66,228 research outputs found
On a Order Reduction Theorem in the Lagrangian Formalism
We provide a new proof of a important theorem in the Lagrangian formalism
about necessary and sufficient conditions for a second-order variational system
of equations to follow from a first-order Lagrangian.Comment: 9 pages, LATEX, no figures; appear in Il Nuovo Cimento
The Education of Real Estate Salespeople and the Value of the Firm
In order to protect the public, most states require salespeople and brokers to meet specific licensing requirements, typically in the form of classroom instruction and/or successful completion of an examination. Frequently, however, many real estate brokers require their sales staff to undertake education that exceeds these minimum requirements. In this study, we derive a theoretical model that shows how optimally-timed, firm provided education that exceeds legal minimums can increase staff productivity, reduce litigation risks and perhaps raise and/or maximize the expected value of the firm.
Eccentricity and Spin-Orbit Misalignment in Short-Period Stellar Binaries as a Signpost of Hidden Tertiary Companions
Eclipsing binaries are observed to have a range of eccentricities and
spin-orbit misalignments (stellar obliquities). Whether such properties are
primordial, or arise from post-formation dynamical interactions remains
uncertain. This paper considers the scenario in which the binary is the inner
component of a hierarchical triple stellar system, and derives the requirements
that the tertiary companion must satisfy in order to raise the eccentricity and
obliquity of the inner binary. Through numerical integrations of the secular
octupole-order equations of motion of stellar triples, coupled with the spin
precession of the oblate primary star due to the torque from the secondary, we
obtain a simple, robust condition for producing spin-orbit misalignment in the
inner binary: In order to excite appreciable obliquity, the precession rate of
the stellar spin axis must be smaller than the orbital precession rate due to
the tertiary companion. This yields quantitative requirements on the mass and
orbit of the tertiary. We also present new analytic expressions for the maximum
eccentricity and range of inclinations allowing eccentricity excitation
(Lidov-Kozai window), for stellar triples with arbitrary masses and including
the non-Keplerian potentials introduced by general relativity, stellar tides
and rotational bulges. The results of this paper can be used to place
constraints on unobserved tertiary companions in binaries that exhibit high
eccentricity and/or spin-orbit misalignment, and will be helpful in guiding
efforts to detect external companions around stellar binaries. As an
application, we consider the eclipsing binary DI Herculis, and identify the
requirements that a tertiary companion must satisfy to produce the observed
spin-orbit misalignment.Comment: 19 pages, 15 figures, accepted for publication in MNRA
Properties of the Scalar Universal Equations
The variational properties of the scalar so--called ``Universal'' equations
are reviewed and generalised. In particular, we note that contrary to earlier
claims, each member of the Euler hierarchy may have an explicit field
dependence. The Euler hierarchy itself is given a new interpretation in terms
of the formal complex of variational calculus, and is shown to be related to
the algebra of distinguished symmetries of the first source form.Comment: 15 pages, LaTeX articl
Chaotic Dynamics of Stellar Spin in Binaries and the Production of Misaligned Hot Jupiters
Many exoplanetary systems containing hot Jupiters are observed to have highly
misaligned orbital axes relative to the stellar spin axes. Kozai-Lidov
oscillations of orbital eccentricity/inclination induced by a binary companion,
in conjunction with tidal dissipation, is a major channel for the production of
hot Jupiters. We demonstrate that gravitational interaction between the planet
and its oblate host star can lead to chaotic evolution of the stellar spin axis
during Kozai cycles. As parameters such as the planet mass and stellar rotation
period vary, periodic islands can appear in an ocean of chaos, in a manner
reminiscent of other dynamical systems. In the presence of tidal dissipation,
the complex spin evolution can leave an imprint on the final spin-orbit
misalignment angles.Comment: 26 pages, 13 figures. Includes supplementary materials. To be
published in the September 12, 2014 edition of Science Magazine. For
additional information, please visit
http://astro.cornell.edu/~dong/sciencepaper.htm
Children's Databases - Safety and Privacy
This report describes in detail the policy background, the systems that are being built, the problems with them, and the legal situation in the UK. An appendix looks at Europe, and examines in particular detail how France and Germany have dealt with these issues. Our report concludes with three suggested regulatory action strategies for the Commissioner: one minimal strategy in which he tackles only the clear breaches of the law, one moderate strategy in which he seeks to educate departments and agencies and guide them towards best practice, and finally a vigorous option in which he would seek to bring UK data protection practice in these areas more in line with normal practice in Europe, and indeed with our obligations under European law
The Principle of Symmetric Criticality in General Relativity
We consider a version of Palais' Principle of Symmetric Criticality (PSC)
that is applicable to the Lie symmetry reduction of Lagrangian field theories.
PSC asserts that, given a group action, for any group-invariant Lagrangian the
equations obtained by restriction of Euler-Lagrange equations to
group-invariant fields are equivalent to the Euler-Lagrange equations of a
canonically defined, symmetry-reduced Lagrangian. We investigate the validity
of PSC for local gravitational theories built from a metric. It is shown that
there are two independent conditions which must be satisfied for PSC to be
valid. One of these conditions, obtained previously in the context of
transverse symmetry group actions, provides a generalization of the well-known
unimodularity condition that arises in spatially homogeneous cosmological
models. The other condition seems to be new. The conditions that determine the
validity of PSC are equivalent to pointwise conditions on the group action
alone. These results are illustrated with a variety of examples from general
relativity. It is straightforward to generalize all of our results to any
relativistic field theory.Comment: 46 pages, Plain TeX, references added in revised versio
Presymplectic current and the inverse problem of the calculus of variations
The inverse problem of the calculus of variations asks whether a given system
of partial differential equations (PDEs) admits a variational formulation. We
show that the existence of a presymplectic form in the variational bicomplex,
when horizontally closed on solutions, allows us to construct a variational
formulation for a subsystem of the given PDE. No constraints on the
differential order or number of dependent or independent variables are assumed.
The proof follows a recent observation of Bridges, Hydon and Lawson and
generalizes an older result of Henneaux from ordinary differential equations
(ODEs) to PDEs. Uniqueness of the variational formulation is also discussed.Comment: v2: 17 pages, no figures, BibTeX; minor corrections, close to
published versio
The bottom of the white dwarf cooling sequence in the old open cluster NGC 2158
We use 10 orbits of Advanced Camera for Surveys observations to reach the end
of the white dwarf cooling sequence in the solar-metallicity open cluster NGC
2158. Our photometry and completeness tests show that the end falls at
magnitude m_F606W = 27.5 +/- 0.15, which implies an age between ~1.8 and ~2.0
Gyr, consistent with the age of 1.9 +/- 0.2 Gyr obtained from fits to the
main-sequence turn-off. The faintest white dwarfs show a clear turn toward
bluer colors, as predicted by theoretical isochrones.Comment: 12 pages, 4 figures (2 in low resolution, and 1 bonus for
astro-ph-only). ApJ Letter accepted on December 1, 200
Two Phase Collective Modes in Josephson Vortex Lattice in Intrinsic Josephson Junction BiSrCaCuO
Josephson plasma excitations in the high superconductor
BiSrCaCuO have been investigated in a wide microwave
frequency region (9.8 -- 75 GHz), in particular, in magnetic field applied
parallel to the plane of the single crystal. In sharp contrast to the case
for magnetic fields parallel to the c axis or tilted from the plane, it
was found that there are two kinds of resonance modes, which are split in
energy and possess two distinctly different magnetic field dependences. One
always lies higher in energy than the other and has a shallow minimum at about
0.8 kOe, then increases linearly with magnetic field. On the other hand,
another mode begins to appear only in a magnetic field (from a few kOe and
higher) and has a weakly decreasing tendency with increasing magnetic field. By
comparing with a recent theoretical model the higher energy mode can naturally
be attributed to the Josephson plasma resonance mode propagating along the
primitive reciprocal lattice vector of the Josephson vortex lattice, whereas
the lower frequency mode is assigned to the novel phase collective mode of the
Josephson vortex lattice, which has never been observed before.Comment: 11 pages and 10 figure
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