21,521 research outputs found
Breaking and restoration of rotational symmetry for irreducible tensor operators on the lattice
We study the breaking of rotational symmetry on the lattice for irreducible
tensor operators and practical methods for suppressing this breaking. We
illustrate the features of the general problem using an cluster model
for Be. We focus on the lowest states with non-zero angular momentum and
examine the matrix elements of multipole moment operators. We show that the
physical reduced matrix element is well reproduced by averaging over all
possible orientations of the quantum state, and this is expressed as a sum of
matrix elements weighted by the corresponding Clebsch-Gordan coefficients. For
our cluster model we find that the effects of rotational symmetry
breaking can be largely eliminated for lattice spacings of fm, and
we expect similar improvement for actual lattice Monte Carlo calculations.Comment: 8 pages, 4 figure
Precise determination of lattice phase shifts and mixing angles
We introduce a general and accurate method for determining lattice phase
shifts and mixing angles, which is applicable to arbitrary, non-cubic lattices.
Our method combines angular momentum projection, spherical wall boundaries and
an adjustable auxiliary potential. This allows us to construct radial lattice
wave functions and to determine phase shifts at arbitrary energies. For coupled
partial waves, we use a complex-valued auxiliary potential that breaks
time-reversal invariance. We benchmark our method using a system of two
spin-1/2 particles interacting through a finite-range potential with a strong
tensor component. We are able to extract phase shifts and mixing angles for all
angular momenta and energies, with precision greater than that of extant
methods. We discuss a wide range of applications from nuclear lattice
simulations to optical lattice experiments.Comment: 7 pp, 4 figs, 1 tabl
A new fabrication method for precision antenna reflectors for space flight and ground test
Communications satellites are using increasingly higher frequencies that require increasingly precise antenna reflectors for use in space. Traditional industry fabrication methods for space antenna reflectors employ successive modeling techniques using high- and low-temperature molds for reflector face sheets and then a final fit-up of the completed honeycomb sandwich panel antenna reflector to a master pattern. However, as new missions are planned at much higher frequencies, greater accuracies will be necessary than are achievable using these present methods. A new approach for the fabrication of ground-test solid-surface antenna reflectors is to build a rigid support structure with an easy-to-machine surface. This surface is subsequently machined to the desired reflector contour and coated with a radio-frequency-reflective surface. This method was used to fabricate a 2.7-m-diameter ground-test antenna reflector to an accuracy of better than 0.013 mm (0.0005 in.) rms. A similar reflector for use on spacecraft would be constructed in a similar manner but with space-qualified materials. The design, analysis, and fabrication of the 2.7-m-diameter precision antenna reflector for antenna ground tests and the extension of this technology to precision, space-based antenna reflectors are described
Perturbation theory for the effective diffusion constant in a medium of random scatterer
We develop perturbation theory and physically motivated resummations of the
perturbation theory for the problem of a tracer particle diffusing in a random
media. The random media contains point scatterers of density uniformly
distributed through out the material. The tracer is a Langevin particle
subjected to the quenched random force generated by the scatterers. Via our
perturbative analysis we determine when the random potential can be
approximated by a Gaussian random potential. We also develop a self-similar
renormalisation group approach based on thinning out the scatterers, this
scheme is similar to that used with success for diffusion in Gaussian random
potentials and agrees with known exact results. To assess the accuracy of this
approximation scheme its predictions are confronted with results obtained by
numerical simulation.Comment: 22 pages, 6 figures, IOP (J. Phys. A. style
Comment on "Ab Initio study of 40-Ca with an importance-truncated no-core shell model"
In a recent Letter [Phys. Rev. Lett. 99, 092501 (2007)], Roth and Navratil
present an importance-truncation scheme for the no-core shell model. The
authors claim that their truncation scheme leads to converged results for the
ground state of 40-Ca. We believe that this conclusion cannot be drawn from the
results presented in the Letter. Furthermore, the claimed convergence is at
variance with expectations of many-body theory. In particular, coupled-cluster
calculations indicate that a significant fraction of the correlation energy is
missing.Comment: 1 page, comment on arXiv:0705.4069 (PRL 99, 092501 (2007)
Effective diffusion constant in a two dimensional medium of charged point scatterers
We obtain exact results for the effective diffusion constant of a two
dimensional Langevin tracer particle in the force field generated by charged
point scatterers with quenched positions. We show that if the point scatterers
have a screened Coulomb (Yukawa) potential and are uniformly and independently
distributed then the effective diffusion constant obeys the
Volgel-Fulcher-Tammann law where it vanishes. Exact results are also obtained
for pure Coulomb scatterers frozen in an equilibrium configuration of the same
temperature as that of the tracer.Comment: 9 pages IOP LaTex, no figure
Viability of carbon-based life as a function of the light quark mass
The Hoyle state plays a crucial role in the helium burning of stars that have
reached the red giant stage. The close proximity of this state to the
triple-alpha threshold is needed for the production of carbon, oxygen, and
other elements necessary for life. We investigate whether this life-essential
condition is robust or delicately fine-tuned by measuring its dependence on the
fundamental constants of nature, specifically the light quark mass and the
strength of the electromagnetic interaction. We show that there exist strong
correlations between the alpha-particle binding energy and the various energies
relevant to the triple-alpha process. We derive limits on the variation of
these fundamental parameters from the requirement that sufficient amounts of
carbon and oxygen be generated in stars. We also discuss the implications of
these results for an anthropic view of the universe.Comment: 4 pages, 2 figures, version published in Phys. Rev. Lett., title
changed in journa
Conjugating binary systems for spacecraft thermal control
The materials search was directed to liquid pairs which can form hydrogen bonds of just the right strength, i.e., strong enough to give a high heat of mixing, but weak enough to enable phase change to occur. The cursory studies performed in the area of additive effects indicate that Conjugating Binary (CB) performance can probably be fine-tuned by this means. The Fluid Loop Test Systems (FLTS) tests of candidate CBs indicate that the systems Triethylamine (TEA)/water and propionaldehyde/water show close to the ideal, reversible behavior, at least initially. The Quick Screening Tests QSTs and FLTS tests, however, both suffer from rather severe static due either to inadequate stirring or temperature control. Thus it is not possible to adequately evaluate less than ideal CB performers. Less than ideal performers, it should be noted, may have features that make them better practical CBs than ideal performers. Improvement of the evaluation instrumentation is thus indicated
Recurrent cerebellar architecture solves the motor-error problem
Current views of cerebellar function have been heavily influenced by the models of Marr and Albus, who suggested that the climbing fibre input to the cerebellum acts as a teaching signal for motor learning. It is commonly assumed that this teaching signal must be motor error (the difference between actual and correct motor command), but this approach requires complex neural structures to estimate unobservable motor error from its observed sensory consequences.
We have proposed elsewhere a recurrent decorrelation control architecture in which Marr-Albus models learn without requiring motor error. Here, we prove convergence for this architecture and demonstrate important advantages for the modular control of systems with multiple degrees of freedom. These results are illustrated by modelling adaptive plant compensation for the three-dimensional vestibular ocular reflex. This provides a functional role for recurrent cerebellar connectivity, which may be a generic anatomical feature of projections between regions of cerebral and cerebellar cortex
- …