Random Skew Plane Partitions and the Pearcey Process

We study random skew 3D partitions weighted by q ^vol and, specifically, the q → 1 asymptotics of local correlations near various points of the limit shape. We obtain sine-kernel asymptotics for correlations in the bulk of the disordered region, Airy kernel asymptotics near a general point of the frozen boundary, and a Pearcey kernel asymptotics near a cusp of the frozen boundary.     

Non-linear applications of microstructured optical fibres

The enhancement of different non-linear processes in microstructured optical fibres can be achieved through manipulation of the dispersion characteristics of the fibre. This is demonstrated by extending the region of short wavelength operation of high power supercontinuum generation through four wave mixing in a cascaded fibre geometry where the dispersion of each fibre decreased on propagation. The technique is further refined in a demonstration utilizing long lengths of dispersion decreasing tapered microstructured fibres, where the supercontinuum extends to around 300 nm with spectral power densities in excess of 2 mW/nm in the uv. These long length tapers can also be utilized for adiabatic soliton pulse compression in new spectral regions, allowing the compression of 655 fs pulses to 45 fs.     

Transfection and imaging of diamond nanocrystals as scattering optical labels

We report on the first demonstration of nanodiamond (ND) as a scattering optical label in a biological environment. NDs were efficiently transfected into cells using cationic liposomes, and imaged using differential interference and Hoffman modulation ‘space’ contrast microscopy techniques. We have shown that 55 nm NDs are biologically inert and produce a bright signal compared to the cell background. ND as a scattering label presents the possibility for extended biological imaging with relatively little thermal or biochemical perturbations due to the optical transparency and biologically inert nature of diamond.     

Study of conformations and hydrogen bonds in the configurational isomers of pyrrole‐2‐carbaldehyde oxime by 1H, 13C and 15N NMR spectroscopy combined with MP2 and DFT calculations and NBO analysis

The ¹H, ¹³C and ¹⁵N NMR studies have shown that the E and Z isomers of pyrrole‐2‐carbaldehyde oxime adopt preferable conformation with the syn orientation of the oxime group with respect to the pyrrole ring. The syn conformation of E and Z isomers of pyrrole‐2‐carbaldehyde oxime is stabilized by the N? H···N and N? H···O intramolecular hydrogen bonds, respectively. The N? H···N hydrogen bond in the E isomer causes the high‐frequency shift of the bridge proton signal by about 1 ppm and increase the ¹J(N, H) coupling by ～3 Hz. The bridge proton shows further deshielding and higher increase of the ¹J(N, H) coupling constant due to the strengthening of the N? H···O hydrogen bond in the Z isomer. The MP2 calculations indicate that the syn conformation of E and Z isomers is by ～3.5 kcal/mol energetically less favorable than the anti conformation. The calculations of ¹H shielding and ¹J(N, H) coupling in the syn and anti conformations allow the contribution to these constants from the N? H···N and N? H···O hydrogen bondings to be estimated. The NBO analysis suggests that the N? H···N hydrogen bond in the E isomer is a pure electrostatic interaction while the charge transfer from the oxygen lone pair to the antibonding orbital of the N? H bond through the N? H···O hydrogen bond occurs in the Z isomer. Copyright © 2010 John Wiley & Sons, Ltd.     

Hahn-echoes from N in solids by the stray-field method: prospects for imaging using Long Echo-Train Summation

We have observed Hahn-echoes resulting from Powles–Mansfield pulse-sequences for a variety of nitrogen containing solids which exhibit a range of ¹⁴N electric quadrupole coupling constants (C_q) from 0 to 4.9 MHz. Long echo-decays were frequently obtained which allowed the collection of many echoes in one echo-train, so that the method of Long Echo-Train Summation (LETS), could be used to accumulate signal. A one-dimensional STRAFI-profile is shown for solid ammonium nitrate. The spatial resolution is discussed as a function of C_q.     

Analysis for an N-stepped Rayleigh bar with sections of complex geometry

In this paper we analyse the vibrations of an N-stepped Rayleigh bar with sections of complex geometry, supported by end lumped masses and springs. Equations of motion and boundary conditions are derived from the Hamilton’s variational principal. The solutions for tapered and exponential sections are given. Two types of orthogonality for the eigenfunctions are obtained. The analytic solution to the N-stepped Rayleigh model is constructed in terms of Green function.