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.     

Low-lying energy levels of the FeH molecule

Multireference configuration interaction (MRCI) and complete active space second-order perturbation theory (CASPT2) calculations are performed on Fe₂ and Fe^? ₂. Although it is not possible to definitively identify the ground states of Fe₂ and Fe^? ₂, the calculations suggest that the ground state of Fe^? ₂ in ⁸Σ^? _u derived from 3d¹³4σ² _g4σ² _u and that the states observed in photodetachment are the ⁹Σ^? _g and ⁷Σ^? _g states with a 3d¹³4σ² _g4σ¹ _u occupation, but that the ground state of Fe₂ is ⁷Δ_u(3d¹⁴4σ² _g) and is not observed in the photo-detachment spectra.     

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.     

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.     

Thermal Characterizations of Inorganic and Organometallic Polymers

This review emphasizes the breadth of metallic and metallic-like polymers evaluated as to thermal properties. Techniques usefully applied to particular systems are noted with the aim of suggesting their application to other systems.     

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.     

Gårding's Theory of Hyperbolic Polynomials

This paper presents a simple, self‐contained account of Gårding's theory of hyperbolic polynomials, together with a recent convexity result of Bauschke‐Güler‐Lewis‐Sendov and an inequality of Gurvits. This account begins by establishing some new results. The first concerns the existence of a pointwise arrangement of the eigenvalues so that they become global real analytic functions. The second asserts that the associated “branches” are independent of the choice of hyperbolic direction. © 2013 Wiley Periodicals, Inc.