The stationary and non-stationary stokes system in exterior domains with non-zero divergence and non-zero boundary values

In an exterior domain Ω??ⁿ, n ? 2, we consider the generalized Stokes resolvent problem in L^q-space where the divergence g = div u and inhomogeneous boundary values u = ψ with zero flux ∫_?Ωψ·N do = 0 may be prescribed. A crucial step in our approach is to find and to analyse the right space for the divergence g. We prove existence, uniqueness and a priori estimates of the solution and get new results for the divergence problem. Further, we consider the non-stationary Stokes system with non-homogeneous divergence and boundary values and prove estimates of the solution in L⁵(0, T;L^q(Ω)) for 1 < s, q < ∞.     

Ion Flux from the Cathode Region of a Vacuum Arc

This paper reviews the properties of the cathode ion flux generated in the vacuum arc. The structure and distribution of mass erosion from individual cathode spots and the characteristics of current carriers from the cathode region at moderate arc currents are described. An appreciable ion flux (～10% of total arc current) is emitted from the cathode of a vacuum arc. This ion flux is strongly peaked in the direction of the anode, though some ion flux may be seen even at angles below the plane of the cathode surface. The observed spatial distribution of the ion flux is expressed quite well as an exponential function of solid angle. The ion flux is quite energetic, with average ion potentials much larger than the arc voltage, and generally contains a considerable fraction of multiply-charged ions. The average ion potential and ion multiplicity increase significantly for cathode materials with higher arc voltages, but decrease with increasing arc current for a particular material. The main theories concerning ion acceleration in cathode spots are the potential hump theory (PH), which assumes that all ions are created at the same potential, and the gas dynamic theory (GD), which assumes that all ions are created with the same flow velocity. Experimental data on the potentials and energies of individual ions indicates that these theories in their original forms are not quite correct, however extensions or modifications of the PH and GD theories seem very likely to be able to predict correct values for the charge states, potentials, and energies of individual ions.     

Speckle metrology employing LCTV spatial light modulators

Liquid crystal televisions have been employed as spatial light modulators in a variety of optical image processing applications. We have used such devices to develop techniques in speckle metrology for the electronic addition of speckle patterns and the display of speckle correlation, and also for the real-time display of object motion. Factors which affect the performance in terms of the useful working range and the accuracy of displacement measurement are discussed. Some modifications to the LCTV which should increase the potential of these devices as spatial light modulators, when used in both amplitude and phase modulation, are considered briefly.     

The Computable Dimension of I-Trees of Infinite Height

We study computable trees with distinguished initial subtree (briefly, I-trees). It is proved that all I-trees of infinite height are computably categorical, and moreover, they all have effectively infinite computable dimension.     

Covariance estimation under spatial dependence

Correlated multivariate processes have a dependence structure which must be taken into account when estimating the covariance matrix. The natural estimator of the covariance matrix is introduced and is shown that to be biased under the dependence structure. This bias is studied under two different asymptotic models, namely increasing the domain by increasing the number of observations, and increasing the number of observations in the fixed domain. Using the first asymptotic model, we quantify the convergence rate of the bias and of the covariance between the components of the estimated covariance matrix. The second asymptotic model serves to derive a fast and accurate bias correction. As shown, under mild hypotheses, the asymptotic normality of the estimated covariance matrix holds and can be used to test whether the bias is significant, for example, in the sense that the eigenvectors of the estimated and true covariance matrices are significantly different.     

Time-domain simulations of sound propagation through screen-induced turbulence

A flow model in combination with a statistical-dynamical turbulence generator and a linearised Euler time-domain model for sound waves were used to simulate the effect of screen-induced turbulence on the noise level in the acoustical shadow of a screen in wind. Instead of simulating a great number of different frozen turbulence realisations, the concept of transient turbulence was successfully tested and applied. This concept is adequate to the time-domain model and reduces the computational demands. Several two-dimensional simulations allowed to isolate the individual effects of wind and screen on the propagation of 500 Hz sound waves over a 4-m high noise barrier. At a distance of 250 m from the source (240 m behind the screen) the sheltering effect of the screen and the refraction effect of the wind are in the order of 6 and 4 dB, respectively. The screen-induced turbulence leads to fluctuations in the noise level with a standard deviation of 1.2 dB and a maximum amplitude of 3 dB. However, the time averaged effect turned out to be in the order of merely 0.2 dB. The effect of the screen-induced turbulence on the average noise level behind the screen is therefore negligible.     

Recognition of subgroups of direct products of hyperbolic groups

We give examples of direct products of three hyperbolic groups in which there cannot exist an algorithm to decide which finitely presented subgroups are isomorphic.

     

Differentiation between acutely ischemic myocardium and zones of completed infarction in dogs on the basis of frequency-dependent backscatter

The goal of this work was to determine whether the frequency dependence of apparent backscatter coefficient (not corrected for attenuation within the myocardium) could differentiate completed, remote infarction from acute myocardial injury in vivo. Myocardial infarcts were produced in six dogs by coronary artery occlusion. One to 12 months later, acute ischemic injury was induced in each dog by ligation of a coronary artery that supplied a region of myocardium adjacent to the established infarct. Infarct, ischemic, and normal regions were interrogated with a 5-MHz, circular, 0.5-in. diam, broadband, focused, piezoelectric transducer mounted in a water-filled stand-off device placed against the exposed, beating heart. Apparent backscatter coefficients were measured over the range of frequencies from 3-7 MHz. The frequency dependence was obtained from the slope of log apparent backscatter coefficient versus log frequency. No significant difference in frequency dependence was found between normal and acutely ischemic myocardium for periods of up to 2 h of ischemia. In contrast, frequency dependence in regions of remote infarct (1.8 +/- 0.1, mean +/- standard error) was significantly lower than that in acutely ischemic or nonischemic regions (2.3 +/- 0.1) (p less than 0.01). These results suggest that remote myocardial infarction can be differentiated from acutely injured but still potentially salvageable myocardium in vivo on the basis of the frequency dependence of backscatter.