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 $\sim$ 100 $M_{\odot}$ ${\rm yr}^{-1}$) 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