Classical and nonclassical symmetries of a generalized Boussinesq equation

We apply the Lie-group formalism and the nonclassical method due to Bluman and Cole to deduce symmetries of the generalized Boussinesq equation, which has the classical Boussinesq equation as an special case. We study the class of functions $f(u)$ for which this equation admit either the classical or the nonclassical method. The reductions obtained are derived. Some new exact solutions can be derived

High-power diode-bar-pumped Nd:YLF laser at 1.053-µm

Scaling diode-pumped solid-state lasers to multiwatt average power levels is an area which has attracted growing interest over recent years, stimulated by the wide commercial availability and relatively low cost of high-power cw diode-bar pump sources. Recent developments in this area have included; efficient, TEM00, end-pumped Nd:YVO4 and side-pumped Nd:YLF lasers at 1.064µm and 1.047µm respectively with cw powers in excess of 13W. So far, the scaling of diode-pumped solid-state lasers to >10W average power, whilst retaining high overall efficiency has generally been restricted to only the highest gain Nd transitions. Extension of efficient high average power operation to include other useful, but lower gain, transitions such as the 1.053µm transition in Nd:YLF, has been hindered by the inconvenient shape of the diode bar's output beam. The diode bar, with its highly elongated emitting region produces an output having M2 beam quality factors ~1 in the plane perpendicular to the array, but >1000 in the plane of the array. It is therefore difficult to focus to the small beam sizes required, particularly for low gain transitions in efficient end-pumped configurations

Symmetries of a class of nonlinear fourth order partial differential equations

In this paper we study symmetry reductions of a class of nonlinear fourth order partial differential equations \be u_{tt} = \left(\kappa u + \gamma u^2\right)_{xx} + u u_{xxxx} +\mu u_{xxtt}+\alpha u_x u_{xxx} + \beta u_{xx}^2, \ee where $\alpha$, $\beta$, $\gamma$, $\kappa$ and $\mu$ are constants. This equation may be thought of as a fourth order analogue of a generalization of the Camassa-Holm equation, about which there has been considerable recent interest. Further equation (1) is a ``Boussinesq-type'' equation which arises as a model of vibrations of an anharmonic mass-spring chain and admits both ``compacton'' and conventional solitons. A catalogue of symmetry reductions for equation (1) is obtained using the classical Lie method and the nonclassical method due to Bluman and Cole. In particular we obtain several reductions using the nonclassical method which are no} obtainable through the classical method

Halide Control of N,N-Coordination versus N,C-Cyclometalation and Stereospecific Phenyl Ring Deuteration of Osmium(II) p-Cymene Phenylazobenzothiazole Complexes

YesWe report the synthesis of halido Os(II) p-cymene complexes bearing bidentate chelating phenylazobenzothiazole (AZBTZ) ligands. Unlike the analogous phenylazopyridine (AZPY) complexes, AZBTZ-NMe2 is capable of both N,N-coordination to Os(II) and cyclometalation to form N,C-coordinated species. N,C-Coordination occurs via an azo nitrogen and an ortho carbon on the aniline ring, as identified by 1H NMR and X-ray crystallography of [Os(p-cym)(N,N-AZBTZ-NMe2)Cl]PF6 (1a), [Os(p-cym)(N,N-AZBTZ-NMe2)Br]PF6 (2a), [Os(p-cym)(N,C-AZBTZ-NMe2)Br] (2b), and [Os(p-cym)(N,C-AZBTZ-NMe2)I] (3b). The N,C-coordinated species is more stable and is not readily converted to the N,N-coordinated complex. Analysis of the crystal structures suggests that their formation is influenced by steric interactions between the p-cym and AZBTZ-NMe2 ligands: in particular, larger monodentate halide ligands favor N,C-coordination. The complexes [Os(p-cym)(N,N-Me2-AZBTZ-NH2)Cl]PF6 (4) and [Os(p-cym)(N,N-Me2-AZBTZ-NH2)I]PF6 (5) were synthesized with methyl groups blocking the ortho positions on the aniline ring, forcing an N,N-coordination geometry. 1H NMR NOE experiments confirmed hindered rotation of the arene ligand and steric crowding around the metal center. Complex 2b exhibited unexpected behavior under acidic conditions, involving regiospecific deuteration of the aniline ring at the meta position, as observed by 1H NMR and high-resolution ESI-MS. Deuterium exchange occurs only under acidic conditions, suggesting an associative mechanism. The calculated partial charges on 2b show that the meta carbon is significantly more negatively charged, which may account for the regiospecificity of deuterium exchange.ERC, EPSRC, The Royal Societ

Probing the time dependence of dark energy

A new method to investigate a possible time-dependence of the dark energy equation of state $w$ is proposed. We apply this methodology to two of the most recent data sets of type Ia supernova (Union2 and SDSS) and the baryon acoustic oscillation peak at $z = 0.35$. For some combinations of these data, we show that there is a clear departure from the standard $\Lambda$CDM model at intermediary redshifts, although a non-evolving dark energy component ($dw/dz = 0$) cannot be ruled out by these data. The approach developed here may be useful to probe a possible evolving dark energy component when applied to upcoming observational data.Comment: 6 pages, 3 figures, LaTe

Coal and Coal Constituent Studies by Advanced EMR Techniques.

Advanced electronic magnetic resonance (EMR) methods are used to examine properties of coals, chars, and molecular species related to constituents of coal. During this grant period, progress was made on a high frequency EMR system particularly appropriate for such studies and on low-frequency dynamic nuclear polarization (DNP) to examine the interaction between fluids such as water and the surface of suspended char particles

The role of simulation in designing for universal access

It is known that the adoption of user-centred design processes can lead to more universally accessible products and services. However, the most frequently cited approach to user-centred design, i.e. participatory design, can be both problematic and expensive to implement., particularly over the difficulty of finding and recruiting suitable participants. Simulation aids offer a potentially cost-effective replacement or complement to participatory design. This paper examines a number of the issues associated with the use of simulation aids when designing for Universal Access. It concludes that simulation aids can play an effective role, but need to be used with due consideration over what insights they provide

Systems mapping workshops and their role in understanding medication errors in healthcare

In this paper for Applied Ergonomics, one of the two leading journals for ergonomics/human factors, Buckle et al. discuss the role of mapping workshops in understanding medication errors in healthcare. They draw upon research that used mapping workshops as a method that systems designers, including human factors/ergonomics specialists, can use to help generate a knowledge base for better design requirements. Buckle et al. applied systems mapping workshops for the first time to the problem of medication errors in healthcare. The workshops were designed using experiential group work principles. They involved a range of stakeholders from within the health service as well as those who supply the health sector, including designers who may be able to enhance the safety of products and systems used in healthcare. The opportunity for using these methods to study patient safety issues arose as a result of a scoping study undertaken on behalf of the UK Department of Health and The Design Council. As the scope of patient safety issues within the healthcare system and the range of stakeholder groups is large (National Patient Safety Agency 2005), it was believed that mapping workshops might enhance system design in health. The results were rich from a design perspective, giving specific details of actual incidences, contexts and practices, with further depth of information emerging in the group working sessions. A wealth of detail on aspects of medication error, especially in the community, emerged from creative, primary, secondary and patient-support group sessions. As a process, similar stakeholder workshops could help designers understand better the complexity and range of factors to be taken into account. The methods are now being used in many areas of healthcare and social care design, for example by the Technology Strategy Board funded research into Telecare (see http://www.aktive.org.uk/)

Fredholm Determinants, Differential Equations and Matrix Models

Orthogonal polynomial random matrix models of NxN hermitian matrices lead to Fredholm determinants of integral operators with kernel of the form (phi(x) psi(y) - psi(x) phi(y))/x-y. This paper is concerned with the Fredholm determinants of integral operators having kernel of this form and where the underlying set is a union of open intervals. The emphasis is on the determinants thought of as functions of the end-points of these intervals. We show that these Fredholm determinants with kernels of the general form described above are expressible in terms of solutions of systems of PDE's as long as phi and psi satisfy a certain type of differentiation formula. There is also an exponential variant of this analysis which includes the circular ensembles of NxN unitary matrices.Comment: 34 pages, LaTeX using RevTeX 3.0 macros; last version changes only the abstract and decreases length of typeset versio