Order conditions for linearly implicit fractional step Runge Kutta methods

^{In this paper, we study the consistency of a variant of fractionalstep Runge–Kutta methods. These methods are designed tointegrate efficiently semi-linear multidimensional parabolicproblems by means of linearly implicit time integration processes.Such time discretization procedures are also related to a splittingof the space differential operator (or the spatial discretizationof it) as a sum of ‘simpler’ linear differentialoperators and a nonlinear term.}     

Strain-induced modification of magnetic structure and new magnetic phases in rare-earth epitaxial films

Rare earths exhibit complex magnetic phase diagrams resulting from the competition between various contributions to the magnetic energy: exchange, anisotropy and magnetostriction. The epitaxy of a rare-earth film on a substrate induces (i) a clamping to the substrate and (ii) pseudomorphic strains. Both these effects are shown to lead to modifications of the magnetic properties in (0 0 1)Dy, (0 0 1)Tb and (1 1 0)Eu films. In Dy and Tb films, spectacular variations of the Curie temperature have been evidenced. Additionally, Tb films exhibit a new large wavelength magnetic modulation. In Eu films, one of the helical magnetic domains disappears at low temperature whereas the propagation vectors of the other helices are tilted. The link between structural and magnetic properties is underlined via magnetoelastic models. Moreover, molecular beam epitaxy permits the growth of Sm in a metastable dhcp phase. The magnetic structure of dhcp Sm has been elucidated for the first time. In this review, neutron scattering is shown to be a powerful technique to reveal the magnetic structures of rare-earth films.     

Electro-optic pulse response of ferroelectric liquid crystals

The electro-optic response of ferroelectric smectic C* liquid crystals has been studied. Anomalous switching behaviour of such materials which possess a negative dielectric anisotropy has been reported. These materials show a minimum in response time at a sufficiently high field. We present results showing the dependency of this minimum upon spontaneous polarisation and the effect of AC bias. Calculations based upon the equation of motion of the director around the cone are presented which describe this effect and its dependence on the relative magnitudes of the spontaneous polarization and dielectric anisotropy of the material. Good agreement with the experimental results is found.     

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.     

On some p-adic properties of Siegel-Eisenstein series

We introduce a formula for the p-adic Siegel-Eisenstein series which demonstrates a connection with the genus theta series and the twisted Eisenstein series with level p. We then prove a generalization of Serre's formula in the elliptic modular case.     

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.     

Depth profile analysis of polyimide film treated by potassium hydroxide

The structural change in the depth direction of a polyimide (UPILEX‐S) film treated in alkaline solution, which was a representative surface treatment used to form a seed layer for plating and to improve the adhesive strength, was analyzed by means of micro Fourier transform infrared attenuated total reflection (FTIR‐ATR) line analysis with gradient shaving preparation. The polyimide film was treated with KOH. The imide ring opened through the alkaline treatment, and the amide structure and carboxylic acid salt were formed. The attainment depth of this structural change was almost proportional to the treatment time, and it reached about 8 μm after a 30‐min treatment. The degree of structural change through the alkaline treatment was almost constant after it reached a considerably degraded stage, and the chemically changed region penetrated into the inner part of the film from the surface. An intermediate layer before the final degraded stage appeared in the treated layer, and its thickness increased with the treatment time. The region that was changed chemically by the alkaline treatment progressed to the inner part simultaneously and continuously as the treatment time increased. The combined use of gradient shaving preparation and micro FTIR‐ATR line analysis was found to be extremely effective for the depth profiling of organic materials. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2071–2078, 2003     

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     

Degradation of ZnS:Cu,Al,Au phosphor powder in different gas mixtures

The ZnS:Cu,Al,Au (P22G) phosphor powder was bombarded by an electron beam in an O₂ ambient, Ar ambient and other mixture of gases. These gases consisted of mixtures of O₂ and CO_x, and O₂, CO_x and Ar gas. Auger electron spectroscopy (AES) was used to monitor changes in the surface composition of the P22G phosphor during electron bombardment. When the P22G phosphor powder was exposed to the electron beam in a water-rich O₂ ambient, a chemically limited ZnO layer was formed on the surface. The electron beam degradation of the P22G phosphor powder was also performed in a dry O₂ ambient and a layer of ZnSO₄ was formed on the surface. The ZnSO₄ formation decayed exponentially with time and it is postulated that this was due to the diffusion of the charge reactants through the ZnSO₄ film to the reaction interfaces. The P22G phosphor exposed to the electron beam in an Ar ambient and to the other gas mixtures degraded at a lower rate than in the case of the O₂ ambient. This suggests that Ar and CO_x may suppress the degradation of the P22G phosphor powder.     

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.