Structure and dynamics of topological defects in a glassy liquid on a negatively curved manifold

We study the low-temperature regime of an atomic liquid on the hyperbolic plane by means of molecular dynamics simulation and we compare the results to a continuum theory of defects in a negatively curved hexagonal background. In agreement with the theory and previous results on positively curved (spherical) surfaces, we find that the atomic configurations consist of isolated defect structures, dubbed "grain boundary scars", that form around an irreducible density of curvature-induced disclinations in an otherwise hexagonal background. We investigate the structure and the dynamics of these grain boundary scars

Quantum Holonomies in (2+1)-Dimensional Gravity

We describe an approach to the quantization of (2+1)--dimensional gravity with topology R x T^2 and negative cosmological constant, which uses two quantum holonomy matrices satisfying a q--commutation relation. Solutions of diagonal and upper--triangular form are constructed, which in the latter case exhibit additional, non--trivial internal relations for each holonomy matrix. This leads to the notion of quantum matrix pairs. These are pairs of matrices with non-commuting entries, which have the same pattern of internal relations, q-commute with each other under matrix multiplication, and are such that products of powers of the matrices obey the same pattern of internal relations as the original pair. This has implications for the classical moduli space, described by ordered pairs of commuting SL(2,R) matrices modulo simultaneous conjugation by SL(2,R) matrices.Comment: 5 pages, to appear in the proceedings of 10th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories (MG X MMIII), Rio de Janeiro, Brazil, 20-26 Jul 200

Discs and Planetary Formation

The formation, structure and evolution of protoplanetary discs is considered. The formation of giant planets within the environment of these models is also discussed.Comment: 22 pages, LaTeX (including 6 figures), uses paspconf.sty, epsf.sty and rotate.sty, to be published in Proceedings of the EC Summer School on 'Astrophysical Discs', eds J. A. Sellwood and J. Goodman, ASP Conf. Serie

Tidally-induced warps in protostellar discs

We review results on the dynamics of warped gaseous discs. We consider tidal perturbation of a Keplerian disc by a companion star orbiting in a plane inclined to the disc. The perturbation induces the precession of the disc, and thus of any jet it could drive. In some conditions the precession rate is uniform, and as a result the disc settles into a warp mode. The tidal torque also leads to the truncation of the disc, to the evolution of the inclination angle (not necessarily towards alignment of the disc and orbital planes) and to a transport of angular momentum in the disc. We note that the spectral energy distribution of such a warped disc is different from that of a flat disc. We conclude by listing observational effects of warps in protostellar discs.Comment: 10 pages, LaTeX (including 1 figure), uses paspconf.sty and epsf.sty, to be published in Proceedings of the EC Summer School on 'Astrophysical Discs', eds J. A. Sellwood and J. Goodman, ASP Conf. Serie

Terrestrial planet formation in low eccentricity warm-Jupiter systems

We examine the effect of giant planet migration on the formation of inner terrestrial planet systems. We consider situations in which the giant planet halts migration at semi-major axes in the range 0.13 - 1.7 AU due to gas disk dispersal. An N-body code is employed that is linked to a viscous gas disk algorithm capable of simulating: gas loss via accretion onto the central star and photoevaporation; gap formation by the giant planet; type II migration of the giant; optional type I migration of protoplanets; gas drag on planetesimals. We find that most of the inner system planetary building blocks survive the passage of the giant planet, either by being shepherded inward or scattered into exterior orbits. Systems of one or more hot-Earths are predicted to form and remain interior to the giant planet, especially if type II migration has been limited, or where type I migration has affected protoplanetary dynamics. Habitable planets in low eccentricity warm-Jupiter systems appear possible if the giant planet makes a limited incursion into the outer regions of the habitable zone (HZ), or traverses its entire width and ceases migrating at a radial distance of less than half that of the HZ's inner edge. We conclude that Type II migration does not prevent terrestrial planet formation.Comment: Accepted for publication in A&A; 18 pages, 12 figures, 2 table

Study to investigate the effects of ionizing radiation on transistor surfaces Third quarterly report, period ending, 31 Mar. 1966

Ionizing radiation effects on transistor surface