5,870 research outputs found
Update rules and interevent time distributions: Slow ordering vs. no ordering in the Voter Model
We introduce a general methodology of update rules accounting for arbitrary
interevent time distributions in simulations of interacting agents. In
particular we consider update rules that depend on the state of the agent, so
that the update becomes part of the dynamical model. As an illustration we
consider the voter model in fully-connected, random and scale free networks
with an update probability inversely proportional to the persistence, that is,
the time since the last event. We find that in the thermodynamic limit, at
variance with standard updates, the system orders slowly. The approach to the
absorbing state is characterized by a power law decay of the density of
interfaces, observing that the mean time to reach the absorbing state might be
not well defined.Comment: 5pages, 4 figure
Dynamics of link states in complex networks: The case of a majority rule
Motivated by the idea that some characteristics are specific to the relations
between individuals and not of the individuals themselves, we study a prototype
model for the dynamics of the states of the links in a fixed network of
interacting units. Each link in the network can be in one of two equivalent
states. A majority link-dynamics rule is implemented, so that in each dynamical
step the state of a randomly chosen link is updated to the state of the
majority of neighboring links. Nodes can be characterized by a link
heterogeneity index, giving a measure of the likelihood of a node to have a
link in one of the two states. We consider this link-dynamics model on fully
connected networks, square lattices and Erd \"os-Renyi random networks. In each
case we find and characterize a number of nontrivial asymptotic configurations,
as well as some of the mechanisms leading to them and the time evolution of the
link heterogeneity index distribution. For a fully connected network and random
networks there is a broad distribution of possible asymptotic configurations.
Most asymptotic configurations that result from link-dynamics have no
counterpart under traditional node dynamics in the same topologies.Comment: 9 pages, 13 figure
Sheffer sequences of polynomials and their applications
In this paper, we investigate some properties of several Sheffer sequences of
several polynomials arising from umbral calculus. From our investigation, we
can derive many interesting identities of several polynomialsComment: 10 page
Some identities of higher-order Bernoulli, Euler and Hermite polynomials arising from umbral calculus
In this paper, we study umbral calculus to have alternative ways of obtaining
our results. That is, we derive some interesting identities of the higher-order
Bernoulli, Euler and Hermite polynomials arising from umbral calculus to have
alternative ways.Comment: 10 page
Dynamics of the Formation of Bright Solitary Waves of Bose-Einstein Condensates in Optical Lattices
We present a detailed description of the formation of bright solitary waves
in optical lattices. To this end, we have considered a ring lattice geometry
with large radius. In this case, the ring shape does not have a relevant effect
in the local dynamics of the condensate, while offering a realistic set up to
implement experiments with conditions usually not available with linear
lattices (in particular, to study collisions). Our numerical results suggest
that the condensate radiation is the relevant dissipative process in the
relaxation towards a self-trapped solution. We show that the source of
dissipation can be attributed to the presence of higher order dispersion terms
in the effective mass approach. In addition, we demonstrate that the stability
of the solitary solutions is linked with particular values of the width of the
wavepacket in the reciprocal space. Our study suggests that these critical
widths for stability depend on the geometry of the energy band, but are
independent of the condensate parameters (momentum, atom number, etc.).
Finally, the non-solitonic nature of the solitary waves is evidenced showing
their instability under collisions.Comment: 7 pages, 7 figures, to appear in PR
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
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