1,737 research outputs found
Numerical solutions of differential equations
Various numerical methods for solving differential equations were analyzed and refined in an effort to develop a method which was adaptable to a large class of problems. The prime capabilities of the method included accuracy, numerical stability, and economic use of computer time. In multistep processes the corrector was changed at each step
Predictor-corrector process in which the selection of an optimum corrector is made each step Quarterly technical report, oct. - Dec. 1965
Numerical solution of differential equations by predictor-corrector process which selects optimum corrector at each ste
The bang of a white hole in the early universe from a 6D vacuum state: Origin of astrophysical spectrum
Using a previously introduced model in which the expansion of the universe is
driven by a single scalar field subject to gravitational attraction induced by
a white hole during the expansion (from a 6D vacuum state), we study the origin
of squared inflaton fluctuations spectrum on astrophysical scales.Comment: Final version to be published in Eur. Phys. J.
Extra symmetry in the field equations in 5D with spatial spherical symmetry
We point out that the field equations in 5D, with spatial spherical symmetry,
possess an extra symmetry that leaves them invariant. This symmetry corresponds
to certain simultaneous interchange of coordinates and metric coefficients. As
a consequence a single solution in 5D can generate very different scenarios in
4D, ranging from static configurations to cosmological situations. A new
perspective emanates from our work. Namely, that different astrophysical and
cosmological scenarios in 4D might correspond to the same physics in 5D. We
present explicit examples that illustrate this point of view.Comment: Typos corrected. Accepted for publication in Classical and Quantum
Gravit
The timing and location of dust formation in the remnant of SN 1987A
The discovery with the {\it Herschel Space Observatory} of bright far
infrared and submm emission from the ejecta of the core collapse supernova
SN\,1987A has been interpreted as indicating the presence of some
0.4--0.7\,M of dust. We have constructed radiative transfer models of
the ejecta to fit optical to far-infrared observations from the literature at
epochs between 615 days and 24 years after the explosion, to determine when and
where this unexpectedly large amount of dust formed.
We find that the observations by day 1153 are consistent with the presence of
310M of dust. Although this is a larger amount than has
previously been considered possible at this epoch, it is still very small
compared to the amount present in the remnant after 24 years, and significantly
higher dust masses at the earlier epochs are firmly ruled out by the
observations, indicating that the majority of the dust must have formed at very
late times. By 8515-9200 days after the explosion, 0.6--0.8\,M of dust
is present, and dust grains with radii greater than 2\,m are required to
obtain a fit to the observed SED. This suggests that the dust mass increase at
late times was caused by accretion onto and coagulation of the dust grains
formed at earlier epochs.
These findings provide further confirmation that core collapse supernovae can
create large quantities of dust, and indicate that the reason for small dust
masses being estimated in many cases is that the vast majority of the dust
forms long after most supernovae have been detectable at mid-infrared
wavelengths.Comment: 13 pages, 16 figures. Accepted for publication in MNRA
Wave Mechanics and General Relativity: A Rapprochement
Using exact solutions, we show that it is in principle possible to regard
waves and particles as representations of the same underlying geometry, thereby
resolving the problem of wave-particle duality
Static Ricci-flat 5-manifolds admitting the 2-sphere
We examine, in a purely geometrical way, static Ricci-flat 5-manifolds
admitting the 2-sphere and an additional hypersurface-orthogonal Killing
vector. These are widely studied in the literature, from different physical
approaches, and known variously as the Kramer - Gross - Perry - Davidson - Owen
solutions. The 2-fold infinity of cases that result are studied by way of new
coordinates (which are in most cases global) and the cases likely to be of
interest in any physical approach are distinguished on the basis of the
nakedness and geometrical mass of their associated singularities. It is argued
that the entire class of solutions has to be considered unstable about the
exceptional solutions: the black string and soliton cases. Any physical theory
which admits the non-exceptional solutions as the external vacuua of a
collapsing object has to accept the possibility of collapse to zero volume
leaving behind the weakest possible, albeit naked, geometrical singularities at
the origin.Finally, it is pointed out that these types of solutions generalize,
in a straightforward way, to higher dimensions.Comment: Generalize, in a straightforward way, to higher dimension
Observational Limits on the Early-time Dust Mass in SN 1987A
In recent years, dust masses of a few tenths of a solar mass have been found in the expanding ejecta of a number of core-collapse supernovae. How dust forms in such quantities remains poorly understood; theories of dust formation predict lower total masses and much faster formation rates than observations imply. One suggestion to reconcile observations and theory was made by Dwek et al., who proposed that the dust forms very rapidly, and because of its optical depth, is not initially observationally detectable, only being gradually revealed as the ejecta expand. Observational dust masses at early times would then only be lower limits. Using a large grid of radiative transfer models covering dust masses from 10−4 to 1 M⊙ to calculate both the spectral energy distribution and the emission line profiles from clumpy dust shells, we show that this cannot be the case. Some clump distributions allow dust masses of ∼0.01 M⊙ to be concealed in clumps and still predict an SED consistent with the observations. However, these geometries predict emission line profiles that are inconsistent with the observations. Similarly, clump geometries that reproduce the observed emission line profiles with dust masses >0.01 M⊙ do not reproduce the SED. However, models with ∼10−3 M⊙ of amorphous carbon can reproduce both the SED and the emission line profiles. We conclude that no large masses of dust can be hidden from view in the ejecta of SN 1987A at early epochs, and that the majority of dust must thus have formed at epochs >1000 days
MHD Memes
The celebration of Allan Kaufman's 80th birthday was an occasion to reflect
on a career that has stimulated the mutual exchange of ideas (or memes in the
terminology of Richard Dawkins) between many researchers. This paper will
revisit a meme Allan encountered in his early career in magnetohydrodynamics,
the continuation of a magnetohydrodynamic mode through a singularity, and will
also mention other problems where Allan's work has had a powerful
cross-fertilizing effect in plasma physics and other areas of physics and
mathematics.Comment: Submitted for publication in IOP Journal of Physics: Conference
Series for publication in "Plasma Theory, Wave Kinetics, and Nonlinear
Dynamics", Proceedings of KaufmanFest, 5-7 October 2007, University of
California, Berkeley, US
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