trajectory close
to a conventional QCP in a heavy fermion material.Comment: 7 pages, 3 figure
Hawks and Doves on Small-World Networks
We explore the Hawk-Dove game on networks with topologies ranging from
regular lattices to random graphs with small-world networks in between. This is
done by means of computer simulations using several update rules for the
population evolutionary dynamics. We find the overall result that cooperation
is sometimes inhibited and sometimes enhanced in those network structures, with
respect to the mixing population case. The differences are due to different
update rules and depend on the gain-to-cost ratio. We analyse and qualitatively
explain this behavior by using local topological arguments.Comment: 12 pages, 8 figure
Estimation of the order parameter exponent of critical cellular automata using the enhanced coherent anomaly method.
The stochastic cellular automaton of Rule 18 defined by Wolfram [Rev. Mod.
Phys. 55 601 (1983)] has been investigated by the enhanced coherent anomaly
method. Reliable estimate was found for the critical exponent, based on
moderate sized () clusters.Comment: 6 pages, RevTeX file, figure available from [email protected]
Controlling Light Through Optical Disordered Media : Transmission Matrix Approach
We experimentally measure the monochromatic transmission matrix (TM) of an
optical multiple scattering medium using a spatial light modulator together
with a phase-shifting interferometry measurement method. The TM contains all
information needed to shape the scattered output field at will or to detect an
image through the medium. We confront theory and experiment for these
applications and we study the effect of noise on the reconstruction method. We
also extracted from the TM informations about the statistical properties of the
medium and the light transport whitin it. In particular, we are able to isolate
the contributions of the Memory Effect (ME) and measure its attenuation length
Universal patterns in sound amplitudes of songs and music genres
We report a statistical analysis over more than eight thousand songs.
Specifically, we investigate the probability distribution of the normalized
sound amplitudes. Our findings seems to suggest a universal form of
distribution which presents a good agreement with a one-parameter stretched
Gaussian. We also argue that this parameter can give information on music
complexity, and consequently it goes towards classifying songs as well as music
genres. Additionally, we present statistical evidences that correlation aspects
of the songs are directly related with the non-Gaussian nature of their sound
amplitude distributions.Comment: Accepted for publication as a Brief Report in Physical Review
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