On the inversion of diffusion NMR data: Tikhonov regularization and optimal choice of the regularization parameter

The analysis of diffusion NMR data in terms of distributions of diffusion coefficients is hampered by the ill-posed nature of the required inverse Laplace transformation. Na?ve approaches such as multiexponential fitting or standard least-squares algorithms are numerically unstable and often fail. This paper updates the CONTIN approach of the application of Tikhonov regularization to stabilise this numerical inversion problem and demonstrates two methods for automatically choosing the optimal value of the regularization parameter. These approaches are computationally efficient and easy to implement using standard matrix algebra techniques. Example analyses are presenting using both synthetic data and experimental results of diffusion NMR studies on the azo-dye sunset yellow and some polymer molecular weight reference standards.     

Empirical correction of crosstalk in a low-background germanium γ–γ analysis system

The Pacific Northwest National Laboratory (PNNL) is currently developing a custom software suite capable of automating many of the tasks required to accurately analyze coincident signals within gamma spectrometer arrays. During the course of this work, significant crosstalk was identified in the energy determination for spectra collected with a new low-background intrinsic germanium (HPGe) array at PNNL. The HPGe array is designed for high detection efficiency, ultra-low-background performance, and sensitive γ–γ coincidence detection. The first half of the array, a single cryostat containing seven HPGe crystals, was recently installed into a new shallow underground laboratory facility. This update will present a brief review of the germanium array, describe the observed crosstalk, and present a straight-forward empirical correction that significantly reduces the impact of this crosstalk on the spectroscopic performance of the system.     

Femtosecond fabrication of waveguide-like micro-structures in a photorefractive polymer

In this letter, we report on, for the first time, the successful femtosecond micro-fabrication of continuous waveguide-like channels in the photorefractive polymer consisting of the nonlinear chromophore 2,5-dimethyl-4-(p-nitrophenylazo)anisole (DMNPAA), the photosensitive compound 2,4,7-trinitro-9-flourenone (TNF), and the plasticiser N-ethylcarbazole (ECZ) all doped in the polymer matrix poly (methyl methacry-late) (PMMA). These channels are caused by the change in refractive index as a result of the localised heating of the polymer and therefore have an important potential for micro-photonic devices in future.     

Simple Singularities for Hamilton-Jacobi Equations with Max-Concave Hamiltonians and Generalized Characteristics

We consider piecewise smooth viscosity solutions to a Hamilton-Jacobi equation, for which the Hamiltonian is the maximum of a finite number of smooth concave functions. We describe the possible types of “basic” singularities, namely jump discontinuities in either the derivative of the solution or the Hamiltonian, which occur across a smooth hypersurface. Each such type of singularity is described in terms of the properties of the Hamiltonian and the classical characteristics in the regions on either side of the singularity. Where appropriate, singular characteristic equations of the types developed by Melikyan are formulated which can be used in constructions.     

Optimization of Oligosaccharide Synthesis from Cellobiose by Dextransucrase

There is a growing market for oligosaccharides as sweeteners, prebiotics, anticariogenic compounds, and immunostimulating agents in both food and pharmaceutical industries. Interest in novel carbohydrate-based products has grown because of their reduced toxicity and low immune response. Cellobiose is potentially valuable as a nondigestible sugar. The reaction of cellobiose, as an acceptor with a sucrose as a donor, catalyzed by a dextransucrase from Leuconostoc mesenteroides B-512FMCM, produced a series of cellobio-oligosaccharides. This production system was optimized using a Box–Behnken experimental design for 289 mM of sucrose and 250 mM of cellobiose and 54 U of the enzyme at pH 5.2 and 30 °C, to produce maximum yields of oligosaccharide.     

The uncatalyzed hydrosilation reaction

Summary The reactions of ethylene with silane, chlorosilane, fluorosilane, and dichlorosilane, and of propylene with silane are considered usingab initio electronic structure calculations. At both the MP2 and MP4 levels of theory with both DZP and TZP quality basis sets, the energy barriers for all reactions are found to be in excess of 50 kcal/mol.