Quantum fields, dark matter and non-standard Wigner classes

The Elko field of Ahluwalia and Grumiller is a quantum field for massive spin-1/2 particles. It has been suggested as a candidate for dark matter. We discuss our attempts to interpret the Elko field as a quantum field in the sense of Weinberg. Our work suggests that one should investigate quantum fields based on representations of the full Poincar\'e group which belong to one of the non-standard Wigner classes.Comment: 6 pages. Submitted to proceedings of Dark2009, Christchurch, New Zealand, January 200

Complete Reducibility and Commuting Subgroups

Let G be a reductive linear algebraic group over an algebraically closed field of characteristic p. We study J.-P. Serre's notion of G-complete reducibility for subgroups of G. In particular, for a subgroup H and a normal subgroup N of H, we look at the relationship between G-complete reducibility of N and of H, and show that these properties are equivalent if H/N is linearly reductive, generalizing a result of Serre. We also study the case when H = MN with M a G-completely reducible subgroup of G which normalizes N. We show that if G is connected, N and M are connected commuting G-completely reducible subgroups of G, and p is good for G, then H = MN is also G-completely reducible.Comment: 21 pages; to appear in J. Reine Angew. Math. final for

Layered Fabrication of Branched Networks Using Lindenmayer Systems

A current challenge impeding the growth of bone tissue engineering is the lack of functional scaffolds of geometric sizes greater than 10mm due to the inability of cells to survive deep within the scaffold. It is hypothesized that these scaffolds must have an inbuilt nutrient distribution network to sustain the uniform growth of cells. In this paper, we seek to enhance the design and layered fabrication of scaffold internal architecture through the development of Lindenmayer systems, a graphical language based theory to create nutrient delivery networks. The scaffolds are fabricated using the Texas Instruments DLP™ system through UV‐photopolymerization to produce polyethylene glycol hydrogels with internal branch structures. The paper will discuss the Lindenmayer system, process planning algorithms, layered fabrication of samples, challenges and future tasks.Mechanical Engineerin

Deep Inelastic Lepton-Nucleon Scattering at HERA

Data from the HERA collider experiments, H1 and ZEUS, have been fundamental to the rapid recent development of our understanding of the partonic composition of the proton and of QCD. This report focuses on inclusive measurements of neutral and charged current cross sections at HERA, using the full available data taken to date. The present precision on the proton parton densities and the further requirements for future measurements at the Tevatron and LHC are explored. Emphasis is also placed on the region of very low Bjorken-x and Q^2. In this region, the `confinement' transition takes place from partons to hadrons as the relevant degrees of freedom and novel or exotic QCD effects associated with large parton densities are most likely to be observed. Finally, prospects for the second phase of HERA running are discussed.Comment: 13 pages, 15 figures, to appear in Proceedings of the XXI International Symposium on lepton and Photon Interactions at High Energies, Fermilab, August 200

Instability of Rotationally Tuned Dipolar Bose-Einstein Condensates

The possibility of effectively inverting the sign of the dipole-dipole interaction, by fast rotation of the dipole polarization, is examined within a harmonically trapped dipolar Bose-Einstein condensate. Our analysis is based on the stationary states in the Thomas-Fermi limit, in the corotating frame, as well as direct numerical simulations in the Thomas-Fermi regime, explicitly accounting for the rotating polarization. The condensate is found to be inherently unstable due to the dynamical instability of collective modes. This ultimately prevents the realization of robust and long-lived rotationally tuned states. Our findings have major implications for experimentally accessing this regime.Comment: 9 pages with 5 figure