Enhanced Dimer Relaxation in an Atomic/Molecular BEC

We derive a universal formula for the rate constant \beta for relaxation of a shallow dimer into deeply-bound diatomic molecules in the case of atoms with a large scattering length a. We show that \beta is determined by a and by two 3-body parameters that also determine the binding energies and widths of Efimov states. The rate constant \beta scales like \hbar a/m near the resonance, but the coefficient is a periodic function of ln(a) that may have resonant enhancement at values of a that differ by multiples of 22.7.Comment: 5 pages, revtex4, 2 PS figures, title changed, final versio

Convex Hulls of Multiple Random Walks: A Large-Deviation Study

We study the polygons governing the convex hull of a point set created by the steps of $n$ independent two-dimensional random walkers. Each such walk consists of $T$ discrete time steps, where $x$ and $y$ increments are i.i.d. Gaussian. We analyze area $A$ and perimeter $L$ of the convex hulls. We obtain probability densities for these two quantities over a large range of the support by using a large-deviation approach allowing us to study densities below $10^{-900}$. We find that the densities exhibit a universal scaling behavior as a function of $A/T$ and $L/\sqrt{T}$, respectively. As in the case of one walker ($n=1$), the densities follow Gaussian distributions for $L$ and $\sqrt{A}$, respectively. We also obtained the rate functions for the area and perimeter, rescaled with the scaling behavior of their maximum possible values, and found limiting functions for $T \rightarrow \infty$, revealing that the densities follow the large-deviation principle. These rate functions can be described by a power law for $n \rightarrow \infty$ as found in the $n=1$ case. We also investigated the behavior of the averages as a function of the number of walks $n$ and found good agreement with the predicted behavior.Comment: 11 pages, 14 figure

Astrometric Positions and Proper Motions of 19 Radio Stars

We have used the Very Large Array, linked with the Pie Town Very Long Baseline Array antenna, to determine astrometric positions of 19 radio stars in the International Celestial Reference Frame (ICRF). The positions of these stars were directly linked to the positions of distant quasars through phase referencing observations. The positions of the ICRF quasars are known to 0.25 mas, thus providing an absolute reference at the angular resolution of our radio observations. Average values for the errors in our derived positions for all sources were 13 mas and 16 mas in R.A. and declination respectively, with accuracies approaching 1-2 mas for some of the stars observed. Differences between the ICRF positions of the 38 quasars, and those measured from our observations showed no systematic offsets, with mean values of -0.3 mas in R.A. and -1.0 mas in declination. Standard deviations of the quasar position differences of 17 mas and 11 mas in R.A. and declination respectively, are consistent with the mean position errors determined for the stars. Our measured positions were combined with previous Very Large Array measurements taken from 1978-1995 to determine the proper motions of 15 of the stars in our list. With mean errors of approximately 1.6 mas/yr, the accuracies of our proper motions approach those derived from Hipparcos, and for a few of the stars in our program, are better than the Hipparcos values. Comparing the positions of our radio stars with the Hipparcos catalog, we find that at the epoch of our observations, the two frames are aligned to within formal errors of approximately 3 mas. This result confirms that the Hipparcos frame is inertial at the expected level.Comment: 20 pages, 9 figures Accepted by the Astronomical Journal, 2003 March 1

Time-evolution of the Rule 150 cellular automaton activity from a Fibonacci iteration

The total activity of the single-seeded cellular rule 150 automaton does not follow a one-step iteration like other elementary cellular automata, but can be solved as a two-step vectorial, or string, iteration, which can be viewed as a generalization of Fibonacci iteration generating the time series from a sequence of vectors of increasing length. This allows to compute the total activity time series more efficiently than by simulating the whole spatio-temporal process, or even by using the closed expression.Comment: 4 pages (3 figs included

A revised distance to IRAS 16293−-2422 from VLBA astrometry of associated water masers

IRAS 16293-2422 is a very well studied young stellar system seen in projection towards the L1689N cloud in the Ophiuchus complex. However, its distance is still uncertain with a range of values from 120 pc to 180 pc. Our goal is to measure the trigonometric parallax of this young star by means of H$_2$O maser emission. We use archival data from 15 epochs of VLBA observations of the 22.2 GHz water maser line. By modeling the displacement on the sky of the H$_2$O maser spots, we derived a trigonometric parallax of $7.1\pm1.3$ mas, corresponding to a distance of $141_{-21}^{+30}$ pc. This new distance is in good agreement with recent values obtained for other magnetically active young stars in the L1689 cloud. We relate the kinematics of these masers with the outflows and the recent ejections powered by source A in the system.Comment: 14 pages, 6 tables, 8 figures. Accepted to be published in Astronomy \& Astrophysic

Nongaussian fluctuations arising from finite populations: Exact results for the evolutionary Moran process

The appropriate description of fluctuations within the framework of evolutionary game theory is a fundamental unsolved problem in the case of finite populations. The Moran process recently introduced into this context [Nowak et al., Nature (London) 428, 646 (2004)] defines a promising standard model of evolutionary game theory in finite populations for which analytical results are accessible. In this paper, we derive the stationary distribution of the Moran process population dynamics for arbitrary $2\times{}2$ games for the finite size case. We show that a nonvanishing background fitness can be transformed to the vanishing case by rescaling the payoff matrix. In contrast to the common approach to mimic finite-size fluctuations by Gaussian distributed noise, the finite size fluctuations can deviate significantly from a Gaussian distribution.Comment: 4 pages (2 figs). Published in Physical Review E (Rapid Communications

Database management and analysis of fisheries in Illinois: Final report, 1 March 1999-28 February 2002

Issued May 2002; F-69-RReport issued on: May 200

Coevolutionary Dynamics: From Finite to Infinite Populations

Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics in finite populations. However, the relationship between deterministic and stochastic approaches remained unclear. Here we solve this problem by explicitly considering large populations. In particular, we identify different microscopic stochastic processes that lead to the standard or the adjusted replicator dynamics. Moreover, differences on the individual level can lead to qualitatively different dynamics in asymmetric conflicts and, depending on the population size, can even invert the direction of the evolutionary process.Comment: 4 pages (2 figs included). Published in Phys. Rev. Lett., December 200

Asymmetry in the Spectrum of High-Velocity H2O Maser Emission Features in Active Galactic Nuclei

We suggest a mechanism for the amplification of high-velocity water-vapor maser emission features from the central regions of active galactic nuclei. The model of an emitting accretion disk is considered. The high-velocity emission features originate in the right and left wings of the Keplerian disk. The hyperfine splitting of the signal levels leads to an asymmetry in the spectral profile of the water vapor maser line at a frequency of 22.235 GHz. We show that the gain profile asymmetry must lead to an enhanced brightness of the blueshifted high-velocity emission features compared to the redshifted ones. Such a situation is observed in the source UGC 3789.Comment: 11 pages 3 figure