A simple derivation of the formula to calculated synthetic long-period seismograms in a heterogeneous Earth by normal mode summation

A simple modification of Gilbert's formula to account for slight lateral heterogeneity of the Earth leads to a convenient formula to calculate synthetic long period seismograms. Partial derivatives are easily calculated, thus the formula is suitable for direct inversion of seismograms for lateral heterogeneity of the Earth

Lateral heterogeneity and azimuthal anistropy of the upper mantle: Love and Rayleigh waves 100-250 sec

The lateral heterogeneity and apparent anisotropy of the upper mantle are studied by measuring Rayleigh and Love wave phase velocities in the period range 100-250 sec. Spherical harmonic descriptions of the lateral heterogeneity are obtained for order and degree up to 1=m=10. Slow regions are evident at the East Pacific rise, northeast Africa, Tibet, Tasman sea, southwestern North America and triple junctions in the Northern Atlantic and Indian oceans. Fast regions occur in Australia, western Pacific and the eastern Atlantic. Details which are not evident in previous studies include two fast regions in the central Pacific and the subduction zone in the Scotia Arc region. Inversion for azimuthal dependence showed (1) little correlation between the fast phase velocity directions and the plate motion vector in plate interiors, but (2) correlation of the fast direction with the perpendicular direction to trenches and ridges. Phase velocity is high when waves propagate perpendicular to these structures. Severe tradeoffs exist between heterogeneity and azimuthal dependence because of the yet unsatisfactory path coverage

Harmonic Analysis of Linear Fields on the Nilgeometric Cosmological Model

To analyze linear field equations on a locally homogeneous spacetime by means of separation of variables, it is necessary to set up appropriate harmonics according to its symmetry group. In this paper, the harmonics are presented for a spatially compactified Bianchi II cosmological model -- the nilgeometric model. Based on the group structure of the Bianchi II group (also known as the Heisenberg group) and the compactified spatial topology, the irreducible differential regular representations and the multiplicity of each irreducible representation, as well as the explicit form of the harmonics are all completely determined. They are also extended to vector harmonics. It is demonstrated that the Klein-Gordon and Maxwell equations actually reduce to systems of ODEs, with an asymptotic solution for a special case.Comment: 28 pages, no figures, revised version to appear in JM

Cosmological Family Asymmetry and CP violation

We discuss how the cosmological baryon asymmetry can be achieved by the lepton family asymmetries of heavy Majorana neutrino decays and they are related to CP violation in neutrino oscillation, in the minimal seesaw model with two heavy Majorana neutrinos. We derive the most general formula for CP violation in neutrino oscillation in terms of the heavy Majorana masses and Yukawa mass term. It is shown that the formula is very useful to classify several models in which $e-$, $\mu-$ and $\tau-$leptogenesis can be separately realized and to see how they are connected with low energy CP violaton. To make the models predictive, we take texture with two zeros in the Dirac neutrino Yukawa matrix. In particular, we find some interesting cases in which CP violation in neutrino oscillation can happen while lepton family asymmetries do not exist at all. On the contrary, we can find $e-$, $\mu-$ and $\tau-$leptogenesis scenarios in which the cosmological CP violation and low energy CP violation measurable via neutrino oscillations are very closely related to each other. By determining the allowed ranges of the parameters in the models, we predict the sizes of CP violation in neutrino oscillation and $|V_{e3}^{MNS}|$. Finally, the leptonic unitarity triangles are reconstructed.Comment: 22 pages, 9 figures A figure caption correcte

Waveform inversion of mantle Love waves: The born seismogram approach

Normal mode theory, extended to the slightly laterally heterogeneous Earth by the first-order Born approximation, is applied to the waveform inversion of mantle Love waves (200-500 sec) for the Earth's lateral heterogeneity at l=2 and a spherically symmetric anelasticity (Q sub mu) structure. The data are from the Global Digital Seismograph Network (GDSN). The l=2 pattern is very similar to the results of other studies that used either different methods, such as phase velocity measurements and multiplet location measurements, or a different data set, such as mantle Rayleigh waves from different instruments. The results are carefully analyzed for variance reduction and are most naturally explained by heterogeneity in the upper 420 km. Because of the poor resolution of the data set for the deep interior, however, a fairly large heterogeneity in the transition zones, of the order of up to 3.5% in shear wave velocity, is allowed. It is noteworthy that Love waves of this period range can not constrain the structure below 420 km and thus any model presented by similar studies below this depth are likely to be constrained by Rayleigh waves (spheroidal modes) only

5-State Rotation-Symmetric Number-Conserving Cellular Automata are not Strongly Universal

We study two-dimensional rotation-symmetric number-conserving cellular automata working on the von Neumann neighborhood (RNCA). It is known that such automata with 4 states or less are trivial, so we investigate the possible rules with 5 states. We give a full characterization of these automata and show that they cannot be strongly Turing universal. However, we give example of constructions that allow to embed some boolean circuit elements in a 5-states RNCA