65,121 research outputs found
Classical mappings of the symplectic model and their application to the theory of large-amplitude collective motion
We study the algebra Sp(n,R) of the symplectic model, in particular for the
cases n=1,2,3, in a new way. Starting from the Poisson-bracket realization we
derive a set of partial differential equations for the generators as functions
of classical canonical variables. We obtain a solution to these equations that
represents the classical limit of a boson mapping of the algebra. The
relationship to the collective dynamics is formulated as a theorem that
associates the mapping with an exact solution of the time-dependent Hartree
approximation. This solution determines a decoupled classical symplectic
manifold, thus satisfying the criteria that define an exactly solvable model in
the theory of large amplitude collective motion. The models thus obtained also
provide a test of methods for constructing an approximately decoupled manifold
in fully realistic cases. We show that an algorithm developed in one of our
earlier works reproduces the main results of the theorem.Comment: 23 pages, LaTeX using REVTeX 3.
Novel multipurpose timer for laboratories
Multipurpose digital delay timer simultaneously controls both a buffer pump and a fraction-collector. Timing and control may be in 30-second increments for up to 15 hours. Use of glassware and scintillation vials make it economical
Exact relativistic treatment of stationary counter-rotating dust disks III. Physical Properties
This is the third in a series of papers on the construction of explicit
solutions to the stationary axisymmetric Einstein equations which can be
interpreted as counter-rotating disks of dust. We discuss the physical
properties of a class of solutions to the Einstein equations for disks with
constant angular velocity and constant relative density which was constructed
in the first part. The metric for these spacetimes is given in terms of theta
functions on a Riemann surface of genus 2. It is parameterized by two physical
parameters, the central redshift and the relative density of the two
counter-rotating streams in the disk. We discuss the dependence of the metric
on these parameters using a combination of analytical and numerical methods.
Interesting limiting cases are the Maclaurin disk in the Newtonian limit, the
static limit which gives a solution of the Morgan and Morgan class and the
limit of a disk without counter-rotation. We study the mass and the angular
momentum of the spacetime. At the disk we discuss the energy-momentum tensor,
i.e. the angular velocities of the dust streams and the energy density of the
disk. The solutions have ergospheres in strongly relativistic situations. The
ultrarelativistic limit of the solution in which the central redshift diverges
is discussed in detail: In the case of two counter-rotating dust components in
the disk, the solutions describe a disk with diverging central density but
finite mass. In the case of a disk made up of one component, the exterior of
the disks can be interpreted as the extreme Kerr solution.Comment: 30 pages, 20 figures; to appear in Phys. Rev.
Analysis of the flight dynamics of the Solar Maximum Mission (SMM) off-sun scientific pointing
Algorithms are presented which were created and implemented by the Goddard Space Flight Center's (GSFC's) Solar Maximum Mission (SMM) attitude operations team to support large-angle spacecraft pointing at scientific objectives. The mission objective of the post-repair SMM satellite was to study solar phenomena. However, because the scientific instruments, such as the Coronagraph/Polarimeter (CP) and the Hard X ray Burst Spectrometer (HXRBS), were able to view objects other than the Sun, attitude operations support for attitude pointing at large angles from the nominal solar-pointing attitudes was required. Subsequently, attitude support for SMM was provided for scientific objectives such as Comet Halley, Supernova 1987A, Cygnus X-1, and the Crab Nebula. In addition, the analysis was extended to include the reverse problem, computing the right ascension and declination of a body given the off-Sun angles. This analysis led to the computation of the orbits of seven new solar comets seen in the field-of-view (FOV) of the CP. The activities necessary to meet these large-angle attitude-pointing sequences, such as slew sequence planning, viewing-period prediction, and tracking-bias computation are described. Analysis is presented for the computation of maneuvers and pointing parameters relative to the SMM-unique, Sun-centered reference frame. Finally, science data and independent attitude solutions are used to evaluate the large-angle pointing performance
25 kHz narrow spectral bandwidth of a wavelength tunable diode laser with a short waveguide-based external cavity
We report on the spectral properties of a diode laser with a tunable external
cavity in integrated optics. Even though the external cavity is short compared
to other small-bandwidth external cavity lasers, the spectral bandwidth of this
tunable laser is as small as 25 kHz (FWHM), at a side-mode suppression ratio
(SMSR) of 50 dB. Our laser is also able to access preset wavelengths in as
little as 200 us and able to tune over the full telecom C-band (1530 nm - 1565
nm).Comment: 8 pages, 7 figure
A note on the computation of geometrically defined relative velocities
We discuss some aspects about the computation of kinematic, spectroscopic,
Fermi and astrometric relative velocities that are geometrically defined in
general relativity. Mainly, we state that kinematic and spectroscopic relative
velocities only depend on the 4-velocities of the observer and the test
particle, unlike Fermi and astrometric relative velocities, that also depend on
the acceleration of the observer and the corresponding relative position of the
test particle, but only at the event of observation and not around it, as it
would be deduced, in principle, from the definition of these velocities.
Finally, we propose an open problem in general relativity that consists on
finding intrinsic expressions for Fermi and astrometric relative velocities
avoiding terms that involve the evolution of the relative position of the test
particle. For this purpose, the proofs given in this paper can serve as
inspiration.Comment: 8 pages, 2 figure
Influence of quark boundary conditions on the pion mass in finite volume
We calculate the mass shift for the pion in a finite volume with
renormalization group (RG) methods in the framework of the quark-mesons model.
In particular, we investigate the importance of the quark effects on the pion
mass. As in lattice gauge theory, the choice of quark boundary conditions has a
noticeable effect on the pion mass shift in small volumes, in addition to the
shift due to pion interactions. We compare our results to chiral perturbation
theory calculations and find differences due to the fact that chiral
perturbation theory only considers pion effects in the finite volume.Comment: 24 pages, 5 figures, RevTex4, published version, discussion of
lattice results extende
Approaching equilibrium and the distribution of clusters
We investigate the approach to stable and metastable equilibrium in Ising
models using a cluster representation. The distribution of nucleation times is
determined using the Metropolis algorithm and the corresponding
model using Langevin dynamics. We find that the nucleation rate is suppressed
at early times even after global variables such as the magnetization and energy
have apparently reached their time independent values. The mean number of
clusters whose size is comparable to the size of the nucleating droplet becomes
time independent at about the same time that the nucleation rate reaches its
constant value. We also find subtle structural differences between the
nucleating droplets formed before and after apparent metastable equilibrium has
been established.Comment: 22 pages, 16 figure
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