Optimal extraction of information from gravitational-wave observations of binary black-hole coalescences requires detailed knowledge of the waveforms. Current approaches for representing waveform information are based on spin-weighted spherical harmonic decomposition. Higher-order harmonic modes carrying a few percent of the total power output near merger can supply information critical to dete...

Transients associated with partial discharges in ellipsoidal and spheroidal voids are derived in terms of the concept of induced charges on the electrode. The relationship between the induced charge and the properties which are usually measured are discussed. The method is illustrated by applying it to a spheroidal void in a simple disk-type GIS spacer.

The Ignjatovic theory of chromatic derivatives and series is extended to include other series. In particular series of prolate spheroidal wave functions are used to replace the orthogonal polynomial series in this theory. It is extended further to prolate spheroidal wavelet series that enables us to combine chromatic series with sampling series.

The coordinate transformation technique is applied to the design of perfect lenses and superlenses. In particular, anisotropic metamaterials that magnify two-dimensional planar images beyond the diffraction limit are designed by the use of oblate spheroidal coordinates. The oblate spheroidal perfect lens or superlens can naturally be used in reverse for lithography of planar subwavelength patte...

Smeyers’ procedure (1986) for the determination of linear, isentropic oscillations of the incompressible MacLaurin spheroids is extended to the compressibleMacLaurin spheroids. It is shown that the solutions can be constructed by a direct integration of a finite set of differential equations written in spherical coordinates. Oblate spheroidal coordinates are used with regard to the boundary con...

In the paper, we study the spin-weighted spheroidal wave functions in the case of s = m = 0. Their eigenvalue problem is investigated by the perturbation method in supersymmetric quantum mechanics (SUSYQM). For the ground state, the first three terms of ground eigenvalue and eigenfunction in parameter α = aw are obtained. The obtained ground eigenfunction is elegantly in closed forms. Due to th...

We review a set of algorithms to evaluate associated Legendre functions off the cut; in particular, we consider prolate spheroidal, oblate spheroidal and toroidal harmonics. A similar scheme can be applied to other families of special functions like Bessel and parabolic cylinder functions; we will describe the corresponding algorithm for the evaluation of parabolic cylinder functions.

We have investigated effects of guest colloidal particles on the mesoscopic structures of a surfactant/water system by means of small angle neutron and x-ray scattering techniques. The addition of a small amount of colloidal particles between lamellar slits reduces the undulational fluctuations of lamellae and brings about a lamellar to micelle transition. On the other hand, on addition of coll...

The oscillations of a slowly rotating star have long been classified into spheroidal and toroidal modes. modes include the well-known 5-min acoustic used in helioseismology. Here we report observations Sun’s modes, for which restoring force is Coriolis whose periods are on order solar rotation period. By comparing with normal differentially spherical shell, able to identify many observed These ...