THE ENERGY ASPECT OF THE RECIPROCAL INTERACTIONS OF PAIRS OF TWO DIFFERENT VIBRATION MODES OF A CLAMPED ANNULAR PLATE

The standardized mutual active and reactive sound power of a clamped plate, representing the energy aspect of the reciprocal interactions of two different in vacuo modes, has been computed. It was assumed that the vibrations are axisymmetric, elastic and time harmonic, the plate's transverse deflection is small as compared with the plate's size, and that the vibration velocity is small as compared with the acoustic wavenumber generated. The Kirchhoff-Love theory of a perfectly elastic plate was used. The integral formulae for the mutual sound power were transformed into their Hankel representations which made possible their subsequent computation. A closed path integral was used to express the integral in its Hankel representation to compute the mutual active sound power. The asymptotic stationary phase method was used to compute the two magnitudes, i.e., the mutual active and reactive sound power. The results obtained are the asymptotic formulae valid for the acoustically fast waves. The oscillating as well as the non-oscillating terms have been identified in the formulae to make possible their further separate analysis. The availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power. Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.     

THE NATURE OF ULTRAVIOLET LIGHT-INDUCED STRAND BREAKAGE IN DNA CONTAINING BROMOURACIL

Abstract— Single-strand breaks are produced in the phosphodiester backbone of ultraviolet-light-irradiated 5–bromodeoxyuridine-containing DNA (BU-DNA) after treatment with alkali. No radiation dependent breakage is observed in thymine-containing DNA (thy-DNA). The relative yields of breaks terminated by 5'-hydroxyl and 5'-phosphate groups was determined by measuring the rate of phosphorylation achieved with polynucleotide kinase in BU-DNA single strands before and after treatment with alkaline phosphatase. The ratio of 5'-phosphate to 5' hydroxyl groups ranged from 2.3 to 2.9 in different experiments. When cysteamine was present during irradiation no new end groups were produced.
In order to identify the nucleoside(s) at the 5'-termini, phosphate groups were removed with alkaline phosphatase and the 5'-hydroxyl groups were phosphorylated with polynucleotide kinase. Electrophoresis of enzymatic digests showed a single ³²P-labeled component migrating more rapidly than any of the four usual 5'-mononucleotides. Upon column chromatography this component resolved into a major peak coincident with 5'-dUMP and a lesser unidentified constituent. No 5'-dBUM³²P was observed among these nucleotides.     

Infrared spectral changes with crystallization in poly(vinylchloride): Correlations with X-ray and density data

The influence of crystallinity and stereoregularity on the infrared (IR) spectrum of atactic PVC in the solid state has been studied by many researchers [1-12]. Although the molecules in commercial PVC consist of both syndiotactic and isotactic sequences, the bulk polymer is not highly stereoregular, having approximately 50% syndiotacticity. Its infrared spectrum is different from that of highly syndiotactic PVC [3,5,7,9,10-12], particularly in the carbon-to-chlorine stretching region where there are three bands located at 610(615), 635, and 690 cm^?1. These three bands are known to be of complex origin, since each band consists of more than one absorption frequency and its relative intensity depends on the physical state or history of the specimen [3,5,7,9,10-12]. The spectrum in this region is most rigorously interpreted in terms of chain conformational structure, the spatial arrangement of the atoms around the C-C1 bond. Thus, while changes in absorbance intensities for the bands with history do not necessarily reflect changes in crystallinity, their history dependence renders these bands potentially useful as crystallinity indicators.     

Raman Scattering Tensors in Biological Molecules and Their Assemblies

INTRODUCTION

The tensor associated with a Raman band plays an important role in determining the band intensity and its structural significance. Each Raman tensor interrelates two electric vectors, that of the exciting radiation (i.e. laser photon) and that of the Raman scattered radiation (i.e. the inelastically scattered photon which results from the exchange of a vibrational quantum between the exciting photon and the molecule). The Raman tensor is obtained formally as the first derivative of the molecular polarizability tensor, the derivative being taken with respect to the vibrational normal coordinate. In other words, the Raman tensor associated with a vibrational Raman band is an indicator of how the polarizability of the molecule oscillates with the molecular normal mode of vibration.     

Investigating the mechanisms of diamond polishing using Raman spectroscopy

Recent research has shown that a phase transformation of diamond to a different form of carbon is involved when diamonds are polished in the traditional fashion. The question as to how this phase transformation is activated and maintained to produce high wear rates is of great technological interest since it may radically change the way we view the processing of diamond. This paper describes the use of Raman spectroscopy to examine debris produced on the diamond polishing wheel, both during its preparation and during polishing. In addition, polished diamond surfaces were examined for the possible existence of non-diamond surface layers in an attempt to identify material removal mechanisms. Raman spectroscopy proves ideal for these analyses because its relatively high spatial resolution is well suited to the analysis of small wear features and debris particles, and because of the wealth of information it reveals about chemical structure. This level of structural information has been lacking in previous analyses of diamond polishing debris. In addition to the non-diamond carbon found in the wear debris, significant quantities of two iron oxides, magnetite (Fe₃O₄) and haematite (α-Fe₂O₃), were also found. An interesting observation was that a transformation from magnetite to haematite could be induced either by using high power laser excitation or by frictional heating during polishing. It is suggested that some of the Raman peaks previously attributed to lonsdaleite might better be explained by the presence of these oxides.     

Benchmark calculations with correlated molecular wavefunctions. XIII. Potential energy curves for He2, Ne2 and Ar2 using correlation consistent basis sets through augmented sextuple zeta

The potential energy curves of the rare gas dimers He2, Ne2, and Ar2 have been computed using correlation consistent basis sets ranging from singly augmented aug-cc-pVDZ sets through triply augmented t-aug-cc-pV6Z sets, with the augmented sextuple basis sets being reported herein. Several methods for including electron correlation were investigated, namely Møller—Plesset perturbation theory (MP2, MP3 and MP4) and coupled cluster theory [CCSD and CCSD(T)]. For He2 CCSD(T)/d-aug-cc-pV6Z calculations yield a well depth of 7.35 cm-1 (10.58 K), with an estimated complete basis set (CBS) limit of 7.40 cm-1 (10.65 K). The latter is smaller than the 'exact' well depth (Aziz, R. A., Janzen, A. R., and Moldover, M. R., 1995, Phys. Rev. Lett., 74, 1586) by about 0.2 cm-1 (0.35 K). The Ne2 well depth, computed with the CCSD(T)/d-aug-cc-pV6Z method, is 28.31 cm-1 and the estimated CBS limit is 28.4 cm-1, approximately 1 cm-1 smaller than the empirical potential of Aziz, R. A., and Slaman, M., J., 1989, Chem. Phys., 130, 187. Inclusion of core and core—valence correlation effects has a negligible effect on the Ne2 well depth, decreasing it by only 0.04 cm-1. For Ar2, CCSD(T)/d-aug-cc-pV6Z calculations yield a well depth of 96.2 cm-1. The corresponding HFDID potential of Aziz, R. A., 1993, J. chem. Phys., 99, 4518 predicts of De of 99.7 cm-1. Inclusion of core and core-valence effects in Ar2 increases the well depth and decreases the discrepancy by approximately 1 cm-1.     

Polymerizable derivatives of long-chain fatty acids. IV. Vinyl esters

Contrary to some published reports, the vinyl esters of saturated fatty acids polymerize readily and rapidly. Vinyl oleate, when present in excess of 5%, and oxygen exert marked retarding effects. Techniques are described for the free-radical-initiated polymerization of the vinyl esters of caprylic, capric, lauric, myristic, palmitic, and stearic acids in bulk, dispersion, solution, and emulsion. Some data are given for polymerization in the presence of chain-transfer agents, such as carbon tetrachloride, dodecylmercaptan, and ethylbenzene. Conditions are reported for obtaining degrees of polymerization from about 2 (when chain-transfer agents are employed) to 10,000 (weight average). The weight average degree of polymerization increases markedly as the conversion increases, particularly above 80%. Even up to extremely high conversions, soluble polymers are obtained in most cases. Solubility characteristics, transition point data, molecular weights (osmometric and light-scattering), and isolation and purification techniques are also reported.     

OPTIMAL FISH HARVESTING FOR A POPULATION MODELED BY A NONLINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATION

As the human population continues to grow, there is a need for better management of our natural resources in order for our planet to be able to produce enough to sustain us. One important resource we must consider is marine fish populations. We use the tool of optimal control to investigate harvesting strategies for maximizing yield of a fish population in a heterogeneous, finite domain. We determine whether these solutions include no‐take marine reserves as part of the optimal solution. The fishery stock is modeled using a nonlinear, parabolic partial differential equation with logistic growth, movement by diffusion and advection, and with Robin boundary conditions. The objective for the problem is to find the harvest rate that maximizes the discounted yield. Optimal harvesting strategies are found numerically.