581 research outputs found
Toric anti-self-dual 4-manifolds via complex geometry
Using the twistor correspondence, this article gives a one-to-one
correspondence between germs of toric anti-self-dual conformal classes and
certain holomorphic data determined by the induced action on twistor space.
Recovering the metric from the holomorphic data leads to the classical problem
of prescribing the Cech coboundary of 0-cochains on an elliptic curve covered
by two annuli. The classes admitting Kahler representatives are described; each
such class contains a circle of Kahler metrics. This gives new local examples
of scalar-flat Kahler surfaces and generalises work of Joyce who considered the
case where the distribution orthogonal to the torus action is integrable.Comment: 25 pages, 2 figures, v2 corrected some misprints, v3 corrected more
misprints, published version (minus one typo
A lower limit on the dark particle mass from dSphs
We use dwarf spheroidal galaxies as a tool to attempt to put precise lower
limits on the mass of the dark matter particle, assuming it is a sterile
neutrino. We begin by making cored dark halo fits to the line of sight velocity
dispersions as a function of projected radius (taken from Walker et al. 2007)
for six of the Milky Way's dwarf spheroidal galaxies. We test Osipkov-Merritt
velocity anisotropy profiles, but find that no benefit is gained over constant
velocity anisotropy. In contrast to previous attempts, we do not assume any
relation between the stellar velocity dispersions and the dark matter ones, but
instead we solve directly for the sterile neutrino velocity dispersion at all
radii by using the equation of state for a partially degenerate neutrino gas
(which ensures hydrostatic equilibrium of the sterile neutrino halo). This
yields a 1:1 relation between the sterile neutrino density and velocity
dispersion, and therefore gives us an accurate estimate of the Tremaine-Gunn
limit at all radii. By varying the sterile neutrino particle mass, we locate
the minimum mass for all six dwarf spheroidals such that the Tremaine-Gunn
limit is not exceeded at any radius (in particular at the centre). We find
sizeable differences between the ranges of feasible sterile neutrino particle
mass for each dwarf, but interestingly there exists a small range 270-280eV
which is consistent with all dSphs at the 1- level.Comment: 13 pages, 2 figures, 1 tabl
Minimal cubic cones via Clifford algebras
We construct two infinite families of algebraic minimal cones in . The
first family consists of minimal cubics given explicitly in terms of the
Clifford systems. We show that the classes of congruent minimal cubics are in
one to one correspondence with those of geometrically equivalent Clifford
systems. As a byproduct, we prove that for any , , there is
at least one minimal cone in given by an irreducible homogeneous cubic
polynomial. The second family consists of minimal cones in , ,
defined by an irreducible homogeneous polynomial of degree . These examples
provide particular answers to the questions on algebraic minimal cones posed by
Wu-Yi Hsiang in the 1960's.Comment: Final version, corrects typos in Table
(In)finite extent of stationary perfect fluids in Newtonian theory
For stationary, barotropic fluids in Newtonian gravity we give simple
criteria on the equation of state and the "law of motion" which guarantee
finite or infinite extent of the fluid region (providing a priori estimates for
the corresponding stationary Newton-Euler system). Under more restrictive
conditions, we can also exclude the presence of "hollow" configurations. Our
main result, which does not assume axial symmetry, uses the virial theorem as
the key ingredient and generalises a known result in the static case. In the
axially symmetric case stronger results are obtained and examples are
discussed.Comment: Corrections according to the version accepted by Ann. Henri Poincar
Do quasi-regular structures really exist in the solar photosphere? I. Observational evidence
Two series of solar-granulation images -- the La Palma series of 5 June 1993
and the SOHO MDI series of 17--18 January 1997 -- are analysed both
qualitatively and quantitatively. New evidence is presented for the existence
of long-lived, quasi-regular structures (first reported by Getling and Brandt
(2002)), which no longer appear unusual in images averaged over 1--2-h time
intervals. Such structures appear as families of light and dark concentric
rings or families of light and dark parallel strips (``ridges'' and
``trenches'' in the brightness distributions). In some cases, rings are
combined with radial ``spokes'' and can thus form ``web'' patterns. The
characteristic width of a ridge or trench is somewhat larger than the typical
size of granules. Running-average movies constructed from the series of images
are used to seek such structures. An algorithm is developed to obtain, for
automatically selected centres, the radial distributions of the azimuthally
averaged intensity, which highlight the concentric-ring patterns. We also
present a time-averaged granulation image processed with a software package
intended for the detection of geological structures in aerospace images. A
technique of running-average-based correlations between the brightness
variations at various points of the granular field is developed and indications
are found for a dynamical link between the emergence and sinking of hot and
cool parcels of the solar plasma. In particular, such a correlation analysis
confirms our suggestion that granules -- overheated blobs -- may repeatedly
emerge on the solar surface. Based on our study, the critical remarks by Rast
(2002) on the original paper by Getling and Brandt (2002) can be dismissed.Comment: 21 page, 8 figures; accepted by "Solar Physics
Entanglement without Dissipation: A Touchstone for an exact Comparison of Entanglement Measures
Entanglement, which is an essential characteristic of quantum mechanics, is
the key element in potential practical quantum information and quantum
communication systems. However, there are many open and fundamental questions
(relating to entanglement measures, sudden death, etc.) that require a deeper
understanding. Thus, we are motivated to investigate a simple but non-trivial
correlated two-body continuous variable system in the absence of a heat bath,
which facilitates an \underline{exact} measure of the entanglement at all
times. In particular, we find that the results obtained from all well-known
existing entanglement measures agree with each other but that, in practice,
some are more straightforward to use than others
Uniqueness Theorem for Generalized Maxwell Electric and Magnetic Black Holes in Higher Dimensions
Based on the conformal energy theorem we prove the uniqueness theorem for
static higher dimensional electrically and magnetically charged black holes
being the solution of Einstein (n-2)-gauge forms equations of motion. Black
hole spacetime contains an asymptotically flat spacelike hypersurface with
compact interior and non-degenerate components of the event horizon.Comment: 7 pages, RevTex, to be published in Phys.Rev.D1
Recoil correction to the ground state energy of hydrogenlike atoms
The recoil correction to the ground state energy of hydrogenlike atoms is
calculated to all orders in \alpha Z in the range Z = 1-110. The nuclear size
corrections to the recoil effect are partially taken into account. In the case
of hydrogen, the relativistic recoil correction beyond the Salpeter
contribution and the nonrelativistic nuclear size correction to the recoil
effect, amounts to -7.2(2) kHz. The total recoil correction to the ground state
energy in hydrogenlike uranium (^{238}U^{91+}) constitutes 0.46 eV.Comment: 16 pages, 1 figure (eps), Latex, submitted to Phys.Rev.
Lyapunov exponents for products of complex Gaussian random matrices
The exact value of the Lyapunov exponents for the random matrix product with each , where
is a fixed positive definite matrix and a complex Gaussian matrix with entries standard complex normals, are
calculated. Also obtained is an exact expression for the sum of the Lyapunov
exponents in both the complex and real cases, and the Lyapunov exponents for
diffusing complex matrices.Comment: 15 page
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