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.     

Subword complexes in Coxeter groups

Let (Π,Σ) be a Coxeter system. An ordered list of elements in Σ and an element in Π determine a subword complex, as introduced in Knutson and Miller (Ann. of Math. (2) (2003), to appear). Subword complexes are demonstrated here to be homeomorphic to balls or spheres, and their Hilbert series are shown to reflect combinatorial properties of reduced expressions in Coxeter groups. Two formulae for double Grothendieck polynomials, one of which appeared in Fomin and Kirillov (Proceedings of the Sixth Conference in Formal Power Series and Algebraic Combinatorics, DIMACS, 1994, pp. 183-190), are recovered in the context of simplicial topology for subword complexes. Some open questions related to subword complexes are presented.     

Tuning the band gap in hybrid tin iodide perovskite semiconductors using structural templating

Structural distortions within the extensive family of organic/inorganic hybrid tin iodide perovskite semiconductors are correlated with their experimental exciton energies and calculated band gaps. The extent of the in- and out-of-plane angular distortion of the SnI4(2-) perovskite sheets is largely determined by the relative charge density and steric requirements of the organic cations. Variation of the in-plane Sn-I-Sn bond angle was demonstrated to have the greatest impact on the tuning of the band gap, and the equatorial Sn-I bond distances have a significant secondary influence. Extended Hückel tight-binding band calculations are employed to decipher the crystal orbital origins of the structural effects that fine-tune the band structure. The calculations suggest that it may be possible to tune the band gap by as much as 1 eV using the templating influence of the organic cation.     

Elongated silica nanoparticles with a mesh phase mesopore structure by fluorosurfactant templating

Mesoporous silica materials with pore structures such as 2D hexagonal close packed, bicontinuous cubic, lamellar, sponge, wormhole-like, and rectangular have been made by using surfactant templating sol-gel processes. However, there are still some "intermediate" phases, in particular mesh phases, that are formed by surfactants but which have not been made into analogous silica pore structures. Here, we describe the one-step synthesis of mesoporous silica with a mesh phase pore structure. The cationic fluorinated surfactant 1,1,2,2-tetrahydroperfluorodecylpyridinium chloride (HFDePC) is used as the template. Like many fluorinated surfactants, HFDePC forms intermediate phases in water (including a mesh phase) over a wider range of compositions than do hydrocarbon surfactants. The materials produced by this technique are novel elongated particles in which the layers of the mesh phase are oriented orthogonal to the main axis of the particles.     

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.