Lower bounds for three-dimensional nonoverlapping domain decomposition algorithms

Summary. Lower bounds for the condition numbers of the preconditioned systems are obtained for the wire basket preconditioner and the Neumann-Neumann preconditioner in three dimensions. They show that the known upper bounds are sharp. Received January 28, 2001 / Revised version received September 3, 2001 / Published online January 30, 2002 This work was supported in part by the National Science Foundation under Grant Nos. DMS-9600133 and DMS-0074246     

Effective conductivities of composite materials composed of cubic arrangements of spherical particles embedded in an isotropic matrix

Results are presented for the effective conductivities of simple, face-centered, and body-centered cubic arrays of isotropic spherical particles embedded in an isotropic medium possessing a different conductivity. With the use of a multipole expansion technique, numerical and conceptual errors in the prior work of others are corrected. Agreement with existing experimental data is found to be excellent.

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Zusammenfassung Für die Leitfähigkeit einer einfachen körper-zentrierten kubischen Anordnung von isotropen kugelfömigen Teilchen, die in einem isotropen Medium mit einer verschiedenen Lefähigkeit eingebettet sind, werden Resultate angegeben. Mit Hilfe einer Multipole-Entwicklung werden gewisse numerische und konzeptuelle Fehler früherer Arbeiten korrigiert. Sehr gute Uebereinstimmung mit den vorhandenen experimentellen Resultaten wurde festgestellt.

     

Measuring the motions in the human middle ear by Laser Doppler Vibrometry

For the detection of tiny motions which are caused by the tympanic membrane under normal hearing conditions, the touch-free method of Laser Doppler Vibrometry was used. Spectra containing information about the motions of the middle ear bones were recorded within 1 min when the umbo was chosen as the detection point and acoustic stimulation was performed via white noise excitation. It was observed that these spectra correlate to middle ear diseases, which had been artificially induced by manipulations in the chain of the middle ear bones in human temporal bones. The dosimetry of the applied laser radiation was found to be harmless to the tympanic membrane, which opened the way for successful in vivo measurements.     

Direct measurement of the quantum yield for the creation of mobile excitons from localized states using optically detected electron spin coherence

Optically detected spin locking and adiabatic demagnetization in the rotating frame are used to directly measure the rate constants for trap-to-band promotion and trap-to-trap energy migration in 1,2,4,5-tetrachlorobenzene. Comparison of these rate constants at a given temperature gives the quantum yield for the decay of a promoted localized state into a mobile exciton state. Its dependence on temperature is also determined.     

The ambiguity function as a polar display of the OTF

It is shown that the Ambiguity function of the generalized pupil function of an optical system, is a polar display of the optical transfer function with the focus error as variable. This geometrical interpretation allows one to obtain the OTF for any given amount of defocus.