36,308 research outputs found
Almost Commuting Orthogonal Matrices
We show that almost commuting real orthogonal matrices are uniformly close to
exactly commuting real orthogonal matrices. We prove the same for symplectic
unitary matrices. This is in contrast to the general complex case, where not
all pairs of almost commuting unitaries are close to commuting pairs. Our
techniques also yield results about almost normal matrices over the reals and
the quaternions.Comment: 13 pages, 3 figure
Interlacing Families IV: Bipartite Ramanujan Graphs of All Sizes
We prove that there exist bipartite Ramanujan graphs of every degree and
every number of vertices. The proof is based on analyzing the expected
characteristic polynomial of a union of random perfect matchings, and involves
three ingredients: (1) a formula for the expected characteristic polynomial of
the sum of a regular graph with a random permutation of another regular graph,
(2) a proof that this expected polynomial is real rooted and that the family of
polynomials considered in this sum is an interlacing family, and (3) strong
bounds on the roots of the expected characteristic polynomial of a union of
random perfect matchings, established using the framework of finite free
convolutions we recently introduced
Precessing Jets and Molecular Outflows: A 3-D Numerical Study
We present 3-D numerical hydrodynamical simulations of precessing supersonic
heavy jets to explore how well they serve as a model for generating molecular
outflows from Young Stellar Objects. The dynamics are studied with a number of
high resolution simulations on a Cartesian grid (128x128x128 zones) using a
high order finite difference method. A range of cone angles and precession
rates were included in the study. Two higher resolution runs (256x256x256
zones) were made for comparison in order to confirm numerical convergence of
global flow characteristics. Morphological, kinematical and dynamical
characteristics of precessing jets are described and compared to important
properties of straight jets and also to observations of YSOs. In order to
examine the robustness of precessing jets as a mean to produce molecular
outflows around Young Stellar Objects, ``synthetic observations'' of the
momentum distributions of the simulated precessing jets are compared to
observations of molecular outflows. It is found that precessing jets match
better the morphology, highly forward driven momentum and momentum
distributions along the long axis of molecular outflows than do wind-driven or
straight jet-driven flow models.Comment: Accepted by ApJ, 31 pages, using aasms.sty, Also available in
postscript with figures via a gzipped tar file at
ftp://s1.msi.umn.edu/pub/afrank/3DJet/3DJet.tar.gz . For information contact
[email protected]
Twisted Electromagnetic Modes and Sagnac Ring-Lasers
A new approximation scheme, designed to solve the covariant Maxwell equations
inside a rotating hollow slender conducting cavity (modelling a ring-laser), is
constructed. It is shown that for well-defined conditions there exist TE and TM
modes with respect to the longitudinal axis of the cavity. A twisted mode
spectrum is found to depend on the integrated Frenet torsion of the cavity and
this in turn may affect the Sagnac beat frequency induced by a non-zero
rotation of the cavity. The analysis is motivated by attempts to use
ring-lasers to measure terrestrial gravito-magnetism or the Lense-Thirring
effect produced by the rotation of the Earth.Comment: LaTeX 31 pages, 3 Figure
Modeling Ultraviolet Wind Line Variability in Massive Hot Stars
We model the detailed time-evolution of Discrete Absorption Components (DACs)
observed in P Cygni profiles of the Si IV lam1400 resonance doublet lines of
the fast-rotating supergiant HD 64760 (B0.5 Ib). We adopt the common assumption
that the DACs are caused by Co-rotating Interaction Regions (CIRs) in the
stellar wind. We perform 3D radiative transfer calculations with hydrodynamic
models of the stellar wind that incorporate these large-scale density- and
velocity-structures. We develop the 3D transfer code Wind3D to investigate the
physical properties of CIRs with detailed fits to the DAC shape and morphology.
The CIRs are caused by irregularities on the stellar surface that change the
radiative force in the stellar wind. In our hydrodynamic model we approximate
these irregularities by circular symmetric spots on the stellar surface. We use
the Zeus3D code to model the stellar wind and the CIRs, limited to the
equatorial plane. We constrain the properties of large-scale wind structures
with detailed fits to DACs observed in HD 64760. A model with two spots of
unequal brightness and size on opposite sides of the equator, with opening
angles of 20 +/- 5 degr and 30 +/- 5 degr diameter, and that are 20 +/- 5 % and
8 +/- 5 % brighter than the stellar surface, respectively, provides the best
fit to the observed DACs. The recurrence time of the DACs compared to the
estimated rotational period corresponds to spot velocities that are 5 times
slower than the rotational velocity. The mass-loss rate of the structured wind
model for HD 64760 does not exceed the rate of the spherically symmetric smooth
wind model by more than 1 %. The fact that DACs are observed in a large number
of hot stars constrains the clumping that can be present in their winds, as
substantial amounts of clumping would tend to destroy the CIRs.Comment: 58 pages, 16 figures, 1 animation. Accepted for publication in The
Astrophysical Journal, Main Journal. More information and animations are
available at http://alobel.freeshell.org/hotstars.htm
Waste management in the stingless bee Melipona beecheii Bennett (Hymenoptera: Apidae)
Waste management is important in insect societies because waste can be hazardous to adults, brood and food stores. The general organization of waste management and the influence of task partitioning, division of labor and age polyethism on waste processing were studied in three colonies of the tropical American stingless bee Melipona beecheii Bennett in Yucatán, Mexico. Waste generated in the colony (feces, old brood cells, cocoons, dead adults and brood) was collected by workers throughout the nest and taken to specific waste dumps within the nest. During the day, workers based at the waste dumps formed waste pellets, which they directly transferred in 93% of cases, to other workers who subsequently removed them from the nest. This is an example of task partitioning and is hypothesized to improve nest hygiene as has been found in leafcutting ants, Atta. To investigate division of labor and age polyethism we marked a cohort of 144 emerging workers. Workers forming waste pellets were on average 31.2±6.5 days old (±SD, N= 40, range of 18-45 days). The life span of M. beecheii workers was 49.0±14.0 days (N= 144). There was no difference in the life span of workers who formed (52.2±11.6 days, N= 40) or did not form (49.9±11.5 days, N= 97) waste pellets, suggesting that waste work did not increase mortality. Although waste was probably not hazardous to adults and brood, because the dumps are located outside the brood chamber, its presence inside the nests can attract phorid flies and predators, which can harm the colony
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