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