Non-linear behaviour and stability of trapped micron-sized cylindrical gas bubbles in an ultrasonic field

Stable arrays of cylindrical bubbles with diameters 3 and 4 μm were produced by trapping air in the pores of hydrophobic Nuclepore filters. These bubble arrays were irradiated by beams of cw and pulsed ultrasound at carrier frequencies near the resonance frequencies of the trapped bubbles. By examining the frequency spectrum of the field scattered by the arrays it was found that the bubbles may oscillate as non-linear stable cavities of long duration. Using short pulses, the bubbles remain stable up to excitation pressure amplitudes of several bars. Mechanisms for the eventual growth and decay of the bubbles are discussed in light of the observations.     

Generation of basis states via variational methods

A systematic means of generating an optimal set of basis states via variational methods is presented. A calculation for ²⁰Ne has been performed and compared with the exact shell model diagonalization. Very good agreement for the lower-lying states in the eigenvalue spectrum has been obtained with relatively few basis states.     

Graph with given achromatic number

An irreducible (point-determining) graph is one in which distinct vertices have distinct neighbourhoods. Every graph X can be reduced to an irreducible graph X¹ by identifying all vertices with the same neighbourhood; the colourability properties of X¹ carry over to X. Hence irreducible graphs are instrumental in the study of achromatic number. We prove that there are only finitely many irreducible graphs with a given achromatic number, and describe all graphs with achromatic number less than four. We deduce certain bounds on the achromatic number X in terms of the number of vertices of X¹. In the course of the proofs we calculate the achromatic numbers of paths and cycles. Generalizations of the main theorem to homomorphisms other than colourings are discussed.     

Electrical conductivity of N-methyl phenazinium tetracyanoquinodimethanide, (NMP) (TCNQ)

New conductivity, σ, vs. temperature, T, measurements on numerous (NMP)-(TCNQ) samples, as well as older data, can all be fit, in the range 65K<T<400K, by the simple expression σ = σ_oT^-αexp(-900/T). σ_o and α(3<α<4) are sample-dependent constants. We interpret this as representing an activated carrier concentration and strongly T-dependent mobility, μ. We can account for the magnitude and T-dependence of μ by a model involving interaction with the molecular vibrations through the known electron-phonon coupling constants of TCNQ^-.     

The Lie Theory of Two-Variable Hypergeometric Functions

We develop a Lie-algebraic method that associates with each of the 34 distinct second-order hypergeometric functions in two variables a canonical system of partial differential equations. The special functions arise by partial separation of variables in these simple systems. Some consequences are a demonstration that all such functions appear as solutions of the 4-variable wave equation and a classification of the possible imbeddings. In each case the functions are characterized by first- and second-order operators in the enveloping algebra of the conformal symmetry algebra for the wave equation. In some cases the 3-variable wave and heat equations and the 2-variable Helmholtz equation also arise. This intimate relationship between Horn functions and some fundamental equations of mathematical physics shows that these functions are more interesting than was previously recognized and permits use of the powerful tools of Lie theory and separation of variables to obtain properties of the functions.     

Zur Kenntnis des Phosphatstoffwechsels der Hefe, 5. Mitt.: Weitere Untersuchungen über freie Nucleotide in Säureextrakten aus verschiedenen Stoffwechselbedingungen unterworfener Hefe

Zusammenfassung In Fortsetzung früherer Arbeiten wurden die freien Nucleotide in Säureextrakten aus anaerob phosphat-angereicherter Hefe, aus wachsender Hefe, aus sporulierter Hefe und aus Hefe, die ohne Kohlenstoffquelle auf einer Pufferlösung gezogen wurde, bestimmt. Es zeigte sich, daß die seinerzeit unter aeroben Bedingungen beobachtete Abnahme der Nucleotidkonzentration bei Phosphat-anreicherung anaerob nicht eintritt. Die Suche nach reduzierten Pyrimidinnucleotiden in den Säureextrakten aus anaerob phosphat-angereicherter Hefe gab ein negatives Ergebnis.Bei Vergleich der freien Nucleotide aus wachsender, sporulierender und im Hungerzustand gehaltener Hefe zeigte sich deutlich, daß während der Sporulierung der pool der freien Nucleotide fast völlig erschöpft wird, während zwischen dem Nucleotidgehalt wachsender Hefe und solcher im Hungerzustand keine sehr markanten Unterschiede zu beobachten sind. Dieses Ergebnis unterstreicht wiederum die Besonderheit des Sporulierungsvorgangs, dessen morphologische Phänomene in den biochemischen Verhältnissen ein deutliches Korrelat finden.Mit 4 Abbildungen     

Band absorption in nonhomogeneous,isotropically-scattering planetary atmospheres: theory and experiment

A computer program is developed which predicts the vertical distribution of an absorbing species in an isotropically-scattering, finite planetary atmosphere from measurements of the upwelling band radiance determined by a vertically traversing 2-channel radiometer. Comparison is made with experiment.     

Determination of germanium in organo-germanium compounds

Summary A method is described for the determination of germanium in organic compounds after combustion in the oxygen flask. The yellow acetone-stabilised -form of germanomolybdate is formed and measured spectrophotometrically at 430 nm. Interference by silica is prevented by coating the oxygen flask with a non-stick coating material. The results obtained were within the usual limits for microanalysis (±0.3%).

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Zusammenfassung Ein Verfahren zur Germaniumbestimmung in organischen Verbindungen nach deren Verbrennung im Sauerstoffkolben wurde beschrieben. Das gelbe, mit Aceton stabilisierte -Germanomolybdat wird bei 430 nm spektrophotometrisch gemessen. Störungen durch Kieselsäure werden durch Auskleiden des Sauerstoffkolbens mit einem nichtklebenden Film vermieden. Die Resultate liegen innerhalb der mikroanalytischen Fehlergrenzen (±0,3%).

     

Theoretical computations of spontaneous vibration-rotation raman scattering from OH(X 2Φ) and NO(X 2Φ)

Absolute values of Q-branch line intensities for OH(X² Φ) and NO(X² Φ) has been calculated, primarily for use in making measurements in flames. The effects of spin-orbit interaction, spin uncoupling, vibration-rotation interaction, and anharmonicity has been included in the calculations simultaneously in a self-consistent fashion. A-doubling is neglected. Multiconfigurational self-consistent field calculations of static polarizabilities are used to approximate the required electronic matrix elements. Complete derivations and discussion of the wave functions and matrix elements are included for clarity and to point out restrictions and approximations. Results of the calculations for NO agree well with room temperature measurements of Raman cross sections. No experimental data are available for OH.