1,644 research outputs found
Statistical and Dynamical Study of Disease Propagation in a Small World Network
We study numerically statistical properties and dynamical disease propagation
using a percolation model on a one dimensional small world network. The
parameters chosen correspond to a realistic network of school age children. We
found that percolation threshold decreases as a power law as the short cut
fluctuations increase. We found also the number of infected sites grows
exponentially with time and its rate depends logarithmically on the density of
susceptibles. This behavior provides an interesting way to estimate the
serology for a given population from the measurement of the disease growing
rate during an epidemic phase. We have also examined the case in which the
infection probability of nearest neighbors is different from that of short
cuts. We found a double diffusion behavior with a slower diffusion between the
characteristic times.Comment: 12 pages LaTex, 10 eps figures, Phys.Rev.E Vol. 64, 056115 (2001
The Swiss Board Directors Network in 2009
We study the networks formed by the directors of the most important Swiss
boards and the boards themselves for the year 2009. The networks are obtained
by projection from the original bipartite graph. We highlight a number of
important statistical features of those networks such as degree distribution,
weight distribution, and several centrality measures as well as their
interrelationships. While similar statistics were already known for other board
systems, and are comparable here, we have extended the study with a careful
investigation of director and board centrality, a k-core analysis, and a
simulation of the speed of information propagation and its relationships with
the topological aspects of the network such as clustering and link weight and
betweenness. The overall picture that emerges is one in which the topological
structure of the Swiss board and director networks has evolved in such a way
that special actors and links between actors play a fundamental role in the
flow of information among distant parts of the network. This is shown in
particular by the centrality measures and by the simulation of a simple
epidemic process on the directors network.Comment: Submitted to The European Physical Journal
Structure comparison of binary and weighted niche-overlap graphs
In ecological networks, niche-overlap graphs are considered as complex systems. They represent the competition between two predators that share common resources. The purpose of this paper is to investigate the structural properties of these graphs considered as weighted networks and compare their measures with the ones calculated for the binary networks. To conduct this study, we select four classical network measures : the degree of nodes, the clustering coefficient, the assortativity, and the betweenness centrality. These measures were used to analyse different type of networks such as social networks, biological networks, world wide web, etc. Interestingly, we identify significant differences between the structure of the binary and the weighted niche-overlap graphs. This study indicates that weight information reveals different features that may provide other implications on the dynamics of these networks
Effect of TiO2 phase on the photocatalytic degradation of methylene blue dye
Please read abstract in the article.The National Research Foundation of South Africa and the University of Pretoria's Research Development Programme (RDP).http://www.elsevier.com/locate/pce2021-12-29hj2021Chemical Engineerin
Metastable States in Spin Glasses and Disordered Ferromagnets
We study analytically M-spin-flip stable states in disordered short-ranged
Ising models (spin glasses and ferromagnets) in all dimensions and for all M.
Our approach is primarily dynamical and is based on the convergence of a
zero-temperature dynamical process with flips of lattice animals up to size M
and starting from a deep quench, to a metastable limit. The results (rigorous
and nonrigorous, in infinite and finite volumes) concern many aspects of
metastable states: their numbers, basins of attraction, energy densities,
overlaps, remanent magnetizations and relations to thermodynamic states. For
example, we show that their overlap distribution is a delta-function at zero.
We also define a dynamics for M=infinity, which provides a potential tool for
investigating ground state structure.Comment: 34 pages (LaTeX); to appear in Physical Review
Tensionless structure of glassy phase
We study a class of homogeneous finite-dimensional Ising models which were
recently shown to exhibit glassy properties. Monte Carlo simulations of a
particular three-dimensional model in this class show that the glassy phase
obtained under slow cooling is dominated by large scale excitations whose
energy scales with their size as with
. Simulations suggest that in another model of this class,
namely the four-spin model, energy is concentrated mainly in linear defects
making also in this case domain walls tensionless. Two-dimensinal variants of
these models are trivial and energy of excitations scales with the exponent
.Comment: 5 page
Failure time in the fiber-bundle model with thermal noise and disorder
The average time for the onset of macroscopic fractures is analytically and
numerically investigated in the fiber-bundle model with quenched disorder and
thermal noise under a constant load. We find an implicit exact expression for
the failure time in the low-temperature limit that is accurately confirmed by
direct simulations. The effect of the disorder is to lower the energy barrier.Comment: 11 pages, 6 figures; accepted for publication in Phys. Rev.
On Bootstrap Percolation in Living Neural Networks
Recent experimental studies of living neural networks reveal that their
global activation induced by electrical stimulation can be explained using the
concept of bootstrap percolation on a directed random network. The experiment
consists in activating externally an initial random fraction of the neurons and
observe the process of firing until its equilibrium. The final portion of
neurons that are active depends in a non linear way on the initial fraction.
The main result of this paper is a theorem which enables us to find the
asymptotic of final proportion of the fired neurons in the case of random
directed graphs with given node degrees as the model for interacting network.
This gives a rigorous mathematical proof of a phenomena observed by physicists
in neural networks
Percolation model for structural phase transitions in LiHIO mixed crystals
A percolation model is proposed to explain the structural phase transitions
found in LiHIO mixed crystals as a function of the
concentration parameter . The percolation thresholds are obtained from Monte
Carlo simulations on the specific lattices occupied by lithium atoms and
hydrogen bonds. The theoretical results strongly suggest that percolating
lithium vacancies and hydrogen bonds are indeed responsible for the solid
solution observed in the experimental range .Comment: 4 pages, 2 figure
Crystallization of a supercooled liquid and of a glass - Ising model approach
Using Monte Carlo simulations we study crystallization in the
three-dimensional Ising model with four-spin interaction. We monitor the
morphology of crystals which grow after placing crystallization seeds in a
supercooled liquid. Defects in such crystals constitute an intricate and very
stable network which separate various domains by tensionless domain walls. We
also show that the crystallization which occurs during the continuous heating
of the glassy phase takes place at a heating-rate dependent temperature.Comment: 7 page
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