938 research outputs found
On the volume functional of compact manifolds with boundary with constant scalar curvature
We study the volume functional on the space of constant scalar curvature
metrics with a prescribed boundary metric. We derive a sufficient and necessary
condition for a metric to be a critical point, and show that the only domains
in space forms, on which the standard metrics are critical points, are geodesic
balls. In the zero scalar curvature case, assuming the boundary can be
isometrically embedded in the Euclidean space as a compact strictly convex
hypersurface, we show that the volume of a critical point is always no less
than the Euclidean volume bounded by the isometric embedding of the boundary,
and the two volumes are equal if and only if the critical point is isometric to
a standard Euclidean ball. We also derive a second variation formula and apply
it to show that, on Euclidean balls and ''small'' hyperbolic and spherical
balls in dimensions 3 to 5, the standard space form metrics are indeed saddle
points for the volume functional
Parental Attitudes and Their Influence on the Medical Management of Diabetic Adolescents
Competent professional assistance can meet the challenges of keeping parents and patients on a stable and sound emotional course as the diabetic adolescent grows up.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66551/2/10.1177_000992287000900814.pd
Observer dependence for the phonon content of the sound field living on the effective curved space-time background of a Bose-Einstein condensate
We demonstrate that the ambiguity of the particle content for quantum fields
in a generally curved space-time can be experimentally investigated in an
ultracold gas of atoms forming a Bose-Einstein condensate. We explicitly
evaluate the response of a suitable condensed matter detector, an ``Atomic
Quantum Dot,'' which can be tuned to measure time intervals associated to
different effective acoustic space-times. It is found that the detector
response related to laboratory, ``adiabatic,'' and de Sitter time intervals is
finite in time and nonstationary, vanishing, and thermal, respectively.Comment: 9 pages, 2 figures; references updated, as published in Physical
Review
On the asymptotic spectrum of the reduced volume in cosmological solutions of the Einstein equations
Say S is a compact three-manifold with non-positive Yamabe invariant. We
prove that in any long time constant mean curvature Einstein flow over S,
having bounded C^{\alpha} space-time curvature at the cosmological scale, the
reduced volume (-k/3)^{3}Vol(g(k)) (g(k) is the evolving spatial three-metric
and k the mean curvature) decays monotonically towards the volume value of the
geometrization in which the cosmologically normalized flow decays. In more
basic terms, under the given assumptions, there is volume collapse in the
regions where the injectivity radius collapses (i.e. tends to zero) in the long
time. We conjecture that under the curvature assumption above the Thurston
geometrization is the unique global attractor. We validate it in some special
cases.Comment: 25 pages, 2 figure
Chiral Topologically Massive Gravity and Extremal B-F Scalars
At a critical ``chiral'' coupling, topologically massive gravity with a
negative cosmological constant exhibits several unusual features, including the
emergence of a new logarithmic branch of solutions and a linearization
instability for certain boundary conditions. I show that at this coupling, the
linearized theory may be parametrized by a free scalar field at the
Breitenlohner-Freedman bound, and use this description to investigate these
features.Comment: 16 pages; v2: added references, typos correcte
Probing scalar particle and unparticle couplings in e+ e- -> t tbar with transversely polarized beams
In searching for indications of new physics scalar particle and unparticle
couplings in e^+ e^- \to t\bar t, we consider the role of transversely
polarized initial beams at e^+ e^- colliders. By using a general relativistic
spin density matrix formalism for describing the particles spin states, we find
analytical expressions for the squared amplitude of the process with t or \bar
t polarization measured, including the anomalous coupling contributions. Thanks
to the transversely polarized initial beams these contributions are first order
anomalous coupling corrections to the Standard Model (SM) contributions. We
present and analyse the main features of the SM and anomalous coupling
contributions. We show how differences between SM and anomalous coupling
contributions provide means to search for anomalous coupling manifestations at
future e^+ e^- linear colliders.Comment: 28 pages in LaTeX, including 7 encapsulated PostScript figures,
published versio
Effective nonlinear optical properties of composite media of graded spherical particles
We have developed a nonlinear differential effective dipole approximation
(NDEDA), in an attempt to investigate the effective linear and third-order
nonlinear susceptibility of composite media in which graded spherical
inclusions with weak nonlinearity are randomly embedded in a linear host
medium. Alternatively, based on a first-principles approach, we derived exactly
the linear local field inside the graded particles having power-law dielectric
gradation profiles. As a result, we obtain also the effective linear dielectric
constant and third-order nonlinear susceptibility. Excellent agreement between
the two methods is numerically demonstrated. As an application, we apply the
NDEDA to investigate the surface plasma resonant effect on the optical
absorption, optical nonlinearity enhancement, and figure of merit of
metal-dielectric composites. It is found that the presence of gradation in
metal particles yields a broad resonant band in the optical region, and further
enhances the figure of merit.Comment: 20 pages, 5 figure
Low frequency response of a collectively pinned vortex manifold
A low frequency dynamic response of a vortex manifold in type-II
superconductor can be associated with thermally activated tunneling of large
portions of the manifold between pairs of metastable states (two-level
systems). We suggest that statistical properties of these states can be
verified by using the same approach for the analysis of thermal fluctuations
the behaviour of which is well known. We find the form of the response for the
general case of vortex manifold with non-dispersive elastic moduli and for the
case of thin superconducting film for which the compressibility modulus is
always non-local.Comment: 8 pages, no figures, ReVTeX, the final version. Text strongly
modified, all the results unchange
Shape Space Methods for Quantum Cosmological Triangleland
With toy modelling of conceptual aspects of quantum cosmology and the problem
of time in quantum gravity in mind, I study the classical and quantum dynamics
of the pure-shape (i.e. scale-free) triangle formed by 3 particles in 2-d. I do
so by importing techniques to the triangle model from the corresponding 4
particles in 1-d model, using the fact that both have 2-spheres for shape
spaces, though the latter has a trivial realization whilst the former has a
more involved Hopf (or Dragt) type realization. I furthermore interpret the
ensuing Dragt-type coordinates as shape quantities: a measure of
anisoscelesness, the ellipticity of the base and apex's moments of inertia, and
a quantity proportional to the area of the triangle. I promote these quantities
at the quantum level to operators whose expectation and spread are then useful
in understanding the quantum states of the system. Additionally, I tessellate
the 2-sphere by its physical interpretation as the shape space of triangles,
and then use this as a back-cloth from which to read off the interpretation of
dynamical trajectories, potentials and wavefunctions. I include applications to
timeless approaches to the problem of time and to the role of uniform states in
quantum cosmological modelling.Comment: A shorter version, as per the first stage in the refereeing process,
and containing some new reference
Relativistic transition wavelenghts and probabilities for spectral lines of Ne II
Transition wavelengths and probabilities for several 2p4 3p - 2p4 3s and 2p4
3d - 2p4 3p lines in fuorine-like neon ion (NeII) have been calculated within
the multiconfiguration Dirac-Fock (MCDF) method with quantum electrodynamics
(QED) corrections. The results are compared with all existing experimental and
theoretical data
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