Recent changes in A-level Mathematics: is the availability and uptake of mechanics declining yet more?

In the past 6 years changes have occurred in GCE A-levels. Inparticular, there have been several major changes in A-levelMathematics courses. As engineering students are usually requiredto have studied A-level Mathematics, or its equivalent, thesechanges have had an effect on their prior mathematical knowledge.Moreover, engineering students traditionally obtained a goodgrounding in mechanics as part of their A-level Mathematicsqualification. However, mechanics, which was once included inthe core syllabus, is now optional. This article investigatesthe current availability and uptake of mechanics modules withinA-level Mathematics courses in schools. Comparisons are drawnbetween these results and results of a survey of schools in2004 and surveys of first year engineering students conductedin 2004 and 2005. It is found that there is a decline in theavailability of mechanics modules and the uptake of more thanone mechanics module has also decreased. The implications ofthese findings for engineering educators are discussed.     

Effects of tributyltin(IV) chloride on the gametes and fertilization of Ascidia malaca (Ascidiacea: Tunicata)

Ascidia malaca gametes before fertilization incubated in 10^?5 or 10^?7 M solutions of tributyltin(IV) chloride, TBTCl, for 3 h appear highly damaged under transmission electron microscopy observation. Also, the fertilization process is affected by the compound: the damaged spermatozoa are present in the vitelline coat and the egg does not cleave. An increase of microbodies, structurally similar to peroxisomes, have been detected in the egg peripheral cytoplasm, probably in relation to their role in alleviating damage to some cellular components. The results have shown that the reproduction of ascidians under unfavourable environmental conditions is prevented. Copyright © 2003 John Wiley & Sons, Ltd.     

Dynamic mechanical thermal analysis transitions of partially and fully substituted cellulose fatty esters

The main transitions of cellulose fatty esters with different degrees of substitution (DSs) were investigated with dynamic mechanical thermal analysis. Two distinct main relaxations were observed in partially substituted cellulose esters (PSCEs). They were attributed to the glass‐transition temperature and to the chain local motion of the aliphatic substituents. The temperatures of both transitions decreased when DS or the number of carbon atoms (n) of the acyl substituent increased. Conversely, all the transitions of fully substituted cellulose esters occurred within a narrow temperature range, and they did not vary significantly with n. This phenomenon was explained by the formation of a crystalline phase of the fatty substituents. The presence of few residual OH groups in PSCEs was responsible for a large increase in the storage bending modulus, and it eliminated the effect of n on damping. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 281–288, 2003     

Decrease in the group velocity of a light pulse in the Bose-Einstein condensate of a dilute gas

A semiclassical theory of electromagnetically induced transparency in a Bose-Einstein condensate is considered. A nonlinear Schrödinger equation that describes the interaction of the Bose-Einstein condensate with an electromagnetic field is derived. An analysis of the obtained solutions to this equation demonstrates a decrease in the group velocity of the light pulse.     

Photoluminescence of liquid-crystal azo derivatives in nanopores

Optics and Spectroscopy - The fluorescence of the nematic liquid crystal n-butyl-n′-methoxyazoxybenzene (BMAOB) in the form of a layer and in porous glasses with pores of different diameter...     

Random matrix theory and non-parametric model of random uncertainties in vibration analysis

Recently, a new approach, called a non-parametric model of random uncertainties, has been introduced for modelling random uncertainties in linear and non-linear elastodynamics in the low-frequency range. This non-parametric approach differs from the parametric methods for random uncertainties modelling and has been developed in introducing a new ensemble of random matrices constituted of symmetric positive-definite real random matrices. This ensemble differs from the Gaussian orthogonal ensemble (GOE) and from the other known ensembles of the random matrix theory. The present paper has three main objectives. The first one is to study the statistics of the random eigenvalues of random matrices belonging to this new ensemble and to compare with the GOE. The second one is to compare this new ensemble of random matrices with the GOE in the context of the non-parametric approach of random uncertainties in structural dynamics for the low-frequency range. The last objective is to give a new validation for the non-parametric model of random uncertainties in structural dynamics in comparing, in the low-frequency range, the dynamical response of a simple system having random uncertainties modelled by the parametric and the non-parametric methods. These three objectives will allow us to conclude about the validity of the different theories.     

L2 -cohomology of manifolds with flat ends

Geometric and Functional Analysis - We give a topological interpretation of the spaces of L2 -harmonic forms on manifolds with flat ends. We also prove a Chern-Gauss-Bonnet formula for the L2...     

Crack path instabilities in DCDC experiments in the low speed regime

We studied the low speed fracture regime (10⁻⁴-10⁻⁹ m s⁻¹) in different glassy materials (soda-lime glass, glass ceramics) with variable but controlled length scale of heterogeneity. The chosen mechanical system enabled us to work in pure mode I (tensile) and at a fixed load on double cleavage drilled compression specimen. The internal residual stresses of studied samples were carefully relaxed by appropriate thermal treatment. By means of optical and atomic force microscopy techniques fracture surfaces have been examined. We have shown for the first time that the crack front line underwent an out-of-plane oscillating behavior as a result of a reproducible sequence of instabilities. The wavelength of such a phenomenon is in the micrometer range and its amplitude in the nanometer range. These features were observed for different glassy materials providing that a typical length scale characterizing internal heterogeneities was lower than a threshold limit estimated to few nanometers. This effect is the first clear experimental evidence of crack path instabilities in the low speed regime in a uniaxial loading experiment. This phenomenon has been interpreted by referring to the stability criterion for a straight crack propagation as presented by Adda-Bedia et al. [Phys. Rev. Lett. 76 (1996) 1497].     

A microspectroscopic study of the electronic homogeneity of ordered and disordered Sr2FeMoO6

Disordered Sr₂FeMoO₆ shows a drastic reduction in saturation magnetization compared to highly ordered samples, moreover magnetization as a function of the temperature for different disordered samples shows qualitatively different behaviours. We investigate the origin of such diversity by performing spatially resolved photoemission spectroscopy on various disordered samples. Our results establish that e_xtensive electronic inhomogeneity, arising most probably from an underlying chemical inhomogeneity in disordered samples, is responsible for the observed magnetic inhomogeneity. It is further pointed out that these inhomogeneities are connected with composition fluctuations of the type Sr₂Fe_1+x Mo_1-x O₆ with Fe-rich (x > 0) and Mo-rich (x < 0) regions. Dedicated to Prof J Gopalakrishnan on his 62nd birthday.