Scalar fields on SL(2,R) and H^2 x R geometric spacetimes and linear perturbations

Using appropriate harmonics, we study the future asymptotic behavior of massless scalar fields on a class of cosmological vacuum spacetimes. The spatial manifold is assumed to be a circle bundle over a higher genus surface with a locally homogeneous metric. Such a manifold corresponds to the SL(2,R)-geometry (Bianchi VIII type) or the H^2 x R-geometry (Bianchi III type). After a technical preparation including an introduction of suitable harmonics for the circle-fibered Bianchi VIII to separate variables, we derive systems of ordinary differential equations for the scalar field. We present future asymptotic solutions for these equations in a special case, and find that there is a close similarity with those on the circle-fibered Bianchi III spacetime. We discuss implications of this similarity, especially to (gravitational) linear perturbations. We also point out that this similarity can be explained by the "fiber term dominated behavior" of the two models.Comment: 23 pages, no figures, to be published in Class. Quant. Gravi

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

pax1-1 partially suppresses gain-of-function mutations in Arabidopsis AXR3/IAA17

Background: The plant hormone auxin exerts many of its effects on growth and development by controlling transcription of downstream genes. The Arabidopsis gene AXR3/IAA17 encodes a member of the Aux/IAA family of auxin responsive transcriptional repressors. Semi-dominant mutations in AXR3 result in an increased amplitude of auxin responses due to hyperstabilisation of the encoded protein. The aim of this study was to identify novel genes involved in auxin signal transduction by screening for second site mutations that modify the axr3-1 gain-of-function phenotype. Results: We present the isolation of the partial suppressor of axr3-1 (pax1-1) mutant, which partially suppresses almost every aspect of the axr3-1 phenotype, and that of the weaker axr3-3 allele. axr3-1 protein turnover does not appear to be altered by pax1-1. However, expression of an AXR3:: GUS reporter is reduced in a pax1-1 background, suggesting that PAX1 positively regulates AXR3 transcription. The pax1-1 mutation also affects the phenotypes conferred by stabilising mutations in other Aux/IAA proteins; however, the interactions are more complex than with axr3-1. Conclusion: We propose that PAX1 influences auxin response via its effects on AXR3 expression and that it regulates other Aux/IAAs secondarily

Embedding Phenomenological Quark-Lepton Mass Matrices into SU(5) Gauge Models

We construct phenomenological quark-lepton mass matrices based on S$_3$ permutation symmetry in a manner fully compatible with SU(5) grand unification. The Higgs particles we need are {\bf 5}, {\bf 45} and their conjugates. The model gives a charge $-$1/3 quark vs charged lepton mass relation, and also a good fit to mass-mixing relations for the quark sector, as well as an attractive mixing pattern for the lepton sector, explaining a large mixing angle between $\nu_\mu$ and $\nu_\tau$, and either large or small $\nu_e-\nu_\mu$ mixing angle, depending on the choice of couplings, consistent with the currently accepted solutions to the solar neutrino problem.Comment: 12 pages, LaTex file, no figure

Future asymptotic expansions of Bianchi VIII vacuum metrics

Bianchi VIII vacuum solutions to Einstein's equations are causally geodesically complete to the future, given an appropriate time orientation, and the objective of this article is to analyze the asymptotic behaviour of solutions in this time direction. For the Bianchi class A spacetimes, there is a formulation of the field equations that was presented in an article by Wainwright and Hsu, and in a previous article we analyzed the asymptotic behaviour of solutions in these variables. One objective of this paper is to give an asymptotic expansion for the metric. Furthermore, we relate this expansion to the topology of the compactified spatial hypersurfaces of homogeneity. The compactified spatial hypersurfaces have the topology of Seifert fibred spaces and we prove that in the case of NUT Bianchi VIII spacetimes, the length of a circle fibre converges to a positive constant but that in the case of general Bianchi VIII solutions, the length tends to infinity at a rate we determine.Comment: 50 pages, no figures. Erronous definition of Seifert fibred spaces correcte

Phenomenological Bounds on B to Light Semileptonic Form Factors

The form factors for the weak currents between B and light mesons are studied by relating them to the corresponding D form factors at q^2_{max} according to HQET, by evaluating them at q^2=0 by QCD sum rules, and by assuming a polar q^2 dependence. The results found are consistent with the information obtained from exclusive non-leptonic two-body decays and, with the only exception of A_1, with lattice calculations.Comment: 8 LaTeX pages + 2 figures. Will appear in Mod. Phys. Lett.

Formation and transport of oxidized reactive nitrogen, ozone, and secondary organic aerosol in Tokyo

Measurements of the major reactive nitrogen species (NOy)i (NOx, peroxyacyl nitrates, HNO3, and particulate nitrate (NO3-), total reactive nitrogen (NOy), volatile organic compounds, OH and HO2, and organic aerosol were made near the urban center of Tokyo in different seasons of 2003-2004 to study the processes involving oxidized forms of reactive nitrogen and O3. Generally, NOx constituted the dominant fraction of NOy throughout the seasons. The NOx/NOy and HNO3/NOy ratios were lowest and highest, respectively, in summer, owing to the seasonally high OH concentration. The fraction of NOy that remained in the atmosphere after emission (RNOy) decreased with the decrease in the NOx/NOy ratio in summer and fall. It is likely that the median seasonal-diurnal variations Of Ox = O3 + NO2 were controlled by those of the background O3 levels, photochemical O3 formation, and vertical transport. Ox showed large increases during midday under stagnant conditions in mid-August 2004. Their in situ production rates calculated by a box model were too slow to explain the observed increases. The high Ox was likely due to the accumulation of Ox from previous days in the upper part of the boundary layer (BL) followed by transport down to near the surface by mixing after sunrise. Considering the tight correlation between Ox and secondary organic aerosol (SOA), it is likely that SOA also accumulated during the course of sea-land breeze circulation in the BL. Copyright 2008 by the American Geophysical Union

Speed of Sound in the Mass Varying Neutrinos Scenario

We discuss about the speed of sound squared in the Mass Varying Neutrinos scenario (MaVaNs). Recently, it was argued that the MaVaNs has a catastrophic instability which is the emergence of an imaginary speed of sound at the non-relativistic limit of neutrinos. As the result of this instability, the neutrino-acceleron fluid cannot act as the dark energy. However, it is found that the speed of sound squared in the neutrino-acceleron fluid could be positive in our model. We examine the speed of sound in two cases of the scalar potential. One is the small fractional power-law potential and another is the logarithmic one. The power-law potential model with the right-handed neutrinos gives a stable one.Comment: 17 pages, References added, minor modification

Corrections to Gravity due to a Sol Manifold Extra Dimensional Space

The corrections to the gravitational potential due to a Sol extra dimensional compact manifold, denoted as $M_A^3$, are studied. The total spacetime is of the form $M^4\times M_A^3$. The range of the Sol corrections is investigated and compared to the range of the $T^3$ corrections.Comment: 13 pages, 10 figures, published versio

Perturbations of Spatially Closed Bianchi III Spacetimes

Motivated by the recent interest in dynamical properties of topologically nontrivial spacetimes, we study linear perturbations of spatially closed Bianchi III vacuum spacetimes, whose spatial topology is the direct product of a higher genus surface and the circle. We first develop necessary mode functions, vectors, and tensors, and then perform separations of (perturbation) variables. The perturbation equations decouple in a way that is similar to but a generalization of those of the Regge--Wheeler spherically symmetric case. We further achieve a decoupling of each set of perturbation equations into gauge-dependent and independent parts, by which we obtain wave equations for the gauge-invariant variables. We then discuss choices of gauge and stability properties. Details of the compactification of Bianchi III manifolds and spacetimes are presented in an appendix. In the other appendices we study scalar field and electromagnetic equations on the same background to compare asymptotic properties.Comment: 61 pages, 1 figure, final version with minor corrections, to appear in Class. Quant. Gravi