1,445 research outputs found
Probing Non-Integer Dimensions
We show that two-dimensional convection-diffusion problems with a radial sink
or source at the origin may be recast as a pure diffusion problem in a
fictitious space in which the spatial dimension is continuously-tunable with
the Peclet number. This formulation allows us to probe various
diffusion-controlled processes in non-integer dimensions.Comment: 6 pages, 2 column-revtex4 format. Submitted to special issue of
Journal of Physics: Condensed Matter, on "Chemical Kinetics Beyond the
Textbook: Fluctuations, Many-Particle Effects and Anomalous Dynamics", eds.
K. Lindenberg, G. Oshanin, & M. Tachiy
A Billiard-Theoretic Approach to Elementary 1d Elastic Collisions
A simple relation is developed between elastic collisions of freely-moving
point particles in one dimension and a corresponding billiard system. For two
particles with masses m_1 and m_2 on the half-line x>0 that approach an elastic
barrier at x=0, the corresponding billiard system is an infinite wedge. The
collision history of the two particles can be easily inferred from the
corresponding billiard trajectory. This connection nicely explains the classic
demonstrations of the ``dime on the superball'' and the ``baseball on the
basketball'' that are a staple in elementary physics courses. It is also shown
that three elastic particles on an infinite line and three particles on a
finite ring correspond, respectively, to the motion of a billiard ball in an
infinite wedge and on on a triangular billiard table. It is shown how to
determine the angles of these two sets in terms of the particle masses.Comment: 7 pages, 8 figures, 2-column revtex4 format, for submission to the
American Journal of Physics. Introductory text, several references and one
figure added in response to referee comments. A few more additions and
corrections; final version for AJP. Yet a few more changes and one minor
error corrected just before publicatio
Reality Inspired Voter Models: A Mini-Review
This mini-review presents extensions of the voter model that incorporate
various plausible features of real decision-making processes by individuals.
Although these generalizations are not calibrated by empirical data, the
resulting dynamics are suggestive of realistic collective social behaviors.Comment: 13 pages, 16 figures. Version 2 contains various proofreading
improvements. V3: fixed one trivial typ
Fractal and Multifractal Scaling of Electrical Conduction in Random Resistor Networks
This article is a mini-review about electrical current flows in networks from
the perspective of statistical physics. We briefly discuss analytical methods
to solve the conductance of an arbitrary resistor network. We then turn to
basic results related to percolation: namely, the conduction properties of a
large random resistor network as the fraction of resistors is varied. We focus
on how the conductance of such a network vanishes as the percolation threshold
is approached from above. We also discuss the more microscopic current
distribution within each resistor of a large network. At the percolation
threshold, this distribution is multifractal in that all moments of this
distribution have independent scaling properties. We will discuss the meaning
of multifractal scaling and its implications for current flows in networks,
especially the largest current in the network. Finally, we discuss the relation
between resistor networks and random walks and show how the classic phenomena
of recurrence and transience of random walks are simply related to the
conductance of a corresponding electrical network.Comment: 27 pages & 10 figures; review article for the Encyclopedia of
Complexity and System Science (Springer Science
Finding Scientific Gems with Google
We apply the Google PageRank algorithm to assess the relative importance of
all publications in the Physical Review family of journals from 1893--2003.
While the Google number and the number of citations for each publication are
positively correlated, outliers from this linear relation identify some
exceptional papers or "gems" that are universally familiar to physicists.Comment: 6 pages, 4 figures, 2 tables, 2-column revtex4 forma
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