This paper gives a description of all harmonic morphisms from a threedimensional non-simply-connected Euclidean and spherical space form to a surface, by extending the work of Baird-Wood [4, 5] who dealt with the simply-connected case; namely we show that any such harmonic morphism is the composition of a “standard” harmonic morphism and a weakly conformal map. To complete the description we li...

We demonstrate an application of spherical harmonic decomposition to analysis of the human electroencephalogram (EEG). We implement two methods and discuss issues specific to analysis of hemispherical, irregularly sampled data. Performance of the methods and spatial sampling requirements are quantified using simulated data. The analysis is applied to experimental EEG data, confirming earlier re...

Introduction: Models of the interior structure of planets and their satellites rely heavily on the determination of their gravitational potential. In addition, the shapes of the bodies reveal important information about subsurface processes, such as relaxation to a gravitational equilibrium and, when combined with mean density, a quantification of departure from a homogeneous structure [1]. We ...

Spherical harmonics have been important tools for solving geophysical and astrophysical problems. Methods have been developed to effectively implement spherical harmonic expansion approximations. However, the Gibbs phenomenon was already observed by Weyl for spherical harmonic expansion approximations to functions with discontinuities, causing undesirable oscillations over the entire sphere. Re...

Statistical analysis of the global hotspot distribution is made and current state-of-the-art of the theory of mantle plumes is discussed. Both the fractal dimension analysis and the spherical harmonic correlation are performed to infer some constraints on possible hotspots and mantle plumes sources. Such a joint analysis suggests a compound model, in which the upper mantle exerts strong influen...

We report molecular dynamics calculations on a two-component, cold, 15,625 particle, three-dimensional Lennard-Jones fluid. We calculated spherical harmonic components Q(LM) for the density of particles in the first coordination shell of each particle, as well as their spherical invariants , time-correlation functions, and wavelet density decompositions. The spherical invariants show that ...

We apply a spherical harmonic analysis to the Point Source Redshift Survey (PSCz), to compute the real-space galaxy power spectrum and the degree of redshift distortion caused by peculiar velocities. We employ new parameter eigenvector and hierarchical data compression techniques, allowing a much larger number of harmonic modes to be included, and correspondingly smaller error bars. Using 4644 ...

A new technique for continuation of the ground magnetic field caused by ionospheric currents to the ionosphere in spherical geometry is presented that makes use of elementary ionospheric current systems, which were introduced by Amm (1997) in extension of an earlier work by Fukushima (1976). The measured ground magnetic disturbance is expanded in terms of the ground magnetic effect of a spatial...