Finite element three-dimensional analysis of the vibrational behaviour of the Langevin-type transducer

The vibrational behaviour of the Langevin transducer is usually analysed using 1D Mason model which is valid when the lateral dimensions of the transducer are smaller than a quarter wavelength at the fundamental longitudinal resonance. In this work a 3D finite element analysis of the Langevin transducer's behaviour operating in the underwater sonar range of frequencies (30-140 kHz) is presented. Several samples with total length greater, comparable to, and smaller than the diameter of the transducer are analysed. For each sample, the resonance frequencies in the observed frequency range are computed and compared with those obtained experimentally from the measurements carried out using several in-house built prototypes. For the most important aspect ratios the resonance displacement distributions are presented and discussed. The results obtained permit to gain insight into the coupling phenomenon between thickness-extensional and radial modes and suggest that in practical applications transducers with diameters comparable to or greater than total length of the active stack can also be used. The trade-off between the efficiency and power handling ability for different designs is also discussed.     

Study on Planar Whispering Gallery Dielectric Resonators. I. General Properties

Several basic properties of homogeneous planar Whispering Gallery dielectric resonators are investigated through a general approach. In particular the values for the minimum and maximum allowed radius, defined by irradiation and dielectric losses, respectively, are obtained in terms of the complex dielectric constant of the involved media. The same approach is employed in the analysis of the limit allowed frequencies of a fixed family of mode, leading to the definition of the ideal frequency band. The role of the transverse mode is then discussed, and the effective frequency band is introduced and determined both in simple disc and circular ring resonators. The extension of the effective band is limited at least by a factor 3, in terms of decades, in comparison to the extension of the ideal one; this limitation, due to the presence of transverse modes, can be overcome using suitable designed nonhomogeneous resonators, as discussed in a following companion paper.     

Locally compact unimodular groups with atomic duals

Milan Journal of Mathematics - A locally compact commutative group is compact if and only if its dual group is discrete, in other words if its regular representation is atomic. Nevertheless, there...     

Studies on comblike polymers. X. Characterization of comblike polyesters by 13C NMR spectroscopy

The ¹³C NMR spectra of aromatic comblike polyesters obtained from 1,2-icosanediol and isomeric phthalic acids are reported and discussed. The analysis shows that the most informative spectral regions are those of the carbonyl and quaternary carbon resonances, whose peak multiplicities have been interpreted in terms of dyad and triad sequences. The results indicate that the extent of structural characterization possible for the polymers examined is dependent on the type of isomerism of the aromatic acid involved.     

Optically active alternating copolymers of maleic anhydride and alkylvinylethers

Maleic anhydride (MAn) was copolymerized in benzene solution at 60° using AIBN with some optically active alkylvinylethers (RVE) having an asymmetric carbon atom at the α, β, γ or δ position with respect to the oxygen atom [R = (S)-1-methylpropyl, (R)-1-methylbutyl, (S)-2-methylbutyl, (S)-3-methylpentyl, (S)-4-methylhexyl, (S)-1-methylheptyl and (S)-3,7-dimethyloctyl]. Chemical compositions and solubilities of the polymeric products as well as optical rotation properties and spectroscopic measurements (i.r. and NMR) confirmed the formation of copolymers with a predominantly alternating structure. Two Cotton effects of low but definite intensity attributable to $\text{n → π}{}^1$ electronic transitions of carbonyl groups of anhydride moieties were observed between 200 and 250 nm. Failure to achieve complete cleavage of chiral side chains does not enable us to attribute the induced optical activity of anhydride moieties either to the asymmetric carbon atom present in the side chain or to the tertiary chiral centres present in the main chain or both.     

Strongly correlated superconductivity and pseudogap phase near a multiband Mott insulator

Near a Mott transition, strong electron correlations may enhance Cooper pairing. This is demonstrated in the dynamical mean field theory solution of a twofold-orbital degenerate Hubbard model with an inverted on-site Hund rule exchange, favoring local spin-singlet configurations. Close to the Mott insulator (which here is a local version of a valence bond insulator) a pseudogap non-Fermi-liquid metal, a superconductor, and a normal metal appear, in striking similarity with the physics of cuprates. The strongly correlated s-wave superconducting state has a larger Drude weight than the corresponding normal state. The role of the impurity Kondo problem is underscored.     

Nature of urea-fluoride interaction: incipient and definitive proton transfer

1,3-bis(4-nitrophenyl)urea (1) interacts through hydrogen bonding with a variety of oxoanions in an MeCN solution to give bright yellow 1:1 complexes, whose stability decreases with the decreasing basicity of the anion (CH3COO- > C6H5COO- > H2PO4- > NO2- > HSO4- > NO3-). The [Bu4N][1.CH3COO] complex salt has been isolated as a crystalline solid and its molecular structure determined, showing the formation of a discrete adduct held together by two N-H...O hydrogen bonds of moderate strength. On the other hand, the F- ion first establishes a hydrogen-bonding interaction with 1 to give the most stable 1:1 complex, and then on addition of a second equivalent, induces urea deprotonation, due to the formation of HF2-. The orange-red deprotonated urea solution uptakes carbon dioxide from air to give the tetrabutylammonium salt of the hydrogencarbonate H-bond complex, [Bu4N][1.HCO3], whose crystal and molecular structures have been determined.     

Does a Reinforced Kinetic Macrocyclic Effect Exist? The Demetallation in Strong Acid of Copper(II) Complexes with Open and Cyclic Tetramines Containing a Piperazine Fragment

The demetallation in acidic solution of the Cu(II) complexes with open-chain and cyclic tetramines containing a piperazine unit (2 and 3) has been investigated in terms of its kinetic aspects and compared with the behaviour of unsubstituted counterparts (tetramines 1 and 4). The presence of the piperazine fragment slows demetallation of the open-chain-ligand complex owing to the activation barrier associated with the conformational change from boat-to-half-boat; however, it does not affect the demetallation of the macrocyclic complex, which involves the spontaneous boat-to-twist conformational change. Thus, lateral reinforcement of a cyclam-like ligand does not add any further contribution to the typical inertness in demetallation of macrocyclic complexes.