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Spin wave modes in a thin submicron cobalt square with a closure domain structure are obtained by using a micromagnetic equation of motion approach. In addition to modes with amplitude over the whole sample, some low-frequency modes, localized at the center, corners, and diagonals of the square, are also found. In analogy with the modes found in a circular vortex, the nonlocalized modes can be broadly classified into radiallike and azimuthal-like modes, and their frequencies can be understood qualitatively in terms of the dispersion relation of spin wave modes of an unconfined film. Other modes that can be interpreted as the combination of radial and azimuthal modes are also observed.

Inner products of wavelets and their derivatives are presently known as connection coe cients. The numerical calculation of inner products of periodized Daubechies wavelets and their derivatives is reviewed, with the aim at providing potential users of the publicly-available numerical scheme, details of its operation. The numerical scheme for the calculation of connection coe cients is evaluated in the context of approximating di erential operators, information which is useful in the solution of partial di erential equations using wavelet-Galerkin techniques. Speciÿc details of the periodization of inner products in the solution di erential equations are included in this presentation. ?

The lift and drag forces on an isolated particle resulting from an oscillating wall- bounded flow, are approximated using direct numerical simulation and extrapolation techniques. We also confirm the existence of anomalies in the lift force, which arise from the interaction of the vortical field with the particle. Anomalies can also occur for computational reasons and these are discussed as well.This study was motivated by a long-standing question about the importance of lift forces in the dynamics of sediments in oceanic settings. To answer this question we use the numerically generated data as well as extrapolations to compute the ratio of the lift to buoyancy forces on a particle. This analysis suggests that for particles and oceanic conditions typical of the nearshore, the lift force can play a role in the dynamics of sedimentary beds.