12,747 research outputs found
Spherical codes, maximal local packing density, and the golden ratio
The densest local packing (DLP) problem in d-dimensional Euclidean space Rd
involves the placement of N nonoverlapping spheres of unit diameter near an
additional fixed unit-diameter sphere such that the greatest distance from the
center of the fixed sphere to the centers of any of the N surrounding spheres
is minimized. Solutions to the DLP problem are relevant to the realizability of
pair correlation functions for packings of nonoverlapping spheres and might
prove useful in improving upon the best known upper bounds on the maximum
packing fraction of sphere packings in dimensions greater than three. The
optimal spherical code problem in Rd involves the placement of the centers of N
nonoverlapping spheres of unit diameter onto the surface of a sphere of radius
R such that R is minimized. It is proved that in any dimension, all solutions
between unity and the golden ratio to the optimal spherical code problem for N
spheres are also solutions to the corresponding DLP problem. It follows that
for any packing of nonoverlapping spheres of unit diameter, a spherical region
of radius less than or equal to the golden ratio centered on an arbitrary
sphere center cannot enclose a number of sphere centers greater than one more
than the number that can be placed on the region's surface.Comment: 12 pages, 1 figure. Accepted for publication in the Journal of
Mathematical Physic
A fault-tolerant multiprocessor architecture for aircraft, volume 1
A fault-tolerant multiprocessor architecture is reported. This architecture, together with a comprehensive information system architecture, has important potential for future aircraft applications. A preliminary definition and assessment of a suitable multiprocessor architecture for such applications is developed
A Theoretical Interpretation of the Black Hole Fundamental Plane
We examine the origin and evolution of correlations between properties of
supermassive black holes (BHs) and their host galaxies using simulations of
major galaxy mergers, including the effects of gas dissipation, cooling, star
formation, and BH accretion and feedback. We demonstrate that the simulations
predict the existence of a BH 'fundamental plane' (BHFP), of the form M_BH
sigma^(3.0+-0.3)*R_e^(0.43+-0.19) or M_BH
M_bulge^(0.54+-0.17)*sigma^(2.2+-0.5), similar to relations found
observationally. The simulations indicate that the BHFP can be understood
roughly as a tilted intrinsic correlation between BH mass and spheroid binding
energy, or the condition for feedback coupling to power a pressure-driven
outflow. While changes in halo circular velocity, merger orbital parameters,
progenitor disk redshifts and gas fractions, ISM gas pressurization, and other
parameters can drive changes in e.g. sigma at fixed M_bulge, and therefore
changes in the M_BH-sigma or M_BH-M_bulge relations, the BHFP is robust. Given
the empirical trend of decreasing R_e for a given M_bulge at high redshift, the
BHFP predicts that BHs will be more massive at fixed M_bulge, in good agreement
with recent observations. This evolution in the structural properties of merger
remnants, to smaller R_e and larger sigma (and therefore larger M_BH,
conserving the BHFP) at a given M_bulge, is driven by the fact that bulge
progenitors have characteristically larger gas fractions at high redshifts.
Adopting the observed evolution of disk gas fractions with redshift, our
simulations predict the observed trends in both R_e(M_bulge) and M_BH(M_bulge).Comment: 22 pages, 19 figures, replaced with version accepted to ApJ.
Companion paper to arXiv:0707.400
System data communication structures for active-control transport aircraft, volume 2
The application of communication structures to advanced transport aircraft are addressed. First, a set of avionic functional requirements is established, and a baseline set of avionics equipment is defined that will meet the requirements. Three alternative configurations for this equipment are then identified that represent the evolution toward more dispersed systems. Candidate communication structures are proposed for each system configuration, and these are compared using trade off analyses; these analyses emphasize reliability but also address complexity. Multiplex buses are recognized as the likely near term choice with mesh networks being desirable for advanced, highly dispersed systems
Healthcare Barriers of Residents at a Subsidized Housing Community
Introduction: Despite expanded healthcare programs, the low income and elderly lack coverage of vision, hearing, and dental services. Community services are often asked to fill these gaps. To evaluate the situation in Burlington, VT, we surveyed staff and residents in Burlington Housing Authority (BHA) subsidized housing to (1) identify gaps in healthcare coverage and (2) assess barriers to accessing those services in this population.https://scholarworks.uvm.edu/comphp_gallery/1207/thumbnail.jp
System data communication structures for active-control transport aircraft, volume 1
Candidate data communication techniques are identified, including dedicated links, local buses, broadcast buses, multiplex buses, and mesh networks. The design methodology for mesh networks is then discussed, including network topology and node architecture. Several concepts of power distribution are reviewed, including current limiting and mesh networks for power. The technology issues of packaging, transmission media, and lightning are addressed, and, finally, the analysis tools developed to aid in the communication design process are described. There are special tools to analyze the reliability and connectivity of networks and more general reliability analysis tools for all types of systems
Dense sphere packings from optimized correlation functions
Elementary smooth functions (beyond contact) are employed to construct pair
correlation functions that mimic jammed disordered sphere packings. Using the
g2-invariant optimization method of Torquato and Stillinger [J. Phys. Chem. B
106, 8354, 2002], parameters in these functions are optimized under necessary
realizability conditions to maximize the packing fraction phi and average
number of contacts per sphere Z. A pair correlation function that incorporates
the salient features of a disordered packing and that is smooth beyond contact
is shown to permit a phi of 0.6850: this value represents a 45% reduction in
the difference between the maximum for congruent hard spheres in three
dimensions, pi/sqrt{18} ~ 0.7405, and 0.64, the approximate fraction associated
with maximally random jammed (MRJ) packings in three dimensions. We show that,
surprisingly, the continued addition of elementary functions consisting of
smooth sinusoids decaying as r^{-4} permits packing fractions approaching
pi/sqrt{18}. A translational order metric is used to discriminate between
degrees of order in the packings presented. We find that to achieve higher
packing fractions, the degree of order must increase, which is consistent with
the results of a previous study [Torquato et al., Phys. Rev. Lett. 84, 2064,
2000].Comment: 26 pages, 9 figures, 1 table; added references, fixed typos,
simplified argument and discussion in Section IV
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