419 research outputs found
Quantum Dot and Hole Formation in Sputter Erosion
Recently it was experimentally demonstrated that sputtering under normal
incidence leads to the formation of spatially ordered uniform nanoscale islands
or holes. Here we show that these nanostructures have inherently nonlinear
origin, first appearing when the nonlinear terms start to dominate the surface
dynamics. Depending on the sign of the nonlinear terms, determined by the shape
of the collision cascade, the surface can develop regular islands or holes with
identical dynamical features, and while the size of these nanostructures is
independent of flux and temperature, it can be modified by tuning the ion
energy
Quantum Dot and Hole Formation in Sputter Erosion
Recently it was experimentally demonstrated that sputtering under normal
incidence leads to the formation of spatially ordered uniform nanoscale islands
or holes. Here we show that these nanostructures have inherently nonlinear
origin, first appearing when the nonlinear terms start to dominate the surface
dynamics. Depending on the sign of the nonlinear terms, determined by the shape
of the collision cascade, the surface can develop regular islands or holes with
identical dynamical features, and while the size of these nanostructures is
independent of flux and temperature, it can be modified by tuning the ion
energy
Network analysis of online bidding activity
With the advent of digital media, people are increasingly resorting to online
channels for commercial transactions. Online auction is a prototypical example.
In such online transactions, the pattern of bidding activity is more complex
than traditional online transactions; this is because the number of bidders
participating in a given transaction is not bounded and the bidders can also
easily respond to the bidding instantaneously. By using the recently developed
network theory, we study the interaction patterns between bidders (items) who
(that) are connected when they bid for the same item (if the item is bid by the
same bidder). The resulting network is analyzed by using the hierarchical
clustering algorithm, which is used for clustering analysis for expression data
from DNA microarrays. A dendrogram is constructed for the item subcategories;
this dendrogram is compared with a traditional classification scheme. The
implication of the difference between the two is discussed.Comment: 8 pages and 11 figure
Recent advances and open challenges in percolation
Percolation is the paradigm for random connectivity and has been one of the
most applied statistical models. With simple geometrical rules a transition is
obtained which is related to magnetic models. This transition is, in all
dimensions, one of the most robust continuous transitions known. We present a
very brief overview of more than 60 years of work in this area and discuss
several open questions for a variety of models, including classical, explosive,
invasion, bootstrap, and correlated percolation
On continuum modeling of sputter erosion under normal incidence: interplay between nonlocality and nonlinearity
Under specific experimental circumstances, sputter erosion on semiconductor
materials exhibits highly ordered hexagonal dot-like nanostructures. In a
recent attempt to theoretically understand this pattern forming process, Facsko
et al. [Phys. Rev. B 69, 153412 (2004)] suggested a nonlocal, damped
Kuramoto-Sivashinsky equation as a potential candidate for an adequate
continuum model of this self-organizing process. In this study we theoretically
investigate this proposal by (i) formally deriving such a nonlocal equation as
minimal model from balance considerations, (ii) showing that it can be exactly
mapped to a local, damped Kuramoto-Sivashinsky equation, and (iii) inspecting
the consequences of the resulting non-stationary erosion dynamics.Comment: 7 pages, 2 Postscript figures, accepted by Phys. Rev. B corrected
typos, few minor change
Modeling relaxation and jamming in granular media
We introduce a stochastic microscopic model to investigate the jamming and
reorganization of grains induced by an object moving through a granular medium.
The model reproduces the experimentally observed periodic sawtooth fluctuations
in the jamming force and predicts the period and the power spectrum in terms of
the controllable physical parameters. It also predicts that the avalanche
sizes, defined as the number of displaced grains during a single advance of the
object, follow a power-law, , where the exponent is
independent of the physical parameters
A "metric" complexity for weakly chaotic systems
We consider the number of Bowen sets which are necessary to cover a large
measure subset of the phase space. This introduce some complexity indicator
characterizing different kind of (weakly) chaotic dynamics. Since in many
systems its value is given by a sort of local entropy, this indicator is quite
simple to be calculated. We give some example of calculation in nontrivial
systems (interval exchanges, piecewise isometries e.g.) and a formula similar
to the Ruelle-Pesin one, relating the complexity indicator to some initial
condition sensitivity indicators playing the role of positive Lyapunov
exponents.Comment: 15 pages, no figures. Articl
Bidding process in online auctions and winning strategy:rate equation approach
Online auctions have expanded rapidly over the last decade and have become a
fascinating new type of business or commercial transaction in this digital era.
Here we introduce a master equation for the bidding process that takes place in
online auctions. We find that the number of distinct bidders who bid times,
called the -frequent bidder, up to the -th bidding progresses as
. The successfully transmitted bidding rate by the
-frequent bidder is obtained as , independent of
for large . This theoretical prediction is in agreement with empirical data.
These results imply that bidding at the last moment is a rational and effective
strategy to win in an eBay auction.Comment: 4 pages, 6 figure
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