496 research outputs found
Equilibrium Configurations of Homogeneous Fluids in General Relativity
By means of a highly accurate, multi-domain, pseudo-spectral method, we
investigate the solution space of uniformly rotating, homogeneous and
axisymmetric relativistic fluid bodies. It turns out that this space can be
divided up into classes of solutions. In this paper, we present two new classes
including relativistic core-ring and two-ring solutions. Combining our
knowledge of the first four classes with post-Newtonian results and the
Newtonian portion of the first ten classes, we present the qualitative
behaviour of the entire relativistic solution space. The Newtonian disc limit
can only be reached by going through infinitely many of the aforementioned
classes. Only once this limiting process has been consummated, can one proceed
again into the relativistic regime and arrive at the analytically known
relativistic disc of dust.Comment: 8 pages, colour figures, v3: minor additions including one reference,
accepted by MNRA
Differentially rotating disks of dust
We present a three-parameter family of solutions to the stationary
axisymmetric Einstein equations that describe differentially rotating disks of
dust. They have been constructed by generalizing the Neugebauer-Meinel solution
of the problem of a rigidly rotating disk of dust. The solutions correspond to
disks with angular velocities depending monotonically on the radial coordinate;
both decreasing and increasing behaviour is exhibited. In general, the
solutions are related mathematically to Jacobi's inversion problem and can be
expressed in terms of Riemann theta functions. A particularly interesting
two-parameter subfamily represents Baecklund transformations to appropriate
seed solutions of the Weyl class.Comment: 14 pages, 3 figures. To appear in "General Relativity and
Gravitation". Second version with minor correction
On Primordial Magnetic Fields of Electroweak Origin
We consider Vachaspati's primordial magnetic field which is generated at the
electroweak phase transition. Assuming that either the gradients of the Higgs
field or, alternatively, the magnetic field itself are stochastic variables
with a normal distribution, we find that the resulting magnetic field has an
{\em rms} value in the present-day universe which is fully consistent with what
is required for the galactic dynamo mechanism.Comment: 11 pages, Latex, no figures. Preprint NBI-HE-93-3
Nb3Sn wire shape and cross sectional area inhomogeneity in Rutherford cables
During Rutherford cable production the wires are plastically deformed and
their initially round shape is distorted. Using X-ray absorption tomography we
have determined the 3D shape of an unreacted Nb3Sn 11 T dipole Rutherford
cable, and of a reacted and impregnated Nb3Sn cable double stack.
State-of-the-art image processing was applied to correct for tomographic
artefacts caused by the large cable aspect ratio, for the segmentation of the
individual wires and subelement bundles inside the wires, and for the
calculation of the wire cross sectional area and shape variations. The 11 T
dipole cable cross section oscillates by 2% with a frequency of 1.24 mm (1/80
of the transposition pitch length of the 40 wire cable). A comparatively
stronger cross sectional area variation is observed in the individual wires at
the thin edge of the keystoned cable where the wire aspect ratio is largest.Comment: 6 pages, 11 figures, presented at EUCAS 201
Dirichlet Boundary Value Problems of the Ernst Equation
We demonstrate how the solution to an exterior Dirichlet boundary value
problem of the axisymmetric, stationary Einstein equations can be found in
terms of generalized solutions of the Backlund type. The proof that this
generalization procedure is valid is given, which also proves conjectures about
earlier representations of the gravitational field corresponding to rotating
disks of dust in terms of Backlund type solutions.Comment: 22 pages, to appear in Phys. Rev. D, Correction of a misprint in
equation (4
Efficient Set Sharing Using ZBDDs
Set sharing is an abstract domain in which each concrete object is represented by the set of local variables from which it might be reachable. It is a useful abstraction to detect parallelism opportunities, since it contains definite information about which variables do not share in memory, i.e., about when the memory regions reachable from those variables are disjoint. Set sharing is a more precise alternative to pair sharing, in which each domain element is a set of all pairs of local variables from which a common object may be reachable. However, the exponential complexity of some set sharing operations has limited its wider application. This work introduces an efficient implementation of the set sharing domain using Zero-suppressed Binary Decision Diagrams (ZBDDs). Because ZBDDs were designed to represent sets of combinations (i.e., sets of sets), they naturally represent elements of the set sharing domain. We show how to synthesize the operations needed in the set sharing transfer functions from basic ZBDD operations. For some of the operations, we devise custom ZBDD algorithms that perform better in practice. We also compare our implementation of the abstract domain with an efficient, compact, bit set-based alternative, and show that the ZBDD version scales better in terms of both memory usage and running time
On the black hole limit of rotating fluid bodies in equilibrium
Recently, it was shown that the extreme Kerr black hole is the only candidate
for a (Kerr) black hole limit of stationary and axisymmetric, uniformly
rotating perfect fluid bodies with a zero temperature equation of state. In
this paper, necessary and sufficient conditions for reaching the black hole
limit are presented.Comment: 8 pages, v2: one footnote and one reference added, accepted for
publication in CQ
Dynamics of charged fluids and 1/L perturbation expansions
Some features of the calculation of fluid dynamo systems in
magnetohydrodynamics are studied. In the coupled set of the ordinary linear
differential equations for the spherically symmetric dynamos, the
problem represented by the presence of the mixed (Robin) boundary conditions is
addressed and a new treatment for it is proposed. The perturbation formalism of
large expansions is shown applicable and its main technical steps are
outlined.Comment: 16 p
The chromosphere: gateway to the corona, or the purgatory of solar physics?
I argue that one should attempt to understand the solar chromosphere not only
for its own sake, but also if one is interested in the physics of: the corona;
astrophysical dynamos; space weather; partially ionized plasmas; heliospheric
UV radiation; the transition region. I outline curious observations which I
personally find puzzling and deserving of attention.Comment: To appear in the proceedings of the 25th NSO Workshop "Chromospheric
Structure and Dynamics. From Old Wisdom to New Insights", Memorie della
Societa' Astronomica Italiana, Eds. Tritschler et a
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