2,070 research outputs found
Little groups of irreps of O(3), SO(3), and the infinite axial subgroups
Little groups are enumerated for the irreps and their components in any basis
of O(3) and SO(3) up to rank 9, and for all irreps of C, C, C, D and D. The results are obtained
by a new chain criterion, which distinguishes massive (rotationally
inequivalent) irrep basis functions and allows for multiple branching paths,
and are verified by inspection. These results are relevant to the determination
of the symmetry of a material from its linear and nonlinear optical properties
and to the choices of order parameters for symmetry breaking in liquid
crystals.Comment: 28 pages and 3 figure
Elliptic Phases: A Study of the Nonlinear Elasticity of Twist-Grain Boundaries
We develop an explicit and tractable representation of a twist-grain-boundary
phase of a smectic A liquid crystal. This allows us to calculate the
interaction energy between grain boundaries and the relative contributions from
the bending and compression deformations. We discuss the special stability of
the 90 degree grain boundaries and discuss the relation of this structure to
the Schwarz D surface.Comment: 4 pages, 2 figure
General relativistic gravitational field of a rigidly rotating disk of dust: Solution in terms of ultraelliptic functions
In a recent paper we presented analytic expressions for the axis potential,
the disk metric, and the surface mass density of the global solution to
Einstein's field equations describing a rigidly rotating disk of dust. Here we
add the complete solution in terms of ultraelliptic functions and quadratures.Comment: 5 pages, published in 1995 [Phys. Rev. Lett. 75 (1995) 3046
From Lagrangian to Quantum Mechanics with Symmetries
We present an old and regretfully forgotten method by Jacobi which allows one
to find many Lagrangians of simple classical models and also of nonconservative
systems. We underline that the knowledge of Lie symmetries generates Jacobi
last multipliers and each of the latter yields a Lagrangian. Then it is shown
that Noether's theorem can identify among those Lagrangians the physical
Lagrangian(s) that will successfully lead to quantization. The preservation of
the Noether symmetries as Lie symmetries of the corresponding Schr\"odinger
equation is the key that takes classical mechanics into quantum mechanics.
Some examples are presented.Comment: To appear in: Proceedings of Symmetries in Science XV, Journal of
Physics: Conference Series, (2012
Long-Term Population Variability in the Palila, An Endangered Hawaiian Honeycreeper
Annual surveys of the entire range of the endangered Palila
(Loxioides bailleui Oustalet) on Mauna Kea, Hawai'i, were conducted during
1980-1995. The majority of the Palila population was found on the southwestern
slope of Mauna Kea near Pu'u La'au, and the range of Palila has not
changed since 1975. The Palila population was highly variable. Mean population
size during 1980-1995 was 3390 ± 333 SE, but the population ranged
from 1584 ± 324 in 1985 to 5685 ± 535 in 1981. Population size outside the
population center near Pu'u La'au has decreased significantly since 1980
Instabilities of one-dimensional stationary solutions of the cubic nonlinear Schrodinger equation
The two-dimensional cubic nonlinear Schrodinger equation admits a large
family of one-dimensional bounded traveling-wave solutions. All such solutions
may be written in terms of an amplitude and a phase. Solutions with piecewise
constant phase have been well studied previously. Some of these solutions were
found to be stable with respect to one-dimensional perturbations. No such
solutions are stable with respect to two-dimensional perturbations. Here we
consider stability of the larger class of solutions whose phase is dependent on
the spatial dimension of the one-dimensional wave form. We study the spectral
stability of such nontrivial-phase solutions numerically, using Hill's method.
We present evidence which suggests that all such nontrivial-phase solutions are
unstable with respect to both one- and two-dimensional perturbations.
Instability occurs in all cases: for both the elliptic and hyperbolic nonlinear
Schrodinger equations, and in the focusing and defocusing case.Comment: Submitted: 13 pages, 3 figure
The tale of two centres
We study motion in the field of two fixed centres described by a family of
Einstein-dilaton-Maxwell theories. Transitions between regular and chaotic
motion are observed as the dilaton coupling is varied.Comment: 20 pages, RevTeX, 7 figures included, TeX format change
Equal charge black holes and seven dimensional gauged supergravity
We present various supergravity black holes of different dimensions with some
U(1) charges set equal in a simple, common form. Black hole solutions of seven
dimensional U(1)^2 gauged supergravity with three independent angular momenta
and two equal U(1) charges are obtained. We investigate the thermodynamics and
the BPS limit of this solution, and find that there are rotating supersymmetric
black holes without naked closed timelike curves. There are also supersymmetric
topological soliton solutions without naked closed timelike curves that have a
smooth geometry.Comment: 24 pages; v2, v3: minor change
Singular Isothermal Disks: II. Nonaxisymmetric Bifurcations and Equilibria
We review the difficulties of the classical fission and fragmentation
hypotheses for the formation of binary and multiple stars. A crucial missing
ingredient in previous theoretical studies is the inclusion of dynamically
important levels of magnetic fields. As a minimal model for a candidate
presursor to the formation of binary and multiple stars, we therefore formulate
and solve the problem of the equilibria of isopedically magnetized, singular
isothermal disks, without the assumption of axial symmetry. Considerable
analytical progress can be made if we restrict our attention to models that are
scale-free, i.e., that have surface densities that vary inversely with distance
from the rotation axis of the system. In agreement with earlier analysis by
Syer and Tremaine, we find that lopsided (M=1) configurations exist at any
dimensionless rotation rate, including zero. Multiple-lobed (M = 2, 3, 4, ...)
configurations bifurcate from an underlying axisymmetric sequence at
progressively higher dimensionless rates of rotation, but such nonaxisymmetric
sequences always terminate in shockwaves before they have a chance to fission
into M=2, 3, 4, ... separate bodies. On the basis of our experience in this
paper, and the preceding Paper I, we advance the hypothesis that binary and
multiple star-formation from smooth (i.e., not highly turbulent) starting
states that are supercritical but in unstable mechanical balance requires the
rapid (i.e., dynamical) loss of magnetic flux at some stage of the ensuing
gravitational collapse.Comment: 49 pages, 11 figures, LaTeX, needs aaspp4.sty. The Astrophysical
Journal, in pres
Climate of the upper atmosphere
In the frame of the European COST 296 project (Mitigation of Ionospheric Effects on Radio Systems, MIERS)investigations of the climate of the upper atmosphere have been carried out during the last four years to obtain new information on the upper atmosphere. Mainly its ionospheric part has been analysed as the ionosphere is
most essential for the propagation of radio waves. Due to collaboration between different European partners many new results have been derived in the fields of long-term trends of different ionospheric and related atmospheric parameters, the investigations of different types of atmospheric waves and their impact on the ionosphere, the variability of the ionosphere, and the investigation of some space weather effects on the ionosphere.Published273-2991.7. Osservazioni di alta e media atmosferaJCR Journalreserve
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