The Critical Values of a Polynomial

It has been known for a long time that any real sequence y ₁ , . . . ,y _n-1 is the sequence of critical values of some real polynomial. Here we show that any complex sequence w ₁ , . . . ,w _n-1 is the sequence of critical values of some complex polynomial.     

Experimental modal analysis for microelectromechanical systems

The structural dynamics behavior of microelectromechanical systems (MEMS), which include moving, overhung, and compliant subcomponents, plays a pivotal role in determining their performance and reliability. Traditionally, experimental modal analysis is used to characterize the dynamic behavior of structures, as well as to derive, validate, update, and correct analytical and numerical models. Due to their small size, however, conventional modal testing methods cannot be directly applied to microstructures. In this paper we provide an overview of modal testing techniques for microsystems. A particular experimental modal analysis methodology that includes base excitation via a piezoelectric shaker and measurement through a laser interferometer is then described and evaluated. A distinguishing characteristic of the methodology is its simplicity, including its simple setup and off-the-shelf components. The modal model is derived for the base excitation of microcantilever beams. The effectiveness of the methodology is illustrated through various experiments on polysilicon microcantilevers for different geometries and ambient pressures. Analysis of the damping data for different pressures has confirmed the well-documented fact that the structural damping in microsystems can be considerably less than damping arising from interaction with the ambient gases.     

The algebra of bounded holomorphic martingales

The algebra of bounded holomorphic martingales introduced by N. Th. Varopoulos (J. Funct. Anal., in press) is studied. In particular, it is shown that this is a logmodular algebra with a spectrum having no analytic structure.     

A pulsed surface muon beam andμSR facilities proposed for the UK

The Spallation Neutron Source, SNS, under construction in the United Kingdom offers the possibility of an intense pulsed pion or muon source and aSR facility for condensed matter spectroscopy has been proposed.A design and specification is presented for a pulsed surface muon beam. Features include negligible electron contamination, the possibility of rotating the polarisation and — particularly important — the capability of varying the pulse width. Operation with cloud muons of both charge signs up to 70 MeV/c and with pions up to 200 MeV/c would also be possible. The pulsed nature of the source would allow the full muon intensities to be used forSR experiments. The potential performance is such that an optimised facility would increase the world total muon stop rate for conventional time-differentialSR by an order of magnitude.The majority ofSR applications would benefit simply from the increased intensity, some benefit especially from the frame-length and duty cycle. Emphasis is to be placed on longitudinalSR, on the development of RF techniques (particularly for chemical applications) and onSR in conjunction with synchronous pulsed excitation of the sample. A scheme for the excitation of a certain bandwidth within a high frequencySR spectrum, to display individual spectral lines for instance, is proposed.     

Euclidean and hyperbolic lengths of images of arcs

Let f be a function that is analytic in the unit disc. We givenew estimates, and new proofs of existing estimates, of theEuclidean length of the image under f of a radial segment inthe unit disc. Our methods are based on the hyperbolic geometryof plane domains, and we address some new questions that follownaturally from this approach.     

Load absorption and interaction of two adjacent filaments in a fiber-reinforced material

This investigation is concerned with the interaction—as far as load-absorption is concerned—of a pair of identical parallel elastic filaments in a fiber-reinforced composite material. The filaments are assumed to have uniform circular cross-sections, are taken to be semi-infinite, and are supposed to be continuously bonded to an all-around infinite matrix of distinct elastic properties. At infinity the matrix is subjected to uniaxial tension parallel to the filaments. Two separate but related problems are treated. In the first both filaments extend to infinity in the same direction and their terminal cross-sections are coplanar. In the second problem the filaments extend to infinity in opposite directions and their terminal cross-sections need no longer be coplanar, the two filaments being permitted to overlap partly. An approximate scheme based in part on three-dimensional linear elasticity and developed originally by Muki and Sternberg is employed in the analysis. The problems are ultimately reduced to Fredholm integral equations which characterize the distribution of the axial filament force. The integral equations are analyzed asymptotically and numerically. Results are presented which show the variation of filament force with position and the effect on this variation of various relevant geometrical and material parameters. One result is of particular interest. In the second problem, involving the overlapping filaments, for certain cases the filament force exceeds its far-field asymptotic value for a portion of the filament length. Stated another way, this means that the filament is loaded in excess of that which one would calculate by equating axial strains.

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Zusammenfassung Die Wechselwirkung eines identischen parallelen elastischen Fadenpaares in einem faserverstärkten Verbundstoff wird in Bezug auf die Lastaufnahme untersucht. Man nimmt an, dass die Fäden einen gleichmässigen runden Querschnitt haben, halbunendlich sind, und dass sie ohne Unterbrechung an einem überall unendlichen Grundstoff eindeutiger elastischer Eigenschaften anhaften. Im Unendlichen wird der Grundstoff einem einachsigen Zug parallel zu den Fäden ausgezetzt. Es werden zwei verschiedene, aber in Verbindung stehende, Fragenstellungen behandelt. In der Ersten erstrecken sich beide Fäden unendlich lang in derselben Richtung und ihre Endquerschnitte sind koplanar. In der Zweiten erstrecken sie sich unendlich lang in entgegengesetzten Richtungen und ihre Endquerschnitte müssen nicht koplanar sein, obwohl die Fäden sich teilweise überlagern dürfen. Die Analyse wird mit einem von Muki und Sternberg entwickelten Näherungsverfahren durchgeführt, welches zum Teil auf einer dreidimensionalen linearen Elastizitätstheorie beruht. Letzten Endes nehmen diese Probleme die Form Fredholmscher Integralgleichungen an, welche die Verteilung der Fadenlängskraft kenzeichnen. Die Integralgleichungen werden asymptotisch und zahlenmässig analysiert.

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The results communicated in this paper were obtained in the course of an investigation supported in part by the Office of Naval Research under Contract N00014-67-A-0094-0020. The work was carried out during the author's tenure of a National Science Foundation Traineeship.     

Optical mouse digital speckle correlation

The possibilities with which an optical mouse can be applied to obtain scientific measurements are currently limited by the maximum distance possible between the mouse and surface under interrogation. We demonstrate that a simply adapted optical mouse is able to operate as a recording instrument in the digital speckle correlation mode; wherein greater distances between optical mouse and translating surface are possible. Linear (R² > 0.98) and repeatable measurements in the x and y axis were obtained with the optical mouse and translating surface separated at 300 mm. In both cases, the measurement resolution was 0.025 mm. Digital speckle correlation with an optical mouse offers the ability to obtain measurements of displacement and deformation at a fraction of the investment in time and cost of conventional setups.