594 research outputs found
Spreading and shortest paths in systems with sparse long-range connections
Spreading according to simple rules (e.g. of fire or diseases), and
shortest-path distances are studied on d-dimensional systems with a small
density p per site of long-range connections (``Small-World'' lattices). The
volume V(t) covered by the spreading quantity on an infinite system is exactly
calculated in all dimensions. We find that V(t) grows initially as t^d/d for
t>t^*$,
generalizing a previous result in one dimension. Using the properties of V(t),
the average shortest-path distance \ell(r) can be calculated as a function of
Euclidean distance r. It is found that
\ell(r) = r for r<r_c=(2p \Gamma_d (d-1)!)^{-1/d} log(2p \Gamma_d L^d), and
\ell(r) = r_c for r>r_c.
The characteristic length r_c, which governs the behavior of shortest-path
lengths, diverges with system size for all p>0. Therefore the mean separation s
\sim p^{-1/d} between shortcut-ends is not a relevant internal length-scale for
shortest-path lengths. We notice however that the globally averaged
shortest-path length, divided by L, is a function of L/s only.Comment: 4 pages, 1 eps fig. Uses psfi
Scaling for the Percolation Backbone
We study the backbone connecting two given sites of a two-dimensional lattice
separated by an arbitrary distance in a system of size . We find a
scaling form for the average backbone mass: , where
can be well approximated by a power law for : with . This result implies that for the entire range . We also propose a scaling
form for the probability distribution of backbone mass for a given
. For is peaked around , whereas for decreases as a power law, , with . The exponents and satisfy the relation
, and is the codimension of the backbone,
.Comment: 3 pages, 5 postscript figures, Latex/Revtex/multicols/eps
Ising model in small-world networks
The Ising model in small-world networks generated from two- and
three-dimensional regular lattices has been studied. Monte Carlo simulations
were carried out to characterize the ferromagnetic transition appearing in
these systems. In the thermodynamic limit, the phase transition has a
mean-field character for any finite value of the rewiring probability p, which
measures the disorder strength of a given network. For small values of p, both
the transition temperature and critical energy change with p as a power law. In
the limit p -> 0, the heat capacity at the transition temperature diverges
logarithmically in two-dimensional (2D) networks and as a power law in 3D.Comment: 6 pages, 7 figure
Multifractal current distribution in random diode networks
Recently it has been shown analytically that electric currents in a random
diode network are distributed in a multifractal manner [O. Stenull and H. K.
Janssen, Europhys. Lett. 55, 691 (2001)]. In the present work we investigate
the multifractal properties of a random diode network at the critical point by
numerical simulations. We analyze the currents running on a directed
percolation cluster and confirm the field-theoretic predictions for the scaling
behavior of moments of the current distribution. It is pointed out that a
random diode network is a particularly good candidate for a possible
experimental realization of directed percolation.Comment: RevTeX, 4 pages, 5 eps figure
Mean-field solution of the small-world network model
The small-world network model is a simple model of the structure of social
networks, which simultaneously possesses characteristics of both regular
lattices and random graphs. The model consists of a one-dimensional lattice
with a low density of shortcuts added between randomly selected pairs of
points. These shortcuts greatly reduce the typical path length between any two
points on the lattice. We present a mean-field solution for the average path
length and for the distribution of path lengths in the model. This solution is
exact in the limit of large system size and either large or small number of
shortcuts.Comment: 14 pages, 2 postscript figure
Insects complex associated with the tropical basil, Ocimum gratissimum L. (Lamiaceae) in southern Benin.
Tropical basil is an aromatic leafy vegetable used for its medicinal and therapeutic properties in
numerous countries in West Africa (Benin, Nigeria, Togo, etc.). In Benin, it is produced on almost all
urban and periurban garden throughout the year for fresh market. Until now there are few or nearly
no publications about the arthropod community of this specie, even less in the context of Benin.
Thus, to assess this community, basil plots were mowed using a sweep net in three localities (Ouidah,
Togba and Sèmè) of southern Benin.
Preliminary results focus on the different insect families that colonized tropical basil in southern
Benin environmental conditions. These include: Aphididae (Homoptera), Cercopidae (Homoptera),
Chrysomelidae (Coleoptera), Coccinelledidea (Coleoptera), Meloidae (Coleoptera), Braconidae
(Hymenoptera), Ichneumonidae (Hymenoptera), Formicidae (Hymenoptera), Vespidae
(Hymenoptera), Apoidae (Hymenoptera), Reduviidae (Heteroptera), Pentatomidae (Heteroptera),
Pyrgomorphidae (Orthoptera), Acrididae (Orthoptera), Syrphidae (Diptera), Diopsidae (Diptera).
Among these families, there are pests: Aphis gossypii G. (Homoptera: Aphididae), Zonocerus
variegatus L. (Orthoptera: Pyrgomorphidae), etc.; predators: Ischiodon aegyptius W. (Diptera:
Syrphidae), Cheilomenes spp. (Coleoptera: Coccinelledidea), Rhynocoris spp. (Heteroptera:
Reduviidae), etc.; parasitoids and pollinators.
From this study, it appeared that there is a large diversity of families and functional groups (pests,
predators, parasitoids and pollinators) associated with tropical basil . Moreover, the presence of
natural enemies could be an advantage for farmers in intercropping systems. This would help reduce
the use of synthetic insecticides.
This result, which is a first knowledge of the insect fauna associated with tropical basil under the
environmental conditions of Southern Benin, will be supplemented by a spatio temporal study to
assess the variability and the dynamics of this insect fauna
Structure of Growing Networks: Exact Solution of the Barabasi--Albert's Model
We generalize the Barab\'{a}si--Albert's model of growing networks accounting
for initial properties of sites and find exactly the distribution of
connectivities of the network and the averaged connectivity
of a site in the instant (one site is added per unit of
time). At long times at and
at , where the exponent
varies from 2 to depending on the initial attractiveness of sites. We
show that the relation between the exponents is universal.Comment: 4 pages revtex (twocolumn, psfig), 1 figur
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