A new family of exact solutions of the scalar Helmholtz equation is presented. The 0, 0 order of this family represents a new mathematical model for the fundamental mode of a propagating Gaussian beam. The family consists of nonseparable functions in the oblate spheroidal coordinate system and can easily by transformed into a different set of solutions in the prolate spheroidal coordinate syste...

We examine the merits of using prolate spheroidal wave functions (PSWFs) as basis functions when solving hyperbolic PDEs using pseudospectral methods. The relevant approximation theory is reviewed and some new approximation results in Sobolev spaces are established. An optimal choice of the band-limit parameter for PSWFs is derived for single-mode functions. Our conclusion is that one might gai...

We present new results on RR Lyrae stars and anomalous Cepheids in the Draco dwarf spheroidal galaxy. We have increased the number of double-mode RR Lyrae stars and found three new anomalous Cepheids. With period-magnitude and period-amplitude diagrams, we discuss the Oosterhoff classification of Draco. Contradictory results were found in that Draco appears to contain both Oosterhoff I and II t...

• Zircaloy-2 was analysed after in-reactor exposure using APT in voltage mode. Clusters of Fe and Ni were disc-shaped, clusters Cr spheroidal. Fe–Ni Fe–Cr seem to be associated with radiation-induced -loops. segregation the loop plane. smaller denser than clusters. This study is complementary previous atom probe tomography (APT) studies irradiation effects zirconium alloy Zircaloy-2. Using p...

The estimation of radiative modes is a central problem in gravitational wave theory, with essential applications signal modeling and data analysis. This complicated by most astrophysically relevant systems not having that are analytically tractable. A ubiquitous workaround to use modes, but multipole moments defined spin-weighted spherical harmonics. However, only related the without angular mo...

We examine stochastic temperature fluctuations of the cosmic background radiation (CBR) arising via the Sachs-Wolfe effect from gravitational wave perturbations produced in the early universe. We consider spatially flat, perturbed FRW models that begin with an inflationary phase, followed by a mixed phase containing both radiation and dust. The scale factor during the mixed phase takes the form...

The spheroidal wave functions, which are the solutions to the Helmholtz equation in spheroidal coordinates, are notoriously difficult to compute. Because of this, practically no programming language comes equipped with the means to compute them. This makes problems that require their use hard to tackle. We have developed computational software for calculating these special functions. Our softwa...