Viscosity measurement in thin lubricant films using shear ultrasonic reflection

When a shear ultrasonic wave is incident on a solid and liquid boundary, the proportion that is reflected depends on the liquid viscosity. This is the basis for some instruments for on-line measurement of bulk liquid viscosity. In machine elements, the lubricant is usually present in a thin layer between two rubbing solid surfaces. The thin film has a different response to an ultrasonic shear wave than liquid in bulk. In this work, this response is investigated with the aim of measuring viscosity in situ in a lubricating film. The proportion of the wave reflected at a thin layer depends on the layer stiffness. A shear wave is reflected by the shear stiffness of the thin layer. For a thin viscous liquid layer, the stiffness is a complex quantity dependent on the viscosity, wave frequency, and film thickness. This stiffness is incorporated into a quasi-static spring model of ultrasonic reflection. In this way, the viscosity can be determined from shear-wave reflection if the oil-film thickness is known. The approach has been experimentally evaluated on some static oil film between Perspex plates. Predictions of the spring model gave good measurement up to layer thicknesses of around 15 μm. For thicker layers, the shear stiffness reduces to such an extent that almost all the wave is reflected and the difference associated with the layer response is hard to distinguish from background noise

Howe Pairs in the Theory of Vertex Algebras

For any vertex algebra V and any subalgebra A of V, there is a new subalgebra of V known as the commutant of A in V. This construction was introduced by Frenkel-Zhu, and is a generalization of an earlier construction due to Kac-Peterson and Goddard-Kent-Olive known as the coset construction. In this paper, we interpret the commutant as a vertex algebra notion of invariant theory. We present an approach to describing commutant algebras in an appropriate category of vertex algebras by reducing the problem to a question in commutative algebra. We give an interesting example of a Howe pair (ie, a pair of mutual commutants) in the vertex algebra setting.Comment: A few typos corrected, final versio

Invariant chiral differential operators and the W_3 algebra

Attached to a vector space V is a vertex algebra S(V) known as the beta-gamma system or algebra of chiral differential operators on V. It is analogous to the Weyl algebra D(V), and is related to D(V) via the Zhu functor. If G is a connected Lie group with Lie algebra g, and V is a linear G-representation, there is an action of the corresponding affine algebra on S(V). The invariant space S(V)^{g[t]} is a commutant subalgebra of S(V), and plays the role of the classical invariant ring D(V)^G. When G is an abelian Lie group acting diagonally on V, we find a finite set of generators for S(V)^{g[t]}, and show that S(V)^{g[t]} is a simple vertex algebra and a member of a Howe pair. The Zamolodchikov W_3 algebra with c=-2 plays a fundamental role in the structure of S(V)^{g[t]}.Comment: a few typos corrected, final versio

Associations among neighborhood socioeconomic deprivation, physical activity facilities, and physical activity in youth during the transition from childhood to adolescence

BACKGROUND: This study aims to examine the longitudinal association of neighborhood socioeconomic deprivation (SED) with physical activity in youth during the transition from elementary to middle school, and to determine if access to physical activity facilities moderates this relationship. METHODS: Data were obtained from the Transitions and Activity Changes in Kids (TRACK) study, which was a multilevel, longitudinal study designed to identify the factors that influence changes in physical activity as youth transition from elementary to middle school. The analytic sample for the current study included 660 youth with complete data in grades 5 (baseline) and 7 (follow-up). A repeated measures multilevel framework was employed to examine the relationship between SED and physical activity over time and the potential moderating role of elements of the built environment. RESULTS: Decreases in physical activity varied by the degree of neighborhood SED with youth residing in the most deprived neighborhoods experiencing the greatest declines in physical activity. Access to supportive physical activity facilities did not moderate this relationship. CONCLUSION: Future research studies are needed to better understand how neighborhood SED influences youth physical activity over time

General Equilibrium, Markets, Macroeconomics and Money in a Laboratory Experimental Environment

This paper reports on the use of laboratory experimental techniques to create relatively complete economic systems. The creation of these market systems reflects a first attempt to explore the nature of inherently interdependent environments, to assess the ability of simultaneous equations equilibrium models like the classical static general competitive equilibrium model, and to predict aspects of system behaviors. In addition, the impact of the quantity of a fiat money was studied. The economies were successfully created. Classical models capture much of what was observed