Effect of a moving wall on a fully developed, equilibrium turbulent boundary layer

Experiments were conducted in a wind tunnel to assess the effect of a moving wall on a fully developed, equilibrium turbulent boundary layer. Pitot-static and total head probes were used in conjunction with both single- and two-component hot-wire anemometer probes to quantify the effect of wall motion on the boundary layer velocity statistics. A variable speed, seamless belt formed the wind tunnel test section wall. When stationary, the belt was found to possess a fully developed, equilibrium turbulent boundary layer in excellent agreement with archival data. With the tunnel wall moving at the free-stream speed, and at a sufficient distance above the wall, the velocity statistics in the moving-wall boundary layer were found to collapse well when scaled as a self-preserving turbulent wake. The near-wall mean velocity profile of the moving wall was found to exhibit an extended region of linearity compared to canonical turbulent boundary layer and internal flows. This can be attributed to the reduced shear resulting from wall motion and the subsequent reduction in Reynolds stress. Received: 2 June 1999/Accepted: 8 August 2000     

Telemetry System for Stimulation and Monitoring of Freely Moving Patients

A telemetry system is described in which the patient carries small stimulator and monitor units. Typically, the wrist is stimulated with 0.5 ms alternating pulses whose frequency and current (up to 10 mA peak) are remotely controlled by the neurophysiologist via a 20 MHz carrier. At the same time, the synchronized EEG-somatosensory evoked potential is transmitted from C2 via a 100 MHz carrier. The stimulus unit transmits a 100 MHz " flag" signal to the neurophysiologist to indicate that the patient is actually receiving a stimulus signal. Several examples are given in which latencies and amplitudes of the EEG-SEP are recorded.     

Characterizations of continuous and Lipschitz continuous metric selections in normed linear spaces

Characterizations are given of when the metric projection P_M onto a proximal subspace M has a continuous, pointwise Lipschitz continuous, or Lipschitz continuous selection. Moreover, it is shown that ifP_M has a continuous selection, then it has one which is also homogeneous and additive modulo M. An analogous result holds if P_M has a pointwise Lipschitz or Lipschitz continuous selection provided that M is complemented. If dimM < ∞ and P_M is Lipschitz (resp. pointwise Lipschitz) continuous, then P_M has a Lipschitz (resp. pointwise Lipschitz) continuous selection. A conjecture of R. Holmes and B. Kripke (Michigan Math. J. 15 (1968), 225–248) is resolved.     

Lasers and optics in health care

Lasers and optics have affected health care in a myriad of ways. This paper surveys their impact on three aspects of health care: (1) surgery and medicine, (2) biology, and (3) biotechnology. In surgery, fiber optics have enabled the development of endoscopes, which allow access to most sites within the body. Endoscopes have, in turn, led to the development of minimally invasive therapy, which is changing the practice of surgery. Optics contributes to biology via new techniques for visualization, measurement and analysis, and manipulation. In biotechnology, broadly defined as the measurement, manipulation, and manufacture of large biologically significant molecules such as proteins and DNA, optical methods have become important in genetic sequencing and pharmaceutical development     

The thermal decomposition of Mg-containing carbonate apatites

Carbonate apatites precipitated from an aqueous solution and containing Mg²⁺ and Sr²⁺ ion were studied by thermogravimetric, infrared absorption, and X-ray diffraction methods. In the temperature range of 25–350°C water evolves and at 350–905°C carbonate decomposes. Two effects characterize the Mg-containing system: Weight loss during decomposition is related to carbonate in the apatite and to an additional ion; increased formation of whitlockite. The interrelation between these two phenomena and the presence of carbonate and Mg is discussed.     

Accelerating the convergence of the method of alternating projections

The powerful von Neumann-Halperin method of alternating projections (MAP) is an algorithm for determining the best approximation to any given point in a Hilbert space from the intersection of a finite number of subspaces. It achieves this by reducing the problem to an iterative scheme which involves only computing best approximations from the individual subspaces which make up the intersection. The main practical drawback of this algorithm, at least for some applications, is that the method is slowly convergent. In this paper, we consider a general class of iterative methods which includes the MAP as a special case. For such methods, we study an ``accelerated' version of this algorithm that was considered earlier by Gubin, Polyak, and Raik (1967) and by Gearhart and Koshy (1989). We show that the accelerated algorithm converges faster than the MAP in the case of two subspaces, but is, in general, not faster than the MAP for more than two subspaces! However, for a ``symmetric' version of the MAP, the accelerated algorithm always converges faster for any number of subspaces. Our proof seems to require the use of the Spectral Theorem for selfadjoint mappings.

     

Newly calculated absolute cross-section for the electron-impact ionization of C2H2 +

New measurements of the cross-section for electron impact ionization of the molecular ion C₂H₂⁺ have been carried out recently. These data differ significantly from earlier data, because cross-sections corresponding to all the possible dissociative ionization processes were determined. The new data in conjunction with the significant discrepancies between the earlier data and the results of various calculations, which disagreed among themselves by a factor of 3, motivated a renewed attempt to apply the semi-classical Deutsch-M?rk (DM) formalism to the calculation of the absolute electron-impact ionization cross-section of this molecular ion. A quantum chemical molecular orbital population analysis for both the neutral molecule and the ion revealed that in the case of C₂H₂⁺ the singly occupied molecular orbital (i.e. the “missing” electron) is highly localized near the site of a C atom in the molecule. This information is explicitly incorporated in our formalism. The results obtained by taking the ionic character directly into account are in excellent agreement with the recent experimental data.     

The perceived height of octave-related complexes

Subjects were presented with two-part patterns consisting of tones whose partials stood in octave, or near-octave relation. The perceived heights of the tones in the patterns were found to vary depending on their positions along the chroma circle, so that the patterns were perceived quite differently depending on which of two keys they were in. Implications of these findings are discussed.