9,444 research outputs found
Following Knots Down Their Energy Gradients
This paper details a series of experiments in searching for minimal energy
configurations for knots and links using the computer program KnotPlot. The
most interesting phenomena found in these experiments is the dependence of the
trajectories of energy descent upon the initial geometric conditions of the
knotted embedding.Comment: 18 pages, 13 figures, MsWord documen
Formation and evolution of cosmic D-strings
We study the formation of D and F-cosmic strings in D-brane annihilation
after brane inflation. We show that D-string formation by quantum de Sitter
fluctuations is severely suppressed, due to suppression of RR field
fluctuations in compact dimensions. We discuss the resonant mechanism of
production of D and F-strings, which are formed as magnetic and electric flux
tubes of the two orthogonal gauge fields living on the world-volume of the
unstable brane. We outline the subsequent cosmological evolution of the D-F
string network. We also compare the nature of these strings with the ordinary
cosmic strings and point out some differences and similarities.Comment: Added discussion and reference
HST optical spectral index map of the jet of 3C 273
We present HST images at 622 nm and 300 nm of the jet in 3C273 and determine
the run of the optical spectral index at 0.2" along the jet. The smoothness of
spectral index changes shows that the physical conditions are varying smoothly
across the jet. There is no correlation between the optical flux and spectral
index, as would be expected for relativistic electrons suffering strong cooling
due to synchrotron emission. We find no evidence for localized acceleration or
loss sites. This suggests that the spectral shape is not changing much
throughout the jet. We show that relativistic beaming and/or sub-equipartition
magnetic fields cannot remove the discrepancy between light-travel time along
the jet and the lifetime of electrons emitting optical synchrotron radiation.
We consider this further evidence in favour of a distributed electron
acceleration process.Comment: Accepted for publication by Astronomy and Astrophysics (13 pages, 8
figures
Starbursts in multiple galaxy mergers
We numerically investigate stellar and gaseous dynamical evolution of mergers
between five identical late-type disk galaxies with the special emphasis on
star formation history and chemical evolution of multiple galaxy mergers. We
found that multiple encounter and merging can trigger repetitive massive
starbursts (typically 100 ) owing to the
strong tidal disturbance and the resultant gaseous dissipation during merging.
The magnitude of the starburst is found to depend on initial virial ratio
(i.e., the ratio of total kinematical energy to total potential energy) such
that the maximum star formation rate is larger for the merger with smaller
virial ratio. Furthermore we found that the time interval between the epochs of
the triggered starbursts is longer for the merger with the larger virial ratio.
The remnant of a multiple galaxy merger with massive starbursts is found to
have metal-poor gaseous halo that is formed by tidal stripping during the
merging. We accordingly suggest that metal-poor gaseous halo in a field
elliptical galaxy is a fossil record of the past multiple merging events for
the galaxy.Comment: 23 pages 16 figures,2000,ApJ,545 in press. For all ps figures, see
http://newt.phys.unsw.edu.au/~bekki/res.dir/paper.dir/mul.dir/fig.tar.g
Gravitational hydrodynamics of large scale structure formation
The gravitational hydrodynamics of the primordial plasma with neutrino hot
dark matter is considered as a challenge to the bottom-up cold dark matter
paradigm. Viscosity and turbulence induce a top-down fragmentation scenario
before and at decoupling. The first step is the creation of voids in the
plasma, which expand to 37 Mpc on the average now. The remaining matter clumps
turn into galaxy clusters. Turbulence produced at expanding void boundaries
causes a linear morphology of 3 kpc fragmenting protogalaxies along vortex
lines. At decoupling galaxies and proto-globular star clusters arise; the
latter constitute the galactic dark matter halos and consist themselves of
earth-mass H-He planets. Frozen planets are observed in microlensing and
white-dwarf-heated ones in planetary nebulae. The approach also explains the
Tully-Fisher and Faber-Jackson relations, and cosmic microwave temperature
fluctuations of micro-Kelvins.Comment: 6 pages, no figure
Knot Tightening By Constrained Gradient Descent
We present new computations of approximately length-minimizing polygons with
fixed thickness. These curves model the centerlines of "tight" knotted tubes
with minimal length and fixed circular cross-section. Our curves approximately
minimize the ropelength (or quotient of length and thickness) for polygons in
their knot types. While previous authors have minimized ropelength for polygons
using simulated annealing, the new idea in our code is to minimize length over
the set of polygons of thickness at least one using a version of constrained
gradient descent.
We rewrite the problem in terms of minimizing the length of the polygon
subject to an infinite family of differentiable constraint functions. We prove
that the polyhedral cone of variations of a polygon of thickness one which do
not decrease thickness to first order is finitely generated, and give an
explicit set of generators. Using this cone we give a first-order minimization
procedure and a Karush-Kuhn-Tucker criterion for polygonal ropelength
criticality.
Our main numerical contribution is a set of 379 almost-critical prime knots
and links, covering all prime knots with no more than 10 crossings and all
prime links with no more than 9 crossings. For links, these are the first
published ropelength figures, and for knots they improve on existing figures.
We give new maps of the self-contacts of these knots and links, and discover
some highly symmetric tight knots with particularly simple looking self-contact
maps.Comment: 45 pages, 16 figures, includes table of data with upper bounds on
ropelength for all prime knots with no more than 10 crossings and all prime
links with no more than 9 crossing
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