101 research outputs found
The Strange Man in Random Networks of Automata
We have performed computer simulations of Kauffman's automata on several
graphs such as the regular square lattice and invasion percolation clusters in
order to investigate phase transitions, radial distributions of the mean total
damage (dynamical exponent ) and propagation speeds of the damage when one
adds a damaging agent, nicknamed "strange man". Despite the increase in the
damaging efficiency, we have not observed any appreciable change at the
transition threshold to chaos neither for the short-range nor for the
small-world case on the square lattices when the strange man is added in
comparison to when small initial damages are inserted in the system. The
propagation speed of the damage cloud until touching the border of the system
in both cases obeys a power law with a critical exponent that strongly
depends on the lattice. Particularly, we have ckecked the damage spreading when
some connections are removed on the square lattice and when one considers
special invasion percolation clusters (high boundary-saturation clusters). It
is seen that the propagation speed in these systems is quite sensible to the
degree of dilution.Comment: AMS-LaTeX v1.2, 7 pages with 14 figures Encapsulated Postscript, to
be publishe
Adjustment and social choice
We discuss the influence of information contagion on the dynamics of choices
in social networks of heterogeneous buyers. Starting from an inhomogeneous
cellular automata model of buyers dynamics, we show that when agents try to
adjust their reservation price, the tatonement process does not converge to
equilibrium at some intermediate market share and that large amplitude
fluctuations are actually observed. When the tatonnement dynamics is slow with
respect to the contagion dynamics, large periodic oscillations reminiscent of
business cycles appear.Comment: 13 pages, 6 figure
An algorithm for simulating the Ising model on a type-II quantum computer
Presented here is an algorithm for a type-II quantum computer which simulates
the Ising model in one and two dimensions. It is equivalent to the Metropolis
Monte-Carlo method and takes advantage of quantum superposition for random
number generation. This algorithm does not require the ensemble of states to be
measured at the end of each iteration, as is required for other type-II
algorithms. Only the binary result is measured at each node which means this
algorithm could be implemented using a range of different quantum computing
architectures. The Ising model provides an example of how cellular automata
rules can be formulated to be run on a type-II quantum computer.Comment: 14 pages, 11 figures. Accepted for publication in Computer Physics
Communication
Lyapunov Exponents in Random Boolean Networks
A new order parameter approximation to Random Boolean Networks (RBN) is
introduced, based on the concept of Boolean derivative. A statistical argument
involving an annealed approximation is used, allowing to measure the order
parameter in terms of the statistical properties of a random matrix. Using the
same formalism, a Lyapunov exponent is calculated, allowing to provide the
onset of damage spreading through the network and how sensitive it is to
minimal perturbations. Finally, the Lyapunov exponents are obtained by means of
different approximations: through distance method and a discrete variant of the
Wolf's method for continuous systems.Comment: 16 pages, 5 eps-figures included, article submitted to Physica
The effect of the size of the system, aspect ratio and impurities concentration on the dynamic of emergent magnetic monopoles in artificial spin ice systems
In this work we study the dynamical properties of a finite array of
nanomagnets in artificial kagome spin ice at room temperature. The dynamic
response of the array of nanomagnets is studied by implementing a "frustrated
celular aut\'omata" (FCA), based in the charge model and dipolar model. The FCA
simulations, allow us to study in real-time and deterministic way, the dynamic
of the system, with minimal computational resource. The update function is
defined according to the coordination number of vertices in the system. Our
results show that for a set geometric parameters of the array of nanomagnets,
the system exhibits high density of Dirac strings and high density emergent
magnetic monopoles. A study of the effect of disorder in the arrangement of
nanomagnets is incorporated in this work
Transport Phenomena at a Critical Point -- Thermal Conduction in the Creutz Cellular Automaton --
Nature of energy transport around a critical point is studied in the Creutz
cellular automaton. Fourier heat law is confirmed to hold in this model by a
direct measurement of heat flow under a temperature gradient. The thermal
conductivity is carefully investigated near the phase transition by the use of
the Kubo formula. As the result, the thermal conductivity is found to take a
finite value at the critical point contrary to some previous works. Equal-time
correlation of the heat flow is also analyzed by a mean-field type
approximation to investigate the temperature dependence of thermal
conductivity. A variant of the Creutz cellular automaton called the Q2R is also
investigated and similar results are obtained.Comment: 27 pages including 14figure
Dynamical and stationary critical behavior of the Ising ferromagnet in a thermal gradient
In this paper we present and discuss results of Monte Carlo numerical
simulations of the two-dimensional Ising ferromagnet in contact with a heat
bath that intrinsically has a thermal gradient. The extremes of the magnet are
at temperatures , where is the Onsager critical temperature.
In this way one can observe a phase transition between an ordered phase
() by means of a single simulation. By
starting the simulations with fully disordered initial configurations with
magnetization corresponding to , which are then suddenly
annealed to a preset thermal gradient, we study the short-time critical dynamic
behavior of the system. Also, by setting a small initial magnetization ,
we study the critical initial increase of the order parameter. Furthermore, by
starting the simulations from fully ordered configurations, which correspond to
the ground state at T=0 and are subsequently quenched to a preset gradient, we
study the critical relaxation dynamics of the system. Additionally, we perform
stationary measurements () that are discussed in terms of
the standard finite-size scaling theory. We conclude that our numerical
simulation results of the Ising magnet in a thermal gradient, which are
rationalized in terms of both dynamic and standard scaling arguments, are fully
consistent with well established results obtained under equilibrium conditions
Universal Cellular Automata and Class 4
Wolfram has provided a qualitative classification of cellular automata(CA)
rules according to which, there exits a class of CA rules (called Class 4)
which exhibit complex pattern formation and long-lived dynamical activity (long
transients). These properties of Class 4 CA's has led to the conjecture that
Class 4 rules are Universal Turing machines i.e. they are bases for
computational universality. We describe an embedding of a ``small'' universal
Turing machine due to Minsky, into a cellular automaton rule-table. This
produces a collection of cellular automata, all of which are
computationally universal. However, we observe that these rules are distributed
amongst the various Wolfram classes. More precisely, we show that the
identification of the Wolfram class depends crucially on the set of initial
conditions used to simulate the given CA. This work, among others, indicates
that a description of complex systems and information dynamics may need a new
framework for non-equilibrium statistical mechanics.Comment: Latex, 10 pages, 5 figures uuencode
Parametric ordering of complex systems
Cellular automata (CA) dynamics are ordered in terms of two global
parameters, computable {\sl a priori} from the description of rules. While one
of them (activity) has been used before, the second one is new; it estimates
the average sensitivity of rules to small configurational changes. For two
well-known families of rules, the Wolfram complexity Classes cluster
satisfactorily. The observed simultaneous occurrence of sharp and smooth
transitions from ordered to disordered dynamics in CA can be explained with the
two-parameter diagram
Magnetic order in the Ising model with parallel dynamics
It is discussed how the equilibrium properties of the Ising model are
described by an Hamiltonian with an antiferromagnetic low temperature behavior
if only an heat bath dynamics, with the characteristics of a Probabilistic
Cellular Automaton, is assumed to determine the temporal evolution of the
system.Comment: 9 pages, 3 figure
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