6,724 research outputs found
Multi-layer model for the web graph
This paper studies stochastic graph models of the WebGraph. We present a new model that describes the WebGraph as an ensemble of different regions generated by independent stochastic processes (in the spirit of a recent paper by Dill et al. [VLDB 2001]). Models such as the Copying Model [17] and Evolving Networks Model [3] are simulated and compared on several relevant measures such as degree and clique distribution
Diffusion-limited deposition with dipolar interactions: fractal dimension and multifractal structure
Computer simulations are used to generate two-dimensional diffusion-limited
deposits of dipoles. The structure of these deposits is analyzed by measuring
some global quantities: the density of the deposit and the lateral correlation
function at a given height, the mean height of the upper surface for a given
number of deposited particles and the interfacial width at a given height.
Evidences are given that the fractal dimension of the deposits remains constant
as the deposition proceeds, independently of the dipolar strength. These same
deposits are used to obtain the growth probability measure through Monte Carlo
techniques. It is found that the distribution of growth probabilities obeys
multifractal scaling, i.e. it can be analyzed in terms of its
multifractal spectrum. For low dipolar strengths, the spectrum is
similar to that of diffusion-limited aggregation. Our results suggest that for
increasing dipolar strength both the minimal local growth exponent
and the information dimension decrease, while the fractal
dimension remains the same.Comment: 10 pages, 7 figure
Diffusion-limited deposition of dipolar particles
Deposits of dipolar particles are investigated by means of extensive Monte
Carlo simulations. We found that the effect of the interactions is described by
an initial, non-universal, scaling regime characterized by orientationally
ordered deposits. In the dipolar regime, the order and geometry of the clusters
depend on the strength of the interactions and the magnetic properties are
tunable by controlling the growth conditions. At later stages, the growth is
dominated by thermal effects and the diffusion-limited universal regime
obtains, at finite temperatures. At low temperatures the crossover size
increases exponentially as T decreases and at T=0 only the dipolar regime is
observed.Comment: 5 pages, 4 figure
Gel Electrophoresis of DNA Knots in Weak and Strong Electric Fields
Gel electrophoresis allows to separate knotted DNA (nicked circular) of equal
length according to the knot type. At low electric fields, complex knots being
more compact, drift faster than simpler knots. Recent experiments have shown
that the drift velocity dependence on the knot type is inverted when changing
from low to high electric fields. We present a computer simulation on a lattice
of a closed, knotted, charged DNA chain drifting in an external electric field
in a topologically restricted medium. Using a simple Monte Carlo algorithm, the
dependence of the electrophoretic migration of the DNA molecules on the type of
knot and on the electric field intensity was investigated. The results are in
qualitative agreement with electrophoretic experiments done under conditions of
low and high electric fields: especially the inversion of the behavior from low
to high electric field could be reproduced. The knot topology imposes on the
problem the constrain of self-avoidance, which is the final cause of the
observed behavior in strong electric field.Comment: 17 pages, 5 figure
The role of the Berry Phase in Dynamical Jahn-Teller Systems
The presence/absence of a Berry phase depends on the topology of the manifold
of dynamical Jahn-Teller potential minima. We describe in detail the relation
between these topological properties and the way the lowest two adiabatic
potential surfaces get locally degenerate. We illustrate our arguments through
spherical generalizations of the linear T x h and H x h cases, relevant for the
physics of fullerene ions. Our analysis allows us to classify all the spherical
Jahn-Teller systems with respect to the Berry phase. Its absence can, but does
not necessarily, lead to a nondegenerate ground state.Comment: revtex 7 pages, 2 eps figures include
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