Monopole fields from vortex sheets reconciling Abelian and center dominance

We describe a new order parameter for the confinement-deconfinement transition in lattice SU(2) Yang-Mills theory. It is expressed in terms of magnetic monopole field correlators represented as sums over sheets of center vortices. Our construction establishes a link between "abelian" and "center dominance". It avoids an inconsistency in the treatment of small scales present in earlier definitions of monopole fields by respecting Dirac's quantization condition for magnetic fluxes.Comment: LaTeX file, 6 pages; Lattice2001(plenary

Self-actuating grapple automatically engages and releases loads from overhead cranes

Two-piece grapple mechanism consisting of a lift knob secured to the load and a grapple member connected to the crane or lift automatically disengages the load from the overhead lifting device when the load contacts the ground. The key feature is the sliding collar under the lift knob which enables the grapple latch to be stripped off over the lift knob

Supersymmetric quantum theory and (non-commutative) differential geometry

We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in algebraic data consisting of an algebra of functions on a manifold and a family of supersymmetry generators represented on a Hilbert space. We show that known types of differential geometry can be classified in terms of the supersymmetries they exhibit. Replacing commutative algebras of functions by non-commutative *-algebras of operators, while retaining supersymmetry, we arrive at a formulation of non-commutative geometry encompassing and extending Connes' original approach. We explore different types of non-commutative geometry and introduce notions of non-commutative manifolds and non-commutative phase spaces. One of the main motivations underlying our work is to construct mathematical tools for novel formulations of quantum gravity, in particular for the investigation of superstring vacua.Comment: 125 pages, Plain TeX fil

Supersymmetric quantum theory and non-commutative geometry

Classical differential geometry can be encoded in spectral data, such as Connes' spectral triples, involving supersymmetry algebras. In this paper, we formulate non-commutative geometry in terms of supersymmetric spectral data. This leads to generalizations of Connes' non-commutative spin geometry encompassing non-commutative Riemannian, symplectic, complex-Hermitian and (Hyper-)Kaehler geometry. A general framework for non-commutative geometry is developed from the point of view of supersymmetry and illustrated in terms of examples. In particular, the non-commutative torus and the non-commutative 3-sphere are studied in some detail.Comment: 77 pages, PlainTeX, no figures; present paper is a significantly extended version of the second half of hep-th/9612205. Assumptions in Sect. 2.2.5 clarified; final version to appear in Commun.Math.Phy

Forest snow accumulation factors in the Colorado Front Range

August 1969.Includes bibliographical references (pages 88-93).Covers not scanned.Print version deaccessioned 2021.Maximum snowpack water equivalent is measured at 123 points in the Spring of 1966-1968. These points are distributed over three transects within a four square mile area in the 9, 580-10, 800 foot elevation zone of the Little Beaver watershed in the Colorado Front Range. Harsh climatic conditions persist through the snow accumulation season with winds of 9.4 m/s estimated for the mean winds during days with precipitation. Average temperatures for these periods were estimated to be -5.2°C. Snowpack water equivalent at maximum ranged from 6.6 to 9.7 inches over the three years of measurement averaged over all points. Individual points vary widely in their relative accumulation from year to year; the R2 for 1966 vs. 1968 water equivalent is only 25%. Consistency of snowpack density is noted with snow water equivalent vs. snow depth giving r values of 0.86, 0.90 and 0.7 3 for the three years respectively. The single most important variable of those tested in this study is a parameter expressing expanse of and distance from a source area of blowing snow. This source ratio is associated with 40% of the total variance when three years data are pooled and 108 sample points are included. Water equivalent increases an average of 5.0 inches per 1000 feet elevation although only 28% of the total variance in water equivalent is associated with elevation. On the 40 points of mid transect the three topographic variables (source, elevation, and steepness of slope) are associated with 85% of the total variance. However, considering all transects, the topographic variables are effectively supplemented by the use of a canopy variable. Canopy percentage was estimated with a Lemmon spherical densiometer read to indued a 114° arc, a 21° arc and crown cover to the windward. Basal area per acre was derived through the use of a cruising pr ism. These four variables are closely correlated and often interchangeable. The most useful of the four is the 114° arc. About 67% of the total variance is associated with the two major topographic variables (source and elevation) and crown cover in a regression involving 108 points and with the three years data pooled. Crown volume and number of stems or sum of stem diameters do not significantly improve any of the regressions. Roughness variables were derived from profiles of the canopy drawn with the aid of a Kelsh photogrammetric plotter. The most useful of the roughness variables tested is a coefficient indexing the projection of the first tree upwind from the sample point. This variable was selected as the second most important one on the lower transect. With basal area and Coef. 1, the R2 was 38%, and with the addition of elevation and the height of trees to the lee of the sample point the R2 was raised to 58%