5,442 research outputs found
Designer Nets from Local Strategies
We propose a local strategy for constructing scale-free networks of arbitrary
degree distributions, based on the redirection method of Krapivsky and Redner
[Phys. Rev. E 63, 066123 (2001)]. Our method includes a set of external
parameters that can be tuned at will to match detailed behavior at small degree
k, in addition to the scale-free power-law tail signature at large k. The
choice of parameters determines other network characteristics, such as the
degree of clustering. The method is local in that addition of a new node
requires knowledge of only the immediate environs of the (randomly selected)
node to which it is attached. (Global strategies require information on finite
fractions of the growing net.
Broadband THz study of excitonic resonances in the high-density regime
We report the first terahertz study of the intra-excitonic 1s-2p transition
at high excitation densities in GaAs/AlGaAs quantum wells. A strong shift,
broadening, and ultimately the disappearance of this resonance occurs with
increasing density, after ultrafast photoexcitation at the near-infrared
exciton line. Densities of excitons and unbound electron-hole pairs are
followed quantitatively using a model of the composite terahertz dielectric
response. Comparison with near-infrared absorption changes reveals a
significantly enhanced energy shift and broadening of the intra-excitonic
resonance.Comment: 4 pages, 4 figure
Diffusion-Limited One-Species Reactions in the Bethe Lattice
We study the kinetics of diffusion-limited coalescence, A+A-->A, and
annihilation, A+A-->0, in the Bethe lattice of coordination number z.
Correlations build up over time so that the probability to find a particle next
to another varies from \rho^2 (\rho is the particle density), initially, when
the particles are uncorrelated, to [(z-2)/z]\rho^2, in the long-time asymptotic
limit. As a result, the particle density decays inversely proportional to time,
\rho ~ 1/kt, but at a rate k that slowly decreases to an asymptotic constant
value.Comment: To be published in JPCM, special issue on Kinetics of Chemical
Reaction
Percolation in Hierarchical Scale-Free Nets
We study the percolation phase transition in hierarchical scale-free nets.
Depending on the method of construction, the nets can be fractal or small-world
(the diameter grows either algebraically or logarithmically with the net size),
assortative or disassortative (a measure of the tendency of like-degree nodes
to be connected to one another), or possess various degrees of clustering. The
percolation phase transition can be analyzed exactly in all these cases, due to
the self-similar structure of the hierarchical nets. We find different types of
criticality, illustrating the crucial effect of other structural properties
besides the scale-free degree distribution of the nets.Comment: 9 Pages, 11 figures. References added and minor corrections to
manuscript. In pres
Fractal and Transfractal Recursive Scale-Free Nets
We explore the concepts of self-similarity, dimensionality, and
(multi)scaling in a new family of recursive scale-free nets that yield
themselves to exact analysis through renormalization techniques. All nets in
this family are self-similar and some are fractals - possessing a finite
fractal dimension - while others are small world (their diameter grows
logarithmically with their size) and are infinite-dimensional. We show how a
useful measure of "transfinite" dimension may be defined and applied to the
small world nets. Concerning multiscaling, we show how first-passage time for
diffusion and resistance between hub (the most connected nodes) scale
differently than for other nodes. Despite the different scalings, the Einstein
relation between diffusion and conductivity holds separately for hubs and
nodes. The transfinite exponents of small world nets obey Einstein relations
analogous to those in fractal nets.Comment: Includes small revisions and references added as result of readers'
feedbac
Efficient Immunization Strategies for Computer Networks and Populations
We present an effective immunization strategy for computer networks and
populations with broad and, in particular, scale-free degree distributions. The
proposed strategy, acquaintance immunization, calls for the immunization of
random acquaintances of random nodes (individuals). The strategy requires no
knowledge of the node degrees or any other global knowledge, as do targeted
immunization strategies. We study analytically the critical threshold for
complete immunization. We also study the strategy with respect to the
susceptible-infected-removed epidemiological model. We show that the
immunization threshold is dramatically reduced with the suggested strategy, for
all studied cases.Comment: Revtex, 5 pages, 4 ps fig
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