6,743 research outputs found
Square-free class sizes in products of groups
We obtain some structural properties of a factorised group , given
that the conjugacy class sizes of certain elements in are not
divisible by , for some prime . The case when is a mutually
permutable product is especially considered
Routes to thermodynamic limit on scale-free networks
We show that there are two classes of finite size effects for dynamic models
taking place on a scale-free topology. Some models in finite networks show a
behavior that depends only on the system size N. Others present an additional
distinct dependence on the upper cutoff k_c of the degree distribution. Since
the infinite network limit can be obtained by allowing k_c to diverge with the
system size in an arbitrary way, this result implies that there are different
routes to the thermodynamic limit in scale-free networks. The contact process
(in its mean-field version) belongs to this second class and thus our results
clarify the recent discrepancy between theory and simulations with different
scaling of k_c reported in the literature.Comment: 5 pages, 3 figures, final versio
Quasi-chemical approximation for polyatomic mixtures
The statistical thermodynamics of binary mixtures of polyatomic species was
developed on a generalization in the spirit of the lattice-gas model and the
quasi-chemical approximation (QCA). The new theoretical framework is obtained
by combining: (i) the exact analytical expression for the partition function of
non-interacting mixtures of linear -mers and -mers (species occupying
sites and sites, respectively) adsorbed in one dimension, and its extension
to higher dimensions; and (ii) a generalization of the classical QCA for
multicomponent adsorbates and multisite-occupancy adsorption. The process is
analyzed through the partial adsorption isotherms corresponding to both species
of the mixture. Comparisons with analytical data from Bragg-Williams
approximation (BWA) and Monte Carlo simulations are performed in order to test
the validity of the theoretical model. Even though a good fitting is obtained
from BWA, it is found that QCA provides a more accurate description of the
phenomenon of adsorption of interacting polyatomic mixtures.Comment: 27 pages, 8 figure
Multicomponent reaction-diffusion processes on complex networks
We study the reaction-diffusion process on uncorrelated
scale-free networks analytically. By a mean-field ansatz we derive analytical
expressions for the particle pair-correlations and the particle density.
Expressing the time evolution of the particle density in terms of the
instantaneous particle pair-correlations, we determine analytically the
`jamming' effect which arises in the case of multicomponent, pair-wise
reactions. Comparing the relevant terms within the differential equation for
the particle density, we find that the `jamming' effect diminishes in the
long-time, low-density limit. This even holds true for the hubs of the network,
despite that the hubs dynamically attract the particles.Comment: 8 pages, 6 figure
Photon Filamentation in Resonant Media with High Fresnel Numbers
The phenomenon of turbulent photon filamentation occurs in lasers and other
active optical media at high Fresnel numbers. A description of this phenomenon
is suggested. The solutions to evolution equations are presented in the form of
a bunch of filaments chaotically distributed in space and having different
radii. The probability distribution of patterns is defined characterizing the
probabilistic weight of different filaments. The most probable filament radius
and filament number are found, being in good agreement with experiment.Comment: Revtex file, 5 pages. Reference to the English edition of the journal
is give
Low-energy Anti-neutrinos from the Sun
We consider the sensitivity of future neutrino experiments in the low energy
region, such as BOREXINO or HELLAZ, to a solar electron antineutrino signal. We
show that, if neutrino conversions within the Sun result in partial
polarization of initial solar neutrino fluxes, then a new opportunity arises to
observe the electron antineutrinos and thus to probe the Majorana nature of the
neutrinos. This is achieved by comparing the slopes of the energy dependence of
the differential neutrino electron scattering cross section for different
neutrino conversion scenarios. We also show how the \nu_e -> \bar{\nu}_e
conversions may take place for low energy solar neutrinos while being
unobservable at the Kamiokande and Super-Kamiokande experiments.Comment: LaTeX, 14 pages, 3 PS figures included, 3 references adde
Host--parasite models on graphs
The behavior of two interacting populations, ``hosts''and ``parasites'', is
investigated on Cayley trees and scale-free networks. In the former case
analytical and numerical arguments elucidate a phase diagram, whose most
interesting feature is the absence of a tri-critical point as a function of the
two independent spreading parameters. For scale-free graphs, the parasite
population can be described effectively by
Susceptible-Infected-Susceptible-type dynamics in a host background. This is
shown both by considering the appropriate dynamical equations and by numerical
simulations on Barab\'asi-Albert networks with the major implication that in
the termodynamic limit the critical parasite spreading parameter vanishes.Comment: 10 pages, 6 figures, submitted to PRE; analytics redone, new
calculations added, references added, appendix remove
Structure of shells in complex networks
In a network, we define shell as the set of nodes at distance
with respect to a given node and define as the fraction of nodes
outside shell . In a transport process, information or disease usually
diffuses from a random node and reach nodes shell after shell. Thus,
understanding the shell structure is crucial for the study of the transport
property of networks. For a randomly connected network with given degree
distribution, we derive analytically the degree distribution and average degree
of the nodes residing outside shell as a function of . Further,
we find that follows an iterative functional form
, where is expressed in terms of the generating
function of the original degree distribution of the network. Our results can
explain the power-law distribution of the number of nodes found in
shells with larger than the network diameter , which is the average
distance between all pairs of nodes. For real world networks the theoretical
prediction of deviates from the empirical . We introduce a
network correlation function to
characterize the correlations in the network, where is the
empirical value and is the theoretical prediction.
indicates perfect agreement between empirical results and theory. We apply
to several model and real world networks. We find that the networks
fall into two distinct classes: (i) a class of {\it poorly-connected} networks
with , which have larger average distances compared with randomly
connected networks with the same degree distributions; and (ii) a class of {\it
well-connected} networks with
Spreading of sexually transmitted diseases in heterosexual populations
The spread of sexually transmitted diseases (e.g. Chlamydia, Syphilis,
Gonorrhea, HIV) across populations is a major concern for scientists and health
agencies. In this context, both data collection on sexual contact networks and
the modeling of disease spreading, are intensively contributing to the search
for effective immunization policies. Here, the spreading of sexually
transmitted diseases on bipartite scale-free graphs, representing heterosexual
contact networks, is considered. We analytically derive the expression for the
epidemic threshold and its dependence with the system size in finite
populations. We show that the epidemic outbreak in bipartite populations, with
number of sexual partners distributed as in empirical observations from
national sex surveys, takes place for larger spreading rates than for the case
in which the bipartite nature of the network is not taken into account.
Numerical simulations confirm the validity of the theoretical results. Our
findings indicate that the restriction to crossed infections between the two
classes of individuals (males and females) has to be taken into account in the
design of efficient immunization strategies for sexually transmitted diseases.Comment: 7 pages, 3 figures and 2 table
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