Application of the pseudo-spectral method to 2D eigenvalue problems in elasticity

A pseudo-spectral approach to 2D vibrational problems arising in linear elasticity is considerede using differentiation matrices. The governing partial differential equations and associated boundary conditions on regular domains can be translated into matrix eigenvalue problems. Accurate results are obtained to the precision expected in spectral-type methods. However, we show that it is necessary to apply an additional “pole” condition to deal with ther=0 coordinate singularity arising in the case of a 2D disc.     

The kinetics of the epoxy amine cure reaction from a solvation perspective

This article investigates the role of solvation effects in the autocatalysis reaction of the epoxy–amine cure reaction. A single‐phase three component model was developed encompassing a two‐component reaction mix and a single polymeric product. The reaction was modelled as an S_N2 reaction. Association of the nucleophile with each component in the reaction was defined via a binding constant. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3579–3586, 2004     

Direct measurement of mixture fraction in reacting flow using Rayleigh scattering

The mixture fraction variable, , is very useful in describing reaction zone structure in nonpremixed flames. Extinction limits and turbulent mixing are often described as a function of this variable. Experimental evaluation of is critical for improving our understanding of the influence of turbulent mixing on the chemistry process. Heretofore, the evaluation of mixture fraction in combusting flow required multiple simultaneous concentration measurements. In this paper we present a fuel designed to permit measurements of mixture fraction by Rayleigh scattering technique only. A Rayleigh intensity/mixture fraction correspondence has been obtained experimentally in a laminar coflow flame. The influence of strain rate and differential diffusion effects have been investigated using laminar counterflow diffusion flame and shifting equilibrium chemistry models. The results obtained from comparisons between experiments and these models are very encouraging and suggest that the Rayleigh/mixture fraction correspondence established is valid under both the turbulent mixing and laminar strained flamelet combustion regimes.     

Operational Research and the Control of Value Added Tax

This case study in Value Added Tax (VAT) is concerned with organising the activities of some 4000 staff in safeguarding the £billions of tax revenue paid by 1¼ million registered traders. VAT control is achieved principally at traders' premises by a system of verifications to ensure that the traders' tax returns are correct and that their tax accounts are adequate. The scale of the operation can be appreciated from the fact that annually over 300,000 visits are made, resulting in the recovery of more than £100 million of under-declared tax. The project consisted of systematically collecting and analysing data pertaining to the visits made to traders and re-allocating control resources according to factors which were found to relate strongly to the tax behaviour of groups of traders. Keeping the techniques simple allowed management to play a full part in the research and led to the ready implementation of the results.     

Self-assembled growth of nanostructural Ge islands on bromine-passivated Si(111) surfaces at room temperature

We have deposited relatively thick (∼60 nm) Ge layers on Br-passivated Si(111) substrates by thermal evaporation under high vacuum conditions at room temperature. Ge has grown in a layer-plus-island mode although it is different from the Stranski-Krastanov growth mode observed in epitaxial growth. Both the islands and the layer are nanocrystalline. This appears to be a consequence of reduction of surface free energy of the Si(111) substrate by Br-passivation. The size distribution of the Ge nanoislands has been determined. The Br-Si(111) substrates were prepared by a liquid treatment, which may not produce exactly reproducible surfaces. Nevertheless, some basic features of the nanostructural island growth are reasonably reproducible, while there are variations in the details of the island size distribution.     

Prime numbers and the first digit phenomenon

The set of primes which have lead digit 1 does not have relative natural density in the prime numbers. However, Bombieri has shown that this set does have relative Zeta density equal to log₁₀ 2. This means that a prime chosen at random (w.r.t. the Zeta distribution) will have lead digit 1 with the determined probability. Here the question, Is this a special property of Zeta density or a more universal property of primes? is answered. It is shown that for any generalization of relative natural density (obeying a few basic assumptions) if a value is assigned to the relative density of primes of lead digit 1 then this value is always log₁₀ 2. Another density which does converge on this set is also exhibited. Additionally the relative densities of primes beginning with any specified string of digits are found.     

A mild copper catalyzed method for the selective deprotection of aryl allyl ethers

Copper boryl reagents enable the selective cleavage of aryl allyl ethers to the corresponding phenols in good to moderate yields.     

Electrochemical modification of vertically aligned carbon nanotube arrays

Electrochemical oxidation and reduction were utilized to modify vertically aligned carbon nanotube (CNT) arrays grown on a porous network of conductive carbon microfibers. Ultrafast and complete CNT opening and purification were achieved through electrochemical oxidation. Highly dispersed platinum nanoparticles were then uniformly and densely deposited as electrocatalysts onto the surface of these CNTs through electrochemical reduction. Using supercritical drying techniques, we demonstrate that the unidirectionally aligned and laterally spaced geometry of the CNT arrays can be fully retained after being subjected to each step of electrochemical modification. The open-tipped CNTs can also be electrochemically detached in full lengths from the supporting substrates and harvested if needed.     

Application of the Pseudo-Spectral Method to 2D Eigenvalue Problems in Elasticity

A pseudo-spectral approach to 2D vibrational problems arising in linear elasticity is considered using differentiation matrices. The governing partial differential equations and associated boundary conditions on regular domains can be translated into matrix eigenvalue problems. Accurate results are obtained to the precision expected in spectral-type methods. However, we show that it is necessary to apply an additional pole condition to deal with the r=0 coordinate singularity arising in the case of a 2D disc.     

TDP-43 expression in mouse models of amyotrophic lateral sclerosis and spinal muscular atrophy

Background  

Redistribution of nuclear TAR DNA binding protein 43 (TDP-43) to the cytoplasm and ubiquitinated inclusions of spinal motor neurons and glial cells is characteristic of amyotrophic lateral sclerosis (ALS) pathology. Recent evidence suggests that TDP-43 pathology is common to sporadic ALS and familial ALS without SOD1 mutation, but not SOD1-related fALS cases. Furthermore, it remains unclear whether TDP-43 abnormalities occur in non-ALS forms of motor neuron disease. Here, we characterise TDP-43 localisation, expression levels and post-translational modifications in mouse models of ALS and spinal muscular atrophy (SMA).