1,469 research outputs found
Can a few fanatics influence the opinion of a large segment of a society?
Models that provide insight into how extreme positions regarding any social
phenomenon may spread in a society or at the global scale are of great current
interest. A realistic model must account for the fact that globalization and
internet have given rise to scale-free networks of interactions between people.
We propose a novel model which takes into account the nature of the
interactions network, and provides some key insights into this phenomenon,
including: (1) There is a fundamental difference between a hierarchical network
whereby people are influenced by those that are higher on the hierarchy but not
by those below them, and a symmetrical network where person-on-person influence
works mutually. (2) A few "fanatics" can influence a large fraction of the
population either temporarily (in the hierarchical networks) or permanently (in
symmetrical networks). Even if the "fanatics" disappear, the population may
still remain susceptible to the positions advocated by them. The model is,
however, general and applicable to any phenomenon for which there is a degree
of enthusiasm or susceptibility to in the population.Comment: Enlarged to 28 pages including 15 figure
Diffusion in scale-free networks with annealed disorder
The scale-free (SF) networks that have been studied so far contained quenched
disorder generated by random dilution which does not vary with the time. In
practice, if a SF network is to represent, for example, the worldwide web, then
the links between its various nodes may temporarily be lost, and re-established
again later on. This gives rise to SF networks with annealed disorder. Even if
the disorder is quenched, it may be more realistic to generate it by a
dynamical process that is happening in the network. In this paper, we study
diffusion in SF networks with annealed disorder generated by various scenarios,
as well as in SF networks with quenched disorder which, however, is generated
by the diffusion process itself. Several quantities of the diffusion process
are computed, including the mean number of distinct sites visited, the mean
number of returns to the origin, and the mean number of connected nodes that
are accessible to the random walkers at any given time. The results including,
(1) greatly reduced growth with the time of the mean number of distinct sites
visited; (2) blocking of the random walkers; (3) the existence of a phase
diagram that separates the region in which diffusion is possible from one in
which diffusion is impossible, and (4) a transition in the structure of the
networks at which the mean number of distinct sites visited vanishes, indicate
completely different behavior for the computed quantities than those in SF
networks with quenched disorder generated by simple random dilution.Comment: 18 pages including 8 figure
Analysis of Non-stationary Data for Heart-Rate Fluctuations in Terms of Drift and Diffusion Coefficients
We describe a method for analyzing the stochasticity in the non-stationary
data for the beat-to-beat fluctuations in the heart rates of healthy subjects,
as well as those with congestive heart failure. The method analyzes the returns
time series of the data as a Markov process, and computes the Markov time
scale, i.e., the time scale over which the data are a Markov process. We also
construct an effective stochastic continuum equation for the return series. We
show that the drift and diffusion coefficients, as well as the amplitude of the
returns time series for healthy subjects are distinct from those with CHF.
Thus, the method may potentially provide a diagnostic tool for distinguishing
healthy subjects from those with congestive heart failure, as it can
distinguish small differences between the data for the two classes of subjects
in terms of well-defined and physically-motivated quantities.Comment: 6 pages, two columns, 6 figure
Geometrical Phase Transition on WO Surface
A topographical study on an ensemble of height profiles obtained from atomic
force microscopy techniques on various independently grown samples of tungsten
oxide WO is presented by using ideas from percolation theory. We find that
a continuous 'geometrical' phase transition occurs at a certain critical
level-height below which an infinite island appears. By using the
finite-size scaling analysis of three independent percolation observables i.e.,
percolation probability, percolation strength and the mean island-size, we
compute some critical exponents which characterize the transition. Our results
are compatible with those of long-range correlated percolation. This method can
be generalized to a topographical classification of rough surface models.Comment: 3 pages, 4 figures, to appear in Applied Physics Letters (2010
Alternative criterion for two-dimensional wrapping percolation
Based on the differences between a spanning cluster and a wrapping cluster,
an alternative criterion for testing wrapping percolation is provided for
two-dimensional lattices. By following the Newman-Ziff method, the finite size
scaling of estimates for percolation thresholds are given. The results are
consistent with those from Machta's method.Comment: 4 pages, 2 figure
Concentration Gradient, Diffusion, and Flow Through Open Porous Medium Near Percolation Threshold via Computer Simulations
The interacting lattice gas model is used to simulate fluid flow through an
open percolating porous medium with the fluid entering at the source-end and
leaving from the opposite end. The shape of the steady-state concentration
profile and therefore the gradient field depends on the is found to scale with
the porosity according to porosity p. The root mean square (rms) displacements
of fluid and its constituents (tracers) show a drift power-law behavior, in the
asymptotic regime. The flux current density is found to scale with the porosity
according to an exponent near 1.7.Comment: 8 figure
Lattice Boltzmann simulation of fluid flow in fracture networks with rough, self -affine surfaces
Using the lattice Boltzmann method, we study fluid flow in a two-dimensional (2D) model of fracture network of rock. Each fracture in a square network is represented by a 2D channel with rough, self-affine internal surfaces. Various parameters of the model, such as the connectivity and the apertures of the fractures, the roughness profile of their surface, as well as the Reynolds number for flow of the fluid, are systematically varied in order to assess their effect on the effective permeability of the fracture network. The distribution of the fractures’ apertures is approximated well by a log-normal distribution, which is consistent with experimental data. Due to the roughness of the fractures’ surfaces, and the finite size of the networks that can be used in the simulations, the fracture network is anisotropic. The anisotropy increases as the connectivity of the network decreases and approaches the percolation threshold. The effective permeability K of the network follows the power law K∼〈δ〉β, where 〈δ〉 is the average aperture of the fractures in the network and the exponent β may depend on the roughness exponent. A crossover from linear to nonlinear flow regime is obtained at a Reynolds number Re∼O(1), but the precise numerical value of the crossover Re depends on the roughness of the fractures’ surfaces
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