Structural and lithium intercalation studies of Mn(0.5−x)CaxTi2(PO4)3 phases (0≤x≤0.50)

Materials from the Mn_(0.5−x)Ca_xTi₂(PO₄)₃ (0≤x≤0.50) solid solution were obtained by solid-state reaction in air at 1000 °C. Selected compositions were investigated by powder X-ray diffraction analysis, ³¹P nuclear magnetic resonance (NMR) spectroscopy and electrochemical lithium intercalation. The structure of all samples determined by Rietveld analysis is of the Nasicon type with the R space group. Mn²⁺/Ca²⁺ ions occupy only the M1 sites in the Ti₂(PO₄)₃ framework. The divalent cations are ordered in one of two M1 sites, except for the Mn_0.50Ti₂(PO₄)₃ phase, where a small departure from the ideal order is observed by XRD and ³¹P MAS NMR. The electrochemical behaviour of Mn_0.50Ti₂(PO₄)₃ and Mn_(0.5−x)Ca_xTi₂(PO₄)₃ phases was characterised in Li cells. Two Li ions can be inserted without altering the Ti₂(PO₄)₃ framework. In the 0≤y≤2 range, the OCV curves of Li//Li_yMn_0.50Ti₂(PO₄)₃ cells show two main potential plateaus at 2.90 and 2.50–2.30 V. Comparison between the OCV curves of Li//Li_(1+y)Ti₂(PO₄)₃ and Li//Li_yMn_0.50Ti₂(PO₄)₃ shows that the intercalation occurs first in the unoccupied M1 site of Mn_0.50Ti₂(PO₄)₃ at 2.90 V and then, for compositions y>0.50, at the M2 site (2.50–2.30 V voltage range). The effect of calcium substitution in Mn_0.50Ti₂(PO₄)₃ on the lithium intercalation is also discussed from a structural and kinetic viewpoint. In all systems, the lithium intercalation is associated with a redistribution of the divalent cation over all M1 sites. In the case of Mn_0.50Ti₂(PO₄)₃, the stability of Mn²⁺ either in an octahedral or tetrahedral environment facilitates cationic migration.     

Phonon–replica transitions in InGaN/GaN quantum well structures

A side-bump feature in a photoluminescence (PL) spectrum of an InGaN compound was widely observed. With reasonable fitting to PL spectra with three Gaussian distributions, the temperature variations of the peak positions, integrated PL intensities, and peak widths of the main and first side peaks of three InGaN/GaN multiple quantum well samples with different nominal indium contents are shown and interpreted. The existence of the side peaks is attributed to phonon–replica transitions. The variations of the peak position separations and the decreasing trends of the first side peak widths beyond certain temperatures in those samples were explained with the requirement of phonon momentum condition for phonon–replica transitions. In the sample with 25% nominal indium content, the phonon–replica transition could become stronger than the direct transition of localized states.     

Darboux transformation and solitons of Yang-Mills-Higgs equations in R2,1

The Darboux transformations for soliton equations are applied to the Yang-Mills-Higgs equations.New solutions can be obtained from a known one via universal and purely algebraic formulas. SU(N) soliton solutions are constructed with explicit formulas. The interaction of solitons is described by the splitting theorem:each p-soliton is splitting into p single solitons asymptotically as t →±∞.     

Investigations in the amplitude of sounded piano tones

The relationship between final hammer velocity and maximum amplitude of radiated piano sound was investigated. Piano tones with varying hammer velocities were produced by a computer-monitored acoustic piano containing optical sensors and solenoids, and the sounded tones were recorded and digitized for analysis. Maximum amplitudes over the duration of the sounded tones were linearly proportional to piano hammer velocities for a range of frequencies and hammer velocities. Changes in room acoustics did not alter the linear relationship. Measurements of maximum amplitudes of individual tones and combined tones (dyads) also indicated a linear relationship between the sum of the maximum amplitudes of the individual tones and the maximum amplitude of the dyads. These findings indicate that the principle of superposition holds for peak amplitudes of sounded piano tones. Findings are discussed with regard to production and perception of musical dynamics.     

Some effective methods for unconstrained optimization based on the solution of systems of ordinary differential equations

In this paper, we review briefly some methods for minimizing a functionF(x), which proceed by follwoing the solution curve of a system of ordinary differential equations. Such methods have often been thought to be unacceptably expensive; but we show, by means of extensive numerical tests, using a variety of algorithms, that the ODE approach can in fact be implemented in such a way as to be more than competitive with currently available conventional techniques.This work was supported by a SERC research studentship for the first author. Both authors are indebted to Dr. J. J. McKeown and Dr. K. D. Patel of SCICON Ltd, the collaborating establishment, for their advice and encouragement.     

A posteriori error estimators for the Stokes equations

Summary We present two a posteriori error estimators for the mini-element discretization of the Stokes equations. One is based on a suitable evaluation of the residual of the finite element solution. The other one is based on the solution of suitable local Stokes problems involving the residual of the finite element solution. Both estimators are globally upper and locally lower bounds for the error of the finite element discretization. Numerical examples show their efficiency both in estimating the error and in controlling an automatic, self-adaptive mesh-refinement process. The methods presented here can easily be generalized to the Navier-Stokes equations and to other discretization schemes.This work was accomplished at the Universität Heidelberg with the support of the Deutsche Forschungsgemeinschaft     

The first total synthesis of (R)-convolutamydine A

The first total synthesis of (R)-convolutamydine A has been achieved by the organocatalytic addition of acetone to 4,6-dibromoisatin. The absolute configuration was determined by single crystal X-ray diffraction. DFT studies were used to model the transition states for the aldol reaction and equilibrium geometries of the post-aldol reaction intermediates. The DFT study revealed that the aldol bond forming reaction was considerably endothermic.     

Using graphs for some discrete tomography problems

Given a rectangular array whose entries represent the pixels of a digitalized image, we consider the problem of reconstructing an image from the number of occurrences of each color in every column and in every row. The complexity of this problem is still open when there are just three colors in the image. We study some special cases where the number of occurrences of each color is limited to small values. Formulations in terms of edge coloring in graphs and as timetabling problems are used; complexity results are derived from the model.     

The effect of linguistic entropy on speech perception in noise in young and elderly listeners.

The rationale for a method to quantify the information content of linguistic stimuli, i.e., the linguistic entropy, is developed. The method is an adapted version of the letter-guessing procedure originally devised by Shannon [Bell Syst. Tech. J. 30, 50-64 (1951)]. It is applied to sentences included in a widely used test to measure speech-reception thresholds and originally selected to be approximately equally redundant. Results of a first experiment reveal that this method enables one to detect subtle differences between sentences and sentence lists with respect to linguistic entropy. Results of a second experiment show that (1) in young listeners and with the sentences employed, manipulating linguistic entropy can result in an effect on SRT of approximately 4 dB in terms of signal-to-noise ratio; (2) the range of this effect is approximately the same in elderly listeners.