A dipole loudspeaker with a balanced directivity pattern

Analytical equations describing radiation characteristics of an oscillating ring in a circular finite baffle are derived, including the limiting case of a dipole point source at the center. An oscillating sphere would represent the ideal dipole source, having a constant directivity pattern at all frequencies, but would be inconvenient to realize especially in portable devices. It is found that a planar piston with uniform surface velocity but variable phase arranged to emulate the sphere does not have such a smooth on-axis response as the sphere. Instead a planar piston with the same phase distribution but uniform pressure represents an ideal planar source with a smooth on-axis response and near constant directivity. The surface velocity is plotted and it is then shown that a similar response can be achieved using a finite number of concentric rings based on this velocity distribution.     

A two-dimensional cochlear fluid model based on conformal mapping

Using conformal mapping, fluid motion inside the cochlear duct is derived from fluid motion in an infinite half plane. The cochlear duct is represented by a two-dimensional half-open box. Motion of the cochlear fluid creates a force acting on the cochlear partition, modeled by damped oscillators. The resulting equation is one-dimensional, more realistic, and can be handled more easily than existing ones derived by the method of images, making it useful for fast computations of physically plausible cochlear responses. Solving the equation of motion numerically, its ability to reproduce the essential features of cochlear partition motion is demonstrated. Because fluid coupling can be changed independently of any other physical parameter in this model, it allows the significance of hydrodynamic coupling of the cochlear partition to itself to be quantitatively studied. For the model parameters chosen, as hydrodynamic coupling is increased, the simple resonant frequency response becomes increasingly asymmetric. The stronger the hydrodynamic coupling is, the slower the velocity of the resulting traveling wave at the low frequency side is. The model's simplicity and straightforward mathematics make it useful for evaluating more complicated models and for education in hydrodynamics and biophysics of hearing.     

Diosphenol-based approach to the a-ring functionalization of advanced Taxol precursors

Several different approaches to the A-ring functionalization of an advanced, highly functionalized diosphenol precursor to Taxol are described. The first phase of the undertaking consists of an assessment of those reagents conducive to reaction at the enolic oxygen (silylation, methylation, allylation, and acylation). Transformations involving an alternative attack at the enol carbon center (bromination, selenation) have also been defined. Sodium borohydride reduction operates from the beta-face of C-14 as long as the C-1 hydroxyl is not protected so as to offer steric exclusion. Complications associated with various aspects of these methodological undertakings are addressed. The most advanced oxygenation achievements were realized by way of a noteworthy sequence involving epoxidation of the O-methyl ether, methanolysis under mildly acidic conditions, and regioselective oxidation of diol 38 to give 39.     

Snake's perspective on heat: reconstruction of input using an imperfect detection system

Two groups of snakes possess an infrared detection system that is used to create a heat image of their environment. In this Letter we present an explicit reconstruction model, the "virtual lens," which explains how a snake can overcome the optical limitations of a wide aperture pinhole camera, and how ensuing properties of the receptive fields on the infrared-sensitive membrane may explain the behavioral performance of this sensory system. Our model explores the optical quality of the infrared system by detailing how a functional representation of the thermal properties of the environment can be created. The model is easy to implement neuronally and agrees well with available neuronal, physiological, and behavioral data on the snake infrared system.     

Superfluid transition in a rotating fermi gas with resonant interactions

We study a rotating atomic Fermi gas near a narrow s-wave Feshbach resonance in a uniaxial trap with frequencies Omega perpendicular, Omega z. We predict the upper-critical angular velocity, omega c2(delta,T), as a function of temperature T and detuning delta across the BEC-BCS crossover. The suppression of superfluidity at omega c2 is distinct in the BCS and BEC regimes, with the former controlled by depairing and the latter by the dilution of bosonic molecules. At low T and Omega z < Omega perpendicular, in the BCS and crossover regimes of 0 less similar delta less similar delta c, omega c2 is implicitly given by [formula: see text], vanishing as omega c2 approximately Omega perpendicular(1 - delta/delta c)(1/2) near [formula: see text] (with Delta the BCS gap and gamma the resonance width), and extending the bulk result variant Planck's over 2pi omega c2 approximately 2Delta2/epsilonF to a trap. In the BEC regime of delta < 0 we find omega c2-->Omega perpendicular-, where molecular superfluidity is destroyed only by large quantum fluctuations associated with comparable boson and vortex densities.     

Thermodynamics of Complexation of Alkali Metal Cations by a Lower-Rim Calix[4]arene Amino Acid Derivative

Complexation of alkali metal cations with 5,11,17,23-tetra-tert-butyl-26,28,25,27-tetrakis(O-methyl-d-α-phenylglycylcarbonylmethoxy)calix[4]arene (L) in methanol and acetonitrile was studied by means of direct and competitive microcalorimetric titrations at 25 °C. The thermodynamic parameters of complexation reactions showed that all the reactions investigated were enthalpically controlled. In both solvents the reaction enthalpy was most favorable for Na⁺ binding with L leading to the highest affinity of the examined calix[4]arene derivative towards this cation. The solubilities (and consequently the solution Gibbs energies) of the ligand were determined, as were the corresponding solution enthalpies and entropies. No significant difference was observed between the solution thermodynamic quantities of L in the two solvents, whereas the transfer of complex species from methanol to acetonitrile was found to be quite favorable. The interactions of solvent molecules with the free and the complexed ligand were investigated by ¹H NMR spectroscopy. It was concluded that in both cases inclusion of an acetonitrile molecule into the hydrophobic cavity of L occurred, which significantly affected the cation complexation in this solvent. The thermodynamic data were discussed regarding the structural properties of the ligand, the free and the complexed cations as well as the solvation abilities of the solvents examined. In this respect, the specific solvent-solute interactions and the intramolecular NH⋅⋅⋅O=C hydrogen bonds at the lower rim of L were particularly addressed.     

Gas Phase H/D Exchange of Sodiated Amino Acids: Why Do We See Zwitterions?

The gas-phase interaction of sodiated amino acids and sodiated amino acid methyl esters with various deuterium donors is investigated by combining results of H/D exchange reactions with those from density functional theory and molecular dynamics calculations. Discrepancy between experimentally and theoretically obtained structures for sodium cationized amino acids is explained by deuterium donor caused perturbation of the most stable amino acid conformation. Detailed study of H/D exchange mechanism on sodiated amino acids shows that the H/D exchange reaction is preceded by a multistep quasi-isoenergetic transition (perturbation) from a charge solvated to zwitterionic structure in the amino acid. Although the computation refers to the system AlaNa(+) and D(2)O, these mechanisms apply to all amino acids, except those where a functional side-chain group takes part in the perturbation process. The suggested perturbation mechanism applies also for other deuterium donors such as CD(3)OD or even ND(3) and indicates that a single water molecule suffices to convert the sodiated amino acid from charge solvated to zwitterionic form.     

Direct comparison of the response of bicyclic sultam and lactam dienes to photoexcitation. Concerning the propensity of differing bond types to bridgehead nitrogen for homolytic cleavage

A convergent strategy has allowed access to bridgehead sultam 9 and the related carboxamides 10 and 11. The synthetic routing proceeds via the coupling of a suitably constructed dienamine to either o-iodobenzenesulfonyl chloride or o-iodobenzoyl chloride to generate the amides. The application in sequence of ring-closing metathesis and an intramolecular Heck reaction gave rise to advanced tricyclic intermediates. The final two steps involved bromination in liquid bromine and proper 2-fold dehydrobromination. The latter maneuver was best achieved with tetrabutylammonium fluoride in DMSO at elevated temperature. While the irradiation of 9 led principally via SO2-N bond homolysis and [1,5] sigmatropic rearrangement to generate 37, 10 proceeded via disrotatory cyclization to the exo cyclobutene 39, and 11 resisted photoisomerization. The inertness of 11 may stem from its distorted structural features which force its conjugated diene double bonds to be rigidly oriented 32 degrees out-of-plane. The unique ability of the sulfonamide linkage to excited-state homolysis holds comparative interest.     

Gas-phase regiocontrolled generation of charged amino acid and peptide radicals

The combined use of advanced mass spectrometry experiments, condensed-phase synthesis of serine and homoserine nitrate ester radical precursors, and high-level ab initio calculations provides a powerful way of examining the fundamental reactivity of radicals derived from peptides.