A Discrete Theory of Connections on Principal Bundles

Connections on principal bundles play a fundamental role in expressing the equations of motion for mechanical systems with symmetry in an intrinsic fashion. A discrete theory of connections on principal bundles is constructed by introducing the discrete analogue of the Atiyah sequence, with a connection corresponding to the choice of a splitting of the short exact sequence. Equivalent representations of a discrete connection are considered, and an extension of the pair groupoid composition, that takes into account the principal bundle structure, is introduced. Computational issues, such as the order of approximation, are also addressed. Discrete connections provide an intrinsic method for introducing coordinates on the reduced space for discrete mechanics, and provide the necessary discrete geometry to introduce more general discrete symmetry reduction. In addition, discrete analogues of the Levi-Civita connection, and its curvature, are introduced by using the machinery of discrete exterior calculus, and discrete connections.Comment: 38 pages, 11 figures. Fixed labels in figure

Assessment of effects on vegetation of degradation products from alternative fluorocarbons

Concern with the effects of fluorides on plants has been devoted to that resulting from dry deposition (mainly with reference to gaseous HF and secondarily with particulate forms). The occurrence of precipitation as rain or mist and the presence of dew or free water on the foliage has mainly been considered with respect to their effects on the accumulation of air-borne fluoride and not with fluoride in wet deposition. That is, precipitation has been viewed primarily with respect to its facilitation of the solution and subsequent absorption of deposits by the foliar tissues or its elution of deposited fluoride from foliage. Accordingly, our evaluation of inorganic fluoride from fluorocarbon degradation rests upon a comparison with what is known about the effects of industrial emissions and what could be considered the natural condition

Hot-wire anemometry in hypersonic helium flow

Hot-wire anemometry techniques are described that have been developed and used for hypersonic-helium-flow studies. The short run time available dictated certain innovations in applying conventional hot-wire techniques. Some examples are given to show the application of the techniques used. Modifications to conventional equipment are described, including probe modifications and probe heating controls

Report of an exploratory study: Safety and liability considerations for photovoltaic modules/panels

An overview of legal issues as they apply to design, manufacture and use of photovoltaic module/array devices is provided and a methodology is suggested for use of the design stage of these products to minimize or eliminate perceived hazards. Questions are posed to stimulate consideration of this area

Trapping radioactive ^{82}Rb in an optical dipole trap and evidence of spontaneous spin polarization

Optical trapping of selected species of radioactive atoms has great potential in precision measurements for testing fundamental physics such as EDM, PNC and parity violating beta-decay asymmetry correlation coefficients. We report trapping of 10^4 radioactive ^{82}Rb atoms (t_{1/2}=75 s) with a trap lifetime of ~55 seconds in an optical dipole trap. Transfer efficiency from the magneto-optical trap was ~14%. We further report the evidence of spontaneous spin polarization of the atoms in optical dipole trap loading. This advancement is an important step towards a new generation of precision J-beta correlations measurements with polarized ^{82}Rb atoms.Comment: 4 pages, 4 figure

Quarks, Gluons and Frustrated Antiferromagnets

The Contractor Renormalization Group method (CORE) is used to establish the equivalence of various Hamiltonian free fermion theories and a class of generalized frustrated antiferromagnets. In particular, after a detailed discussion of a simple example, it is argued that a generalized frustrated SU(3) antiferromagnet whose single-site states have the quantum numbers of mesons and baryons is equivalent to a theory of free massless quarks. Furthermore, it is argued that for slight modification of the couplings which define the frustrated antiferromagnet Hamiltonian, the theory becomes a theory of quarks interacting with color gauge-fields.Comment: 21 pages, Late

Sub-Natural-Linewidth Quantum Interference Features Observed in Photoassociation of a Thermal Gas

By driving photoassociation transitions we form electronically excited molecules (Na$_2^*$) from ultra-cold (50-300 $\mu$K) Na atoms. Using a second laser to drive transitions from the excited state to a level in the molecular ground state, we are able to split the photoassociation line and observe features with a width smaller than the natural linewidth of the excited molecular state. The quantum interference which gives rise to this effect is analogous to that which leads to electromagnetically induced transparency in three level atomic $\Lambda$ systems, but here one of the ground states is a pair of free atoms while the other is a bound molecule. The linewidth is limited primarily by the finite temperature of the atoms.Comment: 4 pages, 5 figure