313 research outputs found
Stretched Exponential Relaxation Arising from a Continuous Sum of Exponential Decays
Stretched exponential relaxation of a quantity n versus time t according to n
= n_0 exp[-(lambda* t)^beta] is ubiquitous in many research fields, where
lambda* is a characteristic relaxation rate and the stretching exponent beta is
in the range 0 < beta < 1. Here we consider systems in which the stretched
exponential relaxation arises from the global relaxation of a system containing
independently exponentially relaxing species with a probability distribution
P(lambda/lambda*,beta) of relaxation rates lambda. We study the properties of
P(lambda/lambda*,beta) and their dependence on beta. Physical interpretations
of lambda* and beta, derived from consideration of P(lambda/lambda*,beta) and
its moments, are discussed.Comment: 8 pages, 10 figures; version to be published in Phys. Rev.
Relaxation under outflow dynamics with random sequential updating
In this paper we compare the relaxation in several versions of the Sznajd
model (SM) with random sequential updating on the chain and square lattice. We
start by reviewing briefly all proposed one dimensional versions of SM. Next,
we compare the results obtained from Monte Carlo simulations with the mean
field results obtained by Slanina and Lavicka . Finally, we investigate the
relaxation on the square lattice and compare two generalizations of SM, one
suggested by Stauffer and another by Galam. We show that there are no
qualitative differences between these two approaches, although the relaxation
within the Galam rule is faster than within the well known Stauffer rule.Comment: 9 figure
How effective is advertising in duopoly markets?
A simple Ising spin model which can describe the mechanism of advertising in
a duopoly market is proposed. In contrast to other agent-based models, the
influence does not flow inward from the surrounding neighbors to the center
site, but spreads outward from the center to the neighbors. The model thus
describes the spread of opinions among customers. It is shown via standard
Monte Carlo simulations that very simple rules and inclusion of an external
field -- an advertising campaign -- lead to phase transitions.Comment: 7 pages, 6 figures; v2: cosmetic change
Continuous Opinions and Discrete Actions in Opinion Dynamics Problems
A model where agents show discrete behavior regarding their actions, but have
continuous opinions that are updated by interacting with other agents is
presented. This new updating rule is applied to both the voter and Sznajd
models for interaction between neighbors and its consequences are discussed.
The appearance of extremists is naturally observed and it seems to be a
characteristic of this model.Comment: 10 pages, 4 figures, minor changes for improved clarit
Universal relaxation function in nonextensive systems
We have derived the dipolar relaxation function for a cluster model whose
volume distribution was obtained from the generalized maximum Tsallis
nonextensive entropy principle. The power law exponents of the relaxation
function are simply related to a global fractal parameter and for
large time to the entropy nonextensivity parameter . For intermediate times
the relaxation follows a stretched exponential behavior. The asymptotic power
law behaviors both in the time and the frequency domains coincide with those of
the Weron generalized dielectric function derived from an extension of the Levy
central limit theorem. They are in full agreement with the Jonscher
universality principle. Moreover our model gives a physical interpretation of
the mathematical parameters of the Weron stochastic theory and opens new paths
to understand the ubiquity of self-similarity and power laws in the relaxation
of large classes of materials in terms of their fractal and nonextensive
properties.Comment: Two figures. Submitted for publicatio
Irrelevance of information outflow in opinion dynamics models
The Sznajd model for opinion dynamics has attracted a large interest as a
simple realization of the psychological principle of social validation. As its
most salient feature, it has been claimed that the Sznajd model is
qualitatively different from other ordering processes, because it is the only
one featuring outflow of information as opposed to inflow. We show that this
claim is unfounded by presenting a generalized zero-temperature Glauber-type of
dynamics which yields results indistinguishable from those of the Sznajd model.
In one-dimension we also derive an exact expression for the exit probability of
the Sznajd model, that turns out to coincide with the result of an analytical
approach based on the Kirkwood approximation. This observation raises
interesting questions about the applicability and limitations of this approach.Comment: 5 pages, 4 figure
Outflow Dynamics in Modeling Oligopoly Markets: The Case of the Mobile Telecommunications Market in Poland
In this paper we introduce two models of opinion dynamics in oligopoly
markets and apply them to a situation, where a new entrant challenges two
incumbents of the same size. The models differ in the way the two forces
influencing consumer choice -- (local) social interactions and (global)
advertising -- interact. We study the general behavior of the models using the
Mean Field Approach and Monte Carlo simulations and calibrate the models to
data from the Polish telecommunications market. For one of the models
criticality is observed -- below a certain critical level of advertising the
market approaches a lock-in situation, where one market leader dominates the
market and all other brands disappear. Interestingly, for both models the best
fits to real data are obtained for conformity level . This
agrees very well with the conformity level found by Solomon Asch in his famous
social experiment
- …