994 research outputs found
Divergent Time Scale in Axelrod Model Dynamics
We study the evolution of the Axelrod model for cultural diversity. We
consider a simple version of the model in which each individual is
characterized by two features, each of which can assume q possibilities. Within
a mean-field description, we find a transition at a critical value q_c between
an active state of diversity and a frozen state. For q just below q_c, the
density of active links between interaction partners is non-monotonic in time
and the asymptotic approach to the steady state is controlled by a time scale
that diverges as (q-q_c)^{-1/2}.Comment: 4 pages, 5 figures, 2-column revtex4 forma
Nonlinear oscillator with parametric colored noise: some analytical results
The asymptotic behavior of a nonlinear oscillator subject to a multiplicative
Ornstein-Uhlenbeck noise is investigated. When the dynamics is expressed in
terms of energy-angle coordinates, it is observed that the angle is a fast
variable as compared to the energy. Thus, an effective stochastic dynamics for
the energy can be derived if the angular variable is averaged out. However, the
standard elimination procedure, performed earlier for a Gaussian white noise,
fails when the noise is colored because of correlations between the noise and
the fast angular variable. We develop here a specific averaging scheme that
retains these correlations. This allows us to calculate the probability
distribution function (P.D.F.) of the system and to derive the behavior of
physical observables in the long time limit
Anomalous lifetime distributions and topological traps in ordering dynamics
We address the role of community structure of an interaction network in
ordering dynamics, as well as associated forms of metastability. We consider
the voter and AB model dynamics in a network model which mimics social
interactions. The AB model includes an intermediate state between the two
excluding options of the voter model. For the voter model we find dynamical
metastable disordered states with a characteristic mean lifetime. However, for
the AB dynamics we find a power law distribution of the lifetime of metastable
states, so that the mean lifetime is not representative of the dynamics. These
trapped metastable states, which can order at all time scales, originate in the
mesoscopic network structure.Comment: 7 pages; 6 figure
Global culture: A noise induced transition in finite systems
We analyze the effect of cultural drift, modeled as noise, in Axelrod's model
for the dissemination of culture. The disordered multicultural configurations
are found to be metastable. This general result is proven rigorously in d=1,
where the dynamics is described in terms of a Lyapunov potential. In d=2, the
dynamics is governed by the average relaxation time T of perturbations. Noise
at a rate r 1/T sustains
disorder. In the thermodynamic limit, the relaxation time diverges and global
polarization persists in spite of a dynamics of local convergence.Comment: 4 pages, 5 figures. For related material visit
http://www.imedea.uib.es/physdept
Collective modes of coupled phase oscillators with delayed coupling
We study the effects of delayed coupling on timing and pattern formation in
spatially extended systems of dynamic oscillators. Starting from a discrete
lattice of coupled oscillators, we derive a generic continuum theory for
collective modes of long wavelength. We use this approach to study spatial
phase profiles of cellular oscillators in the segmentation clock, a dynamic
patterning system of vertebrate embryos. Collective wave patterns result from
the interplay of coupling delays and moving boundary conditions. We show that
the phase profiles of collective modes depend on coupling delays.Comment: 5 pages, 2 figure
Phase Separation in a Simple Model with Dynamical Asymmetry
We perform computer simulations of a Cahn-Hilliard model of phase separation
which has dynamical asymmetry between the two coexisting phases. The dynamical
asymmetry is incorporated by considering a mobility function which is order
parameter dependent. Simulations of this model reveal morphological features
similar to those observed in viscoelastic phase separation. In the early
stages, the minority phase domains form a percolating structure which shrinks
with time eventually leading to the formation of disconnected domains. The
domains grow as L(t) ~ t^{1/3} in the very late stages. Although dynamical
scaling is violated in the area shrinking regime, it is restored at late times.
However, the form of the scaling function is found to depend on the extent of
dynamical asymmetry.Comment: 16 pages in LaTeX format and 6 Postscript figure
Dynamics of localized structures in vector waves
Dynamical properties of topological defects in a twodimensional complex
vector field are considered. These objects naturally arise in the study of
polarized transverse light waves. Dynamics is modeled by a Vector Complex
Ginzburg-Landau Equation with parameter values appropriate for linearly
polarized laser emission. Creation and annihilation processes, and
selforganization of defects in lattice structures, are described. We find
"glassy" configurations dominated by vectorial defects and a melting process
associated to topological-charge unbinding.Comment: 4 pages, 5 figures included in the text. To appear in Phys. Rev.
Lett. (2000). Related material at http://www.imedea.uib.es/Nonlinear and
http://www.imedea.uib.es/Photonics . In this new version, Fig. 3 has been
replaced by a better on
Effect of Shear Flow on the Stability of Domains in Two Dimensional Phase-Separating Binary Fluids
We perform a linear stability analysis of extended domains in
phase-separating fluids of equal viscosity, in two dimensions. Using the
coupled Cahn-Hilliard and Stokes equations, we derive analytically the
stability eigenvalues for long wavelength fluctuations. In the quiescent state
we find an unstable varicose mode which corresponds to an instability towards
coarsening. This mode is stabilized when an external shear flow is imposed on
the fluid. The effect of the shear is seen to be qualitatively similar to that
found in experiments.Comment: 13 pages, RevTeX, 8 eps figures included. Submitted to Phys. Rev.
Polarisation Patterns and Vectorial Defects in Type II Optical Parametric Oscillators
Previous studies of lasers and nonlinear resonators have revealed that the
polarisation degree of freedom allows for the formation of polarisation
patterns and novel localized structures, such as vectorial defects. Type II
optical parametric oscillators are characterised by the fact that the
down-converted beams are emitted in orthogonal polarisations. In this paper we
show the results of the study of pattern and defect formation and dynamics in a
Type II degenerate optical parametric oscillator for which the pump field is
not resonated in the cavity. We find that traveling waves are the predominant
solutions and that the defects are vectorial dislocations which appear at the
boundaries of the regions where traveling waves of different phase or
wave-vector orientation are formed. A dislocation is defined by two topological
charges, one associated with the phase and another with the wave-vector
orientation. We also show how to stabilize a single defect in a realistic
experimental situation. The effects of phase mismatch of nonlinear interaction
are finally considered.Comment: 38 pages, including 15 figures, LATeX. Related material, including
movies, can be obtained from
http://www.imedea.uib.es/Nonlinear/research_topics/OPO
Nonequilibrium transitions in complex networks: a model of social interaction
We analyze the non-equilibrium order-disorder transition of Axelrod's model
of social interaction in several complex networks. In a small world network, we
find a transition between an ordered homogeneous state and a disordered state.
The transition point is shifted by the degree of spatial disorder of the
underlying network, the network disorder favoring ordered configurations. In
random scale-free networks the transition is only observed for finite size
systems, showing system size scaling, while in the thermodynamic limit only
ordered configurations are always obtained. Thus in the thermodynamic limit the
transition disappears. However, in structured scale-free networks, the phase
transition between an ordered and a disordered phase is restored.Comment: 7 pages revtex4, 10 figures, related material at
http://www.imedea.uib.es/PhysDept/Nonlinear/research_topics/Social
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