Modelling of a city canyon problem in a turbulent atmosphere using an equivalent sources approach

The sound propagation into a courtyard shielded from direct exposure is predicted using an equivalent sources approach. The problem is simplified into that of a two-dimensional city canyon. A set of equivalent sources are used to couple the free half-space above the canyon to the cavity inside the canyon. Atmospheric turbulence causes an increase in the expected value of the sound pressure level compared to a homogeneous case. The level increase is estimated using a von Kármán turbulence model and the mutual coherences of all equivalent sources' contributions. For low frequencies the increase is negligible, but at 1.6 kHz it reaches 2-5 dB for the geometries and turbulence parameters used here. A comparison with a ray-based model shows reasonably good agreement.     

Conformationally armed glycosyl donors: reactivity quantification, new donors and one pot reactions

The relative reactivity of conformationally armed thioglycosides is quantified.     

Negative Poisson's ratio materials via isotropic interactions

We show that under tension a classical many-body system with only isotropic pair interactions in a crystalline state can, counterintuitively, have a negative Poisson's ratio, or auxetic behavior. We derive the conditions under which the triangular lattice in two dimensions and lattices with cubic symmetry in three dimensions exhibit a negative Poisson's ratio. In the former case, the simple Lennard-Jones potential can give rise to auxetic behavior. In the latter case, a negative Poisson's ratio can be exhibited even when the material is constrained to be elastically isotropic.     

Optimized structures for photonic quasicrystals

A photonic quasicrystal consists of two or more dielectric materials arranged in a quasiperiodic pattern with noncrystallographic symmetry that has a photonic band gap. We use a novel method to find the pattern with the widest TM-polarized gap for two-component materials. Patterns are obtained by computing a finite sum of density waves, assigning regions where the sum exceeds a threshold to a material with one dielectric constant, epsilon1, and all other regions to another, epsilon0. Compared to optimized crystals, optimized quasicrystals have larger gaps at low constrasts epsilon1/epsilon0 and have gaps that are much more isotropic for all contrasts. For high contrasts, optimized hexagonal crystals have the largest gaps.     

Nonlinear optical and structural properties of langmuir-blodgett films of thiohelicenebisquinones

We provide a detailed investigation of the second-order nonlinear optical and structural properties of Langmuir-Blodgett (LB) films of nonracemic thiohelicenebisquinone (THBQ). We prepare both X- and Y-type films of different thicknesses and characterize them using optical second-harmonic generation and atomic-force microscopy (AFM). We find that the overall nonlinear properties of the samples are essentially independent of the film thickness and the deposition type and arise from susceptibility tensor components associated with chirality. Both X- and Y-type films can be described by D2 symmetry, which is a higher symmetry than the previously assumed C2 of LB films of THBQ and a similar helicenebisquinone (HBQ). However, the two types of films are shown to differ significantly with respect to the orientation of the in-plane axis. For Y type, the axis follows the direction of vertical sample deposition, but for X type, the direction of the axis varies randomly and significantly between different samples. The Y-type samples are therefore more ordered than the X-type samples. This was confirmed by AFM measurements in which the Y type exhibits uniform ordering into columnar structures. Similar structures in X type, on the other hand, are shorter and more randomly oriented, like those earlier observed for racemic samples of HBQ [Verbiest, T., et al. Science 1998, 282, 913]. The common nonlinear properties and different high-level ordering observed here for two different types of nonracemic samples reinforces that the nonlinearity of THBQ (and probably HBQ, as well) originates from the low-level columnar aggregation of the molecules with the higher-level structures playing a lesser role. In addition, within the columns, the molecules likely assume fairly random azimuthal orientations so that the columns themselves exhibit approximate Dinfinity symmetry.     

Schwartz spaces and compact holomorphic mappings

LetE be a locally convex space. We investigate under which conditions onE it is true that every holomorphic mapping fromE intoc ₀ is compact. We show that Schwartzity ofE is a sufficient condition and also a necessary condition ifE is quasi-normable.