329 research outputs found
Kinematic dynamo action in a sphere. II. Symmetry selection
The magnetic fields of the planets are generated by dynamo action in their electrically conducting interiors. The Earth possesses an axial dipole magnetic field but other planets have other configurations: Uranus has an equatorial dipole for example. In a previous paper we explored a two-parameter class of flows, comprising convection rolls, differential rotation (D) and meridional circulation (M), for dynamo generation of steady fields with axial dipole symmetry by solving the kinematic dynamo equations. In this paper we explore generation of the remaining three allowed symmetries: axial quadrupole, equatorial dipole and equatorial quadrupole. The results have implications for the fully nonlinear dynamical dynamo because the flows qualitatively resemble those driven by thermal convection in a rotating sphere, and the symmetries define separable solutions of the nonlinear equations. Axial dipole solutions are generally preferred (they have lower critical magnetic Reynolds number) for D > 0, corresponding to westward surface drift. Axial quadrupoles are preferred for D 0), axial dipoles are preferred. The equatorial dipole must change sign between east and west hemispheres, and is not favoured by any elongation of the flux in longitude (caused by D) or polar concentrations (caused by M): they are preferred for small D and M. Polar and equatorial concentrations can be related to dynamo waves and the sign of Parker's dynamo number. For the three-dimensional flow considered here, the sign of the dynamo number is related to the sense of spiralling of the convection rolls, which must be the same as the surface drif
Decay of flux vacua to nothing
We construct instanton solutions describing the decay of flux
compactifications of a gauge theory by generalizing the Kaluza-Klein
bubble of nothing. The surface of the bubble is described by a smooth
magnetically charged solitonic brane whose asymptotic flux is precisely that
responsible for stabilizing the 4d compactification. We describe several
instances of bubble geometries for the various vacua occurring in a
Einstein-Maxwell theory namely, AdS_4 x S^2, R^{1,3} x S^2, and dS_4 x S^2.
Unlike conventional solutions, the bubbles of nothing introduced here occur
where a {\em two}-sphere compactification manifold homogeneously degenerates.Comment: 31 pages, 15 figure
Can the Arrow of Time be understood from Quantum Cosmology?
I address the question whether the origin of the observed arrow of time can
be derived from quantum cosmology. After a general discussion of entropy in
cosmology and some numerical estimates, I give a brief introduction into
quantum geometrodynamics and argue that this may provide a sufficient framework
for studying this question. I then show that a natural boundary condition of
low initial entropy can be imposed on the universal wave function. The arrow of
time is then correlated with the size of the Universe and emerges from an
increasing amount of decoherence due to entanglement with unobserved degrees of
freedom. Remarks are also made concerning the arrow of time in multiverse
pictures and scenarios motivated by dark energy.Comment: 14 pages, to appear in "The Arrow of Time", ed. by L.
Mersini-Houghton and R. Vaa
Power-Law Inflation from the Rolling Tachyon
Modeling the potential by an inverse square law in terms of the tachyon field
() we find exact solution for spatially flat isotropic
universe.We show that for the model undergoes power-law
inflation. A way to construct other exact solutions is specified and
exemplified.Comment: References added. Matches the version in print. To appear in PR
Epidemiologic Study of Dental Caries Experience and Between-Meal Eating Patterns
The relationship between dental caries and between-meal snacks was investigated in a study of 1,486 high school students. The participants completed a questionnaire on between-meal habits and then were given dental examinations. The lack of differences in dental caries between racial and geographic groups was not related to the frequency of sucrose-containing, between-meal snacks.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66591/2/10.1177_00220345730520022501.pd
Reply Comment: Comparison of Approaches to Classical Signature Change
We contrast the two approaches to ``classical" signature change used by
Hayward with the one used by us (Hellaby and Dray). There is (as yet) no
rigorous derivation of appropriate distributional field equations. Hayward's
distributional approach is based on a postulated modified form of the field
equations. We make an alternative postulate. We point out an important
difference between two possible philosophies of signature change --- ours is
strictly classical, while Hayward's Lagrangian approach adopts what amounts to
an imaginary proper ``time" on one side of the signature change, as is
explicitly done in quantum cosmology. We also explain why we chose to use the
Darmois-Israel type junction conditions, rather than the Lichnerowicz type
junction conditions favoured by Hayward. We show that the difference in results
is entirely explained by the difference in philosophy (imaginary versus real
Euclidean ``time"), and not by the difference in approach to junction
conditions (Lichnerowicz with specific coordinates versus Darmois with general
coordinates).Comment: 10 pages, latex, no figures. Replying to - "Comment on `Failure of
Standard Conservation Laws at a Classical Change of Signature'", S.A.
Hayward, Phys. Rev. D52, 7331-7332 (1995) (gr-qc/9606045
Why Does Inflation Start at the Top of the Hill?
We show why the universe started in an unstable de Sitter state. The quantum
origin of our universe implies one must take a `top down' approach to the
problem of initial conditions in cosmology, in which the histories that
contribute to the path integral, depend on the observable being measured. Using
the no boundary proposal to specify the class of histories, we study the
quantum cosmological origin of an inflationary universe in theories like trace
anomaly driven inflation in which the effective potential has a local maximum.
We find that an expanding universe is most likely to emerge in an unstable de
Sitter state, by semiclassical tunneling via a Hawking-Moss instanton. Since
the top down view is forced upon us by the quantum nature of the universe, we
argue that the approach developed here should still apply when the framework of
quantum cosmology will be based on M-Theory.Comment: 21 pages, 1 figur
Failure of Standard Conservation Laws at a Classical Change of Signature
The Divergence Theorem as usually stated cannot be applied across a change of
signature unless it is re-expressed to allow for a finite source term on the
signature change surface. Consequently all conservation laws must also be
`modified', and therefore insistence on conservation of matter across such a
surface cannot be physically justified. The Darmois junction conditions
normally ensure conservation of matter via Israel's identities for the jump in
the energy-momentum density, but not when the signature changes. Modified
identities are derived for this jump when a signature change occurs, and the
resulting surface effects in the conservation laws are calculated. In general,
physical vector fields experience a jump in at least one component, and a
source term may therefore appear in the corresponding conservation law. Thus
current is also not conserved. These surface effects are a consequence of the
change in the character of physical law. The only way to recover standard
conservation laws is to impose restrictions that no realistic cosmological
model can satisfy.Comment: 15pp, figures available on request from Charles Hellaby at
[email protected]
On Darboux-Treibich-Verdier potentials
It is shown that the four-parameter family of elliptic functions
introduced
by Darboux and rediscovered a hundred years later by Treibich and Verdier, is
the most general meromorphic family containing infinitely many finite-gap
potentials.Comment: 8 page
New hairy black holes with negative cosmological constant
Black hole solutions with nonspherical event horizon topology are shown to
exist in an Einstein-Yang-Mills theory with negative cosmological constant. The
main characteristics of the solutions are presented and differences with
respect to the spherically symmetric case are studied. The stability of these
configurations is also addressed.Comment: 14 pages, 6 Encapsulated PostScript figures, references adde
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