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 Near a boundary, these assumptions are no longer valid and the length scale $\alpha$ is seen to depend on the distance to the nearest wall.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

REACTIVITY OF CHLOROPHYLL a/b-PROTEINS AND MICELLAR TRITON X-100 COMPLEXES OF CHLOROPHYLLS a OR b WITH BOROHYDRIDE

The reaction of several plant chlorophyll-protein complexes with NaBH4 has been studied by absorption spectroscopy. In all the complexes studied, chlorophyll b is more reactive than Chi a, due to preferential reaction of its formyl substituent at C-7. The complexes also show large variations in reactivity towards NaBH4 and the order of reactivity is: LHCI > PSII complex > LHCII > PSI > P700 (investigated as a component of PSI). Differential pools of the same type of chlorophyll have been observed in several complexes. Parallel work was undertaken on the reactivity of micellar complexes of chlorophyll a and of chlorophyll b with NaBH4 to study the effect of aggregation state on this reactivity. In these complexes, both chlorophyll a and b show large variations in reactivity in the order monomer > oligomer > polymer with chlorophyll b generally being more reactive than chlorophyll a. It is concluded that aggregation decreases the reactivity of chlorophylls towards NaBH4 in vitro, and may similarly decrease reactivity in naturally-occurring chlorophyll-protein complexes

From individuals to aggregations: the interplay between behavior and physics

This paper analyses the processes by which organisms form groups and how social forces interact with environmental variability and transport. For aquatic organisms, the latter is especially important—will sheared or turbulent flows disrupt organism groups? To analyse such problems, we use individual-based models to study the environmental and social forces leading to grouping. The models are then embedded in turbulent flow fields to gain an understanding of the interplay between the forces acting on the individuals and the transport induced by the fluid motion. Instead of disruption of groups, we find that flows often enhance grouping by increasing the encounter rate among groups and thereby promoting merger into larger groups; the effect breaks down for strong flows. We discuss the transformation of individual-based models into continuum models for the density of organisms. A number of subtle difficulties arise in this process; however, we find that a direct comparison between the individual model and the continuum model is quite favorable. Finally, we examine the dynamics of group statistics and give an example of building an equation for the spatial and temporal variations of the group-size distribution from individual-based simulations. These studies lay the groundwork for incorporating the effects of grouping into models of the large scale distributions of organisms as well as for examining the evolutionary consequences of group formation. � 1999 Academic Press † Author to whom all correspondence should be addressed. 1

A Sustainable Music Industry for the 21st Century

This essay argues that the current system of music licensing must be completely overhauled. At this time, songwriters are paid a mere pittance when their work is played through Internet streaming services. The paper traces the evolution of compulsory licensing from the early 20th century, when Congress put this system in place due to concerns over the monopolization of the player piano industry, to today. This essay shows how the separation between copyrights for compositions as opposed to public performances contributed to blanket licensing through royalty-collecting organizations like ASCAP and BMI, which — together with government intervention into pricing based on antitrust concerns via consent decrees — has led to an inflexible and tightly controlled market in this context. Last, the essay demonstrates how the focus on classifying streaming services like Pandora based simply on whether they are interactive or not relies on a misunderstanding of the substitution effects and hence decline in music sales that Pandora creates. Eliminating compulsory licenses would allow individual songwriters to set their own prices and negotiate with streaming services, including in ways that would allow for price differentiation grounded in factors such as song popularity. Giving songwriters the same control that copyright owners outside the music context already possess will ensure songwriters\u27 ability to continue providing the public with the works it loves

Feeding poultry litter to beef cattle (2005)

Beef cattle have the ability to digest low-cost feedstuffs that are not usable by other livestock species. One such feedstuff is poultry litter, which provides opportunities or both the poultry producer and the beef cattle producer.New 2/01/5M; Revised 10/0