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.     

Near-infrared spectrophotometric determination of compositions of fullerene samples

A novel method has been developed for the sensitive and accurate determination of compositions of fullerene samples. The method is based on the synergistic use of spectrophotometric measurements and partial least square method. The method is not only simple, inexpensive and fast but also is non-destructive. Compositions of various fullerene samples including fullerite which is the precursor to C(60) and C(70), can be directly and non-destructively determined by this method without any time-consuming separation step as in the HPLC method or destruction as in the MS method.     

Radical polymerization of methyl methacrylate in the presence of stereoregular poly(methyl methacrylate). V. Kinetics of initial template polymerization

The influence of stereoregular poly(methyl methacrylate) (PMMA) as a polymer matrix on the initial rate of radical polymerization of methyl methacrylate (MMA) has been measured between ?11 and +60°C using a dilatometric technique. Under proper conditions an increase in the relative initial rate of template polymerization with respect to a blank polymerization was observed. Viscometric studies showed that the observed effect could be related to the extent of complex formation between the polymer matrix and the growing chain radical. The initial rate was dependent on tacticity and molecular weight of the matrix polymer, solvent type and polymerization temperature. The accelerating effect was most pronounced (a fivefold increase in rate) at the lowest polymerization temperature with the highest molecular weight isotactic PMMA as a matrix in a solvent like dimethylformamide (DMF), which is known to be a good medium for complex formation between isotactic and syndiotactic PMMA. The acceleration of the polymerization below 25°C appeared to be accompanied by a large decrease in the overall energy and entropy of activation. It is suggested that the observed template effects are mainly due to the stereoselection in the propagation step (lower activation entropy Δ S_p^?) and the hindrance of segmental diffusion in the termination step (higher activation energy Δ E_t^?) of complexed growing chain radicals.     

Magnetic switch of permeability for polyelectrolyte microcapsules embedded with Co@Au nanoparticles

We explored using a magnetic field to modulate the permeability of polyelectrolyte microcapsules prepared by layer-by-layer self-assembly. Ferromagnetic gold-coated cobalt (Co@Au) nanoparticles (3 nm diameter) were embedded inside the capsule walls. The final 5 mum diameter microcapsules had wall structures consisting of 4 bilayers of poly(sodium styrene sulfonate)/poly(allylamine hydrochloride) (PSS/PAH), 1 layer of Co@Au, and 5 bilayers of PSS/PAH. External alternating magnetic fields of 100-300 Hz and 1200 Oe were applied to rotate the embedded Co@Au nanoparticles, which subsequently disturbed and distorted the capsule wall and drastically increased its permeability to macromolecules like FITC-labeled dextran. The capsule permeability change was estimated by taking the capsule interior and exterior fluorescent intensity ratio using confocal laser scanning microscopy. Capsules with 1 layer of Co@Au nanoparticles and 10 polyelectrolyte bilayers are optimal for magnetically controlling permeability. A theoretical explanation was proposed for the permeability control mechanisms. "Switching on" of these microcapsules using a magnetic field makes this method a good candidate for controlled drug delivery in biomedical applications.     

Inhomogeneity in Distribution and Conformation of Bovine Serum Albumin in Sol–Gel: A Closer Look with a Near-Infrared Multispectral Imaging Technique

Concentration distributions and conformations of bovine serum albumin (BSA) entrapped in sol–gels were successfully determined for the first time by use of the recently developed NIR multispectral imaging instrument. It was found that BSA molecules were inhomogeneously distributed within the sol–gel matrix, independent of its concentration. At relatively high concentration (366 mg/mL) the encapsulation process does not seem to produce any observable changes in the conformation of BSA. However, when the concentration of BSA was decreased to 220 mg/mL, pronounced changes in the spectra of the protein were observed as a function of (sol–gel reaction) time. The observed inhomogenity might be traced to both a non-uniform concentration distribution of BSA and changes in protein native conformation resulting from interactions between the charged protein and the silicate anions. Results obtained seem to suggest that the protein molecules might adapt themselves to accommodate evolving geometry and sites of the silica network.     

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.