1,264 research outputs found
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 independent two-dimensional random walkers. Each such walk
consists of discrete time steps, where and increments are i.i.d.
Gaussian. We analyze area and perimeter 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 . We find that the densities exhibit a universal scaling
behavior as a function of and , respectively. As in the case
of one walker (), the densities follow Gaussian distributions for and
, 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 , revealing that the
densities follow the large-deviation principle. These rate functions can be
described by a power law for as found in the case.
We also investigated the behavior of the averages as a function of the number
of walks and found good agreement with the predicted behavior.Comment: 11 pages, 14 figure
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
Model States for a Class of Chiral Topological Order Interfaces
Interfaces between topologically distinct phases of matter reveal a
remarkably rich phenomenology. To go beyond effective field theories, we study
the prototypical example of such an interface between two Abelian states,
namely the Laughlin and Halperin states. Using matrix product states, we
propose a family of model wavefunctions for the whole system including both
bulks and the interface. We show through extensive numerical studies that it
unveils both the universal properties of the system, such as the central charge
of the gapless interface mode and its microscopic features. It also captures
the low energy physics of experimentally relevant Hamiltonians. Our approach
can be generalized to other phases described by tensor networks.Comment: Published version. Former supplementary material has been extended
and published as a separate articl
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 162932422 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
HO 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 HO maser spots, we derived a trigonometric parallax of mas,
corresponding to a distance of 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
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
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Recreational mountain biking: A case study of sustainable trail development at Boggs Demonstration State Forest, Cobb, California
This study identifies contemporary research in the field of recreation ecology focusing on ecological impacts of mountain biking and establishing best management practices for sustainable trail development and management.
A site analysis at Boggs Mountain Demonstration State Forest (BMDSF) takes existing knowledge and research on sustainable trail development and applies those lessons through geographic information systems (GIS) analysis and on-site trail observations. This research is timely as trails are being planned and re-built after a catastrophic fire in 2015. GIS analysis can help identify limitations of the site and guide management recommendations
Measurements of permittivity, dieletric loss tangent, and resistivity of float-zone silicon at microwave frequencies
Published versio
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