Higher‐order analogues of the Tracy‐Widom distribution and the Painlevé II hierarchy

We study Fredholm determinants related to a family of kernels that describe the edge eigenvalue behavior in unitary random matrix models with critical edge points. The kernels are natural higher‐order analogues of the Airy kernel and are built out of functions associated with the Painlevé I hierarchy. The Fredholm determinants related to those kernels are higher‐order generalizations of the Tracy‐Widom distribution. We give an explicit expression for the determinants in terms of a distinguished smooth solution to the Painlevé II hierarchy. In addition, we compute large gap asymptotics for the Fredholm determinants. © 2009 Wiley Periodicals, Inc.     

The effect of bond length variations in molecular orbital calculations of π-electron spectra—Aniline

The effect of bond length changes on ground and excited state energies is examined. The results are applied to aniline.     

3D high-resolution acoustic imaging of the sub-seabed

Chirp sub-bottom profilers are marine acoustic devices that use a known and repeatable frequency-modulated source signature to produce vertical seismic reflection cross-sections of the sub-seabed. Here a 3D Chirp system is described that operates in the frequency range of 1.5-13 kHz, to produce a three-dimensional image of the sub-seabed, with typical penetration of 10-30 m and decimetric horizontal and vertical resolution. The system design incorporates a rigid frame that contains the Chirp source array together with 60 receiver elements, with positioning provided by an integrated real-time-kinematic (RTK) global positioning system (GPS). The system can be surface towed from a small survey vessel and can be applied to targets of marine geological, engineering, archaeological and defence interest. Data acquisition and processing are described for a case study which images a buried engineering structure in the Port of Southampton.     

The effect of different catalytic chain transfer agents on particle nucleation and the course of the polymerization in ab initio batch emulsion polymerization of methyl methacrylate

The effect a Co(II) based catalytic chain transfer agent (CCTA) has on the course of the polymerization and the product properties of an emulsion polymerization is governed by the intrinsic activity and the partitioning behavior of the catalyst. The effect on the conversion time history, the molecular weight distribution and the particle size distribution is evaluated in batch emulsion polymerization of methyl methacrylate for three different CCTAs, which cover a range of intrinsic activities and partitioning behaviors. It was demonstrated that radical desorption from the particle phase to the aqueous phase preceded by chain transfer is the main kinetic event controlling the course of the polymerization and the product properties in terms of the particle size distribution. The experimental results show that the aqueous phase solubility of the CCTA is the key parameter controlling the course of the polymerization and the particle size distribution. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1038–1048, 2010