19,313 research outputs found
Schubert Polynomials for the affine Grassmannian of the symplectic group
We study the Schubert calculus of the affine Grassmannian Gr of the
symplectic group. The integral homology and cohomology rings of Gr are
identified with dual Hopf algebras of symmetric functions, defined in terms of
Schur's P and Q-functions. An explicit combinatorial description is obtained
for the Schubert basis of the cohomology of Gr, and this is extended to a
definition of the affine type C Stanley symmetric functions. A homology Pieri
rule is also given for the product of a special Schubert class with an
arbitrary one.Comment: 45 page
Macular Bioaccelerometers on Earth and in Space
Space flight offers the opportunity to study linear bioaccelerometers (vestibular maculas) in the virtual absence of a primary stimulus, gravitational acceleration. Macular research in space is particularly important to NASA because the bioaccelerometers are proving to be weighted neural networks in which information is distributed for parallel processing. Neural networks are plastic and highly adaptive to new environments. Combined morphological-physiological studies of maculas fixed in space and following flight should reveal macular adaptive responses to microgravity, and their time-course. Ground-based research, already begun, using computer-assisted, 3-dimensional reconstruction of macular terminal fields will lead to development of computer models of functioning maculas. This research should continue in conjunction with physiological studies, including work with multichannel electrodes. The results of such a combined effort could usher in a new era in understanding vestibular function on Earth and in space. They can also provide a rational basis for counter-measures to space motion sickness, which may prove troublesome as space voyager encounter new gravitational fields on planets, or must re-adapt to 1 g upon return to earth
Generalized Background-Field Method
The graphical method discussed previously can be used to create new gauges
not reachable by the path-integral formalism. By this means a new gauge is
designed for more efficient two-loop QCD calculations. It is related to but
simpler than the ordinary background-field gauge, in that even the triple-gluon
vertices for internal lines contain only four terms, not the usual six. This
reduction simplifies the calculation inspite of the necessity to include other
vertices for compensation. Like the ordinary background-field gauge, this
generalized background-field gauge also preserves gauge invariance of the
external particles. As a check of the result and an illustration for the
reduction in labour, an explicit calculation of the two-loop QCD
-function is carried out in this new gauge. It results in a saving of
45% of computation compared to the ordinary background-field gauge.Comment: 17 pages, Latex, 18 figures in Postscrip
A mirrorless spinwave resonator
Optical resonance is central to a wide range of optical devices and
techniques. In an optical cavity, the round-trip length and mirror reflectivity
can be chosen to optimize the circulating optical power, linewidth, and
free-spectral range (FSR) for a given application. In this paper we show how an
atomic spinwave system, with no physical mirrors, can behave in a manner that
is analogous to an optical cavity. We demonstrate this similarity by
characterising the build-up and decay of the resonance in the time domain, and
measuring the effective optical linewidth and FSR in the frequency domain. Our
spinwave is generated in a 20 cm long Rb gas cell, yet it facilitates an
effective FSR of 83 kHz, which would require a round-trip path of 3.6 km in a
free-space optical cavity. Furthermore, the spinwave coupling is controllable
enabling dynamic tuning of the effective cavity parameters.Comment: 13 pages, 4 figure
A quantum study of multi-bit phase coding for optical storage
We propose a scheme which encodes information in both the longitudinal and
spatial transverse phases of a continuous-wave optical beam. A split
detector-based interferometric scheme is then introduced to optimally detect
both encoded phase signals. In contrast to present-day optical storage devices,
our phase coding scheme has an information storage capacity which scales with
the power of the read-out optical beam. We analyse the maximum number of
encoding possibilities at the shot noise limit. In addition, we show that using
squeezed light, the shot noise limit can be overcome and the number of encoding
possibilities increased. We discuss a possible application of our phase coding
scheme for increasing the capacities of optical storage devices.Comment: 8 pages, 7 figures (Please email author for a PDF file if the
manuscript does not turn out properly
Systematic and Stochastic Variations in Pulsar Dispersion Measures
We analyze deterministic and random temporal variations in dispersion measure
(DM) from the full three-dimensional velocities of pulsars with respect to the
solar system, combined with electron-density variations on a wide range of
length scales. Previous treatments have largely ignored the pulsar's changing
distance while favoring interpretations involving the change in sky position
from transverse motion. Linear trends in pulsar DMs seen over 5-10~year
timescales may signify sizable DM gradients in the interstellar medium (ISM)
sampled by the changing direction of the line of sight to the pulsar. We show
that motions parallel to the line of sight can also account for linear trends,
for the apparent excess of DM variance over that extrapolated from
scintillation measurements, and for the apparent non-Kolmogorov scalings of DM
structure functions inferred in some cases. Pulsar motions through atomic gas
may produce bow-shock ionized gas that also contributes to DM variations. We
discuss possible causes of periodic or quasi-periodic changes in DM, including
seasonal changes in the ionosphere, annual variation of the solar elongation
angle, structure in the heliosphere-ISM boundary, and substructure in the ISM.
We assess the solar cycle's role on the amplitude of ionospheric and solar-wind
variations. Interstellar refraction can produce cyclic timing variations from
the error in transforming arrival times to the solar system barycenter. We
apply our methods to DM time series and DM gradient measurements in the
literature and assess consistency with a Kolmogorov medium. Finally, we discuss
the implications of DM modeling in precision pulsar timing experiments.Comment: 24 pages, 17 figures, published in Ap
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