A connection between the Camassa-Holm equations and turbulent flows in channels and pipes

In this paper we discuss recent progress in using the Camassa-Holm equations to model turbulent flows. The Camassa-Holm equations, given their special geometric and physical properties, appear particularly well suited for studying turbulent flows. We identify the steady solution of the Camassa-Holm equation with the mean flow of the Reynolds equation and compare the results with empirical data for turbulent flows in channels and pipes. The data suggests that the constant $\alpha$ version of the Camassa-Holm equations, derived under the assumptions that the fluctuation statistics are isotropic and homogeneous, holds to order $\alpha$ distance from the boundaries. Near a boundary, these assumptions are no longer valid and the length scale $\alpha$ is seen to depend on the distance to the nearest wall. Thus, a turbulent flow is divided into two regions: the constant $\alpha$ region away from boundaries, and the near wall region. In the near wall region, Reynolds number scaling conditions imply that $\alpha$ decreases as Reynolds number increases. Away from boundaries, these scaling conditions imply $\alpha$ is independent of Reynolds number. Given the agreement with empirical and numerical data, our current work indicates that the Camassa-Holm equations provide a promising theoretical framework from which to understand some turbulent flows.Comment: tex file, 29 pages, 4 figures, Physics of Fluids (in press

Entanglement between the future and past in the quantum vacuum

We note that massless fields within the future and past light cone may be quantized as independent systems. We show that the vacuum is an entangled state of these systems, exactly mirroring the known entanglement between the spacelike separated Rindler wedges. We describe a detector which exhibits a thermal response to the vacuum when switched on at t=0. The feasibility of experimentally detecting this effect is discussed.Comment: 4 pages, 1 figur

Feed ingredient composition for beef cattle (2005)

It is essential to know feedstuff nutrient content in order to properly formulate beef cattle diets. This publication provides estimates of the nutrient composition of feedstuffs that are used commonly in Missouri.Revised October 2005 -- Extension website

No well-defined remnant Fermi surface in Sr2CuO2Cl2

In angle-resolved photoelectron spectra of the antiferromagnetic insulators Ca2CuO2Cl2 and Sr2CuO2Cl2 a sharp drop of the spectral intensity of the lowest-lying band is observed along a line in k space equivalent to the Fermi surface of the optimally doped high-temperature superconductors. This was interpreted as a signature of the existence of a remnant Fermi surface in the insulating phase of the high-temperature superconductors. In this paper it is shown that the drop of the spectral intensity is not related to the spectral function but is a consequence of the electron-photon matrix elementComment: 4 pages, 3 figure

Hello Barbie: First They Will Monitor You, Then They Will Discriminate Against You. Perfectly.

This Article argues that the evolution of software—and the looming age of the “Internet of Things”—will allow manufacturers to make use of consumer monitoring technologies and restrictive software licenses to price discriminate more perfectly. First, the increasing communication between software and its producers gives more opportunities to monitor consumer behavior and characteristics. Second, attaching restrictive copyright licenses to software—and to goods containing software—enables producers to restrict use and resale of their products. By combining monitoring and restrictive licensing, producers will have increasingly better ability and opportunities to price discriminate among their consumers. This Article explains that increased monitoring and price discrimination will not always happen because, in some cases, it will be against the manufacturers’ financial interests. But in other cases, manufacturers will indeed restrict use of products to facilitate price discrimination. The Article argues that the low marginal cost of distribution of software makes it more likely that price discrimination of software-enabled goods will be welfare enhancing and will result in cross-subsidization from rich to poor so that poor consumers can get more products for lower prices. The Article also demonstrates that the traditional policy reasons to disallow restraints on personal property do not apply to software-enabled devices. We conclude that rather than discouraging the use of restrictive software licenses, the law should adapt to better facilitate such licenses and the more perfect price discrimination that goes with them

Assessment of upper tropospheric HOx sources over the tropical Pacific based on NASA GTE/PEM data: Net effect on HOx and other photochemical parameters

Data for the tropical upper troposphere (8-12 km, 20° N-20° S) collected during NASA's Pacific Exploratory Missions have been used to carry out a detailed examination of the photochemical processes controlling HOx (OH+HO2). Of particular significance is the availability of measurements of nonmethane hydrocarbons, oxygenated hydrocarbons (i.e., acetone, methanol, and ethanol) and peroxides (i.e., H2O2 and CH3OOH). These observations have provided constraints on model calculations permitting an assessment of the potential impact of these species on the levels of HOx, CH3O2, CH2O, as well as ozone budget parameters. Sensitivity calculations using a time-dependent photochemical box model show that when constrained by measured values of the above oxygenated species, model estimated HOx levels are elevated relative to unconstrained calculations. The impact of constraining these species was found to increase with altitude, reflecting the systematic roll-off in water vapor mixing ratios with altitude. At 11-12 km, overall increases in HOx approached a factor of 2 with somewhat larger increases being found for gross and net photochemical production of ozone. While significant, the impact on HOx due to peroxides appears to be less than previously estimated. In particular, observations of elevated H2O2 levels may be more influenced by local photochemistry than by convective transport. Issues related to the uncertainty in high-altitude water vapor levels and the possibility of other contributing sources of HOx are discussed. Finally, it is noted that the uncertainties in gas kinetic rate coefficients at the low temperatures of the upper troposphere and as well as OH sensor calibrations should be areas of continued investigation. Copyright 1999 by the American Geophysical Union