Equivariant Dimensional Reduction and Quiver Gauge Theories

We review recent applications of equivariant dimensional reduction techniques to the construction of Yang-Mills-Higgs-Dirac theories with dynamical mass generation and exactly massless chiral fermions.Comment: 10 pages; Based on invited talk given by the first author at the 2nd School on "Quantum Gravity and Quantum Geometry" session of the 9th Hellenic School on Elementary Particle Physics and Gravity, Corfu, Greece, September 13-20 2009. To be published in General Relativity and Gravitatio

Implications of Particle Acceleration in Active Galactic Nuclei for Cosmic Rays and High Energy Neutrino Astronomy

We consider the production of high energy neutrinos and cosmic rays in radio-quiet active galactic nuclei (AGN) or in the central regions of radio-loud AGN. We use a model in which acceleration of protons takes place at a shock in an accretion flow onto a supermassive black hole, and follow the cascade that results from interactions of the accelerated protons in the AGN environment. We use our results to estimate the diffuse high energy neutrino intensity and cosmic ray intensity due to AGN. We discuss our results in the context of high energy neutrino telescopes under construction, and measurements of the cosmic ray composition in the region of the ``knee'' in the energy spectrum at $\sim 10^7$ GeV.Comment: 37 pages of compressed and uuencoded postscript; hardcopy available on request; to be published in Astroparticle Physics; ADP-AT-94-

Adaptive finite element analysis based on p-convergence

The results of numerical experiments are presented in which a posteriori estimators of error in strain energy were examined on the basis of a typical problem in linear elastic fracture mechanics. Two estimators were found to give close upper and lower bounds for the strain energy error. The potential significance of this is that the same estimators may provide a suitable basis for adaptive redistribution of the degrees of freedom in finite element models

Attractive Bose-Einstein Condensates in three dimensions under rotation: Revisiting the problem of stability of the ground state in harmonic traps

We study harmonically trapped ultracold Bose gases with attractive interparticle interactions under external rotation in three spatial dimensions and determine the critical value of the attraction strength where the gas collapses as a function of the rotation frequency. To this end we examine the stationary state in the corotating frame with a many-body approach as well as within the Gross-Pitaevskii theory of systems in traps with different anisotropies. In contrast to recently reported results [N. A. Jamaludin, N. G. Parker, and A. M. Martin, Phys. Rev. A \textbf{77}, 051603(R) (2008)], we find that the collapse is not postponed in the presence of rotation. Unlike repulsive gases, the properties of the attractive system remain practically unchanged under rotation in isotropic and slightly anisotropic traps.Comment: 15 pages, 1 figure, 1 tabl