Letters to the Editor

The Mathematical Intelligencer encourages comments about the material in this issue. Letters to the editor should be sent to either of the editors-in-chief, Chandler Davis or Marjorie Senechal.     

Adaptive local grid refinement algorithms for finite-element collocation

An adaptive grid refinement procedure allows accurate solutions to advection-dominated, time-dependent flows using finite-element collocation. The technique relies on a data structure that is readily amenable to parallel computing. The paper discusses computational aspects of the method.     

On the excitation of a closely spaced array by a line source

An infinite row of periodically spaced, identical rigid circularcylinders is excited by an acoustic line source which is parallelto the generators of the cylinders. A method for calculatingthe scattered field accurately and efficiently is presented.When the cylinders are sufficiently close together, Rayleigh–Blochsurface waves that propagate energy to infinity along the arrayare excited. An expression is derived which enables the amplitudesof these surface waves to be computed without requiring thesolution to the full scattering problem.     

Variant superfield representations

We discuss some variant superfield representations which can arise by the replacement of some of the usual fields in a multiplet with p-form gauge fields.     

Reductions in overshoot following intense sound exposures

Overshoot refers to the poorer detectability of brief signals presented soon after the onset of a masking noise compared to those presented after longer delays. In the present experiment, brief tonal signals were presented 2 or 190 ms following the onset of a broadband masker that was 200 ms in duration. These two conditions of signal delay were tested before and after a series of exposures to a tone intense enough to induce temporary threshold shift (TTS). The magnitude of the overshoot was reduced after the exposure when a TTS of at least 10 dB was induced, but not when smaller amounts of TTS were induced. The reduction in overshoot was due to a decrease in the masked thresholds with the 2-ms delay; masked thresholds with the 190-ms delay were not different pre- and post-exposure. The implication is that the mechanisms responsible for the normal overshoot effect are temporarily inactivated by the same stimulus manipulations that produce a mild exposure-induced hearing loss. Thus the result is the paradox that exposure to intense sounds can produce a loss of signal detectability in certain stimulus conditions and a simultaneous improvement in detectability in other stimulus conditions.     

Estimates for transition probabilities on a compact manifold

The purpose of this note is to describe a procedure for transferring familiar estimates for transition probabilities on RN to transition probabilities on compact manifolds.     

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.