The twisted fourth moment of the Riemann zeta function

We compute the asymptotics of the fourth moment of the Riemann zeta function times an arbitrary Dirichlet polynomial of length $T^{{1/11} - \epsilon}$Comment: 28 pages. v2: added reference

Multiple and variable speed electrical generator systems for large wind turbines

A cost effective method to achieve increased wind turbine generator energy conversion and other operational benefits through variable speed operation is presented. Earlier studies of multiple and variable speed generators in wind turbines were extended for evaluation in the context of a specific large sized conceptual design. System design and simulation have defined the costs and performance benefits which can be expected from both two speed and variable speed configurations

Persistent random walk on a one-dimensional lattice with random asymmetric transmittances

We study the persistent random walk of photons on a one-dimensional lattice of random asymmetric transmittances. Each site is characterized by its intensity transmittance t (t') for photons moving to the right (left) direction. Transmittances at different sites are assumed independent, distributed according to a given probability density Distribution. We use the effective medium approximation and identify two classes of probability density distribution of transmittances which lead to the normal diffusion of photons. Monte Carlo simulations confirm our predictions.Comment: 7 pages, submitted to Phys. Rev.

Genetic distance predicts trait differentiation at the subpopulation but not the individual level in eelgrass, Zostera marina.

Ecological studies often assume that genetically similar individuals will be more similar in phenotypic traits, such that genetic diversity can serve as a proxy for trait diversity. Here, we explicitly test the relationship between genetic relatedness and trait distance using 40 eelgrass (Zostera marina) genotypes from five sites within Bodega Harbor, CA. We measured traits related to nutrient uptake, morphology, biomass and growth, photosynthesis, and chemical deterrents for all genotypes. We used these trait measurements to calculate a multivariate pairwise trait distance for all possible genotype combinations. We then estimated pairwise relatedness from 11 microsatellite markers. We found significant trait variation among genotypes for nearly every measured trait; however, there was no evidence of a significant correlation between pairwise genetic relatedness and multivariate trait distance among individuals. However, at the subpopulation level (sites within a harbor), genetic (FST) and trait differentiation were positively correlated. Our work suggests that pairwise relatedness estimated from neutral marker loci is a poor proxy for trait differentiation between individual genotypes. It remains to be seen whether genomewide measures of genetic differentiation or easily measured "master" traits (like body size) might provide good predictions of overall trait differentiation

Quasars, their host galaxies, and their central black holes

We present the final results from our deep HST imaging study of the hosts of radio-quiet quasars (RQQs), radio-loud quasars (RLQs) and radio galaxies (RGs). We describe new WFPC2 R-band observations for 14 objects and model these images in conjunction with the data already reported in McLure et al (1999). We find that spheroidal hosts become more prevalent with increasing nuclear luminosity such that, for nuclear luminosities M_V < -23.5, the hosts of both radio-loud and radio-quiet AGN are virtually all massive ellipticals. Moreover we demonstrate that the basic properties of these hosts are indistinguishable from those of quiescent, evolved, low-redshift ellipticals of comparable mass. This result kills any lingering notion that radio-loudness is determined by host-galaxy morphology, and also sets severe constraints on evolutionary schemes which attempt to link low-z ULIRGs with RQQs. Instead, we show that our results are as expected given the relationship between black-hole and spheroid mass established for nearby galaxies, and apply this relation to estimate the mass of the black hole in each object. The results agree very well with completely-independent estimates based on nuclear emission-line widths; all the quasars in our sample have M(bh) > 5 x 10^8 solar masses, while the radio-loud objects are confined to M(bh) > 10^9 solar masses. This apparent mass-threshold difference, which provides a natural explanation for why RQQs outnumber RLQs by a factor of 10, appears to reflect the existence of a minimum and maximum level of black-hole radio output which is a strong function of black-hole mass. Finally, we use our results to estimate the fraction of massive spheroids/black-holes which produce quasar-level activity. This fraction is \~0.1% at the present day, rising to > 10% at z = 2-3.Comment: Revised version accepted for publication in Monthly Notices of the Royal Astronomical Society. 46 pages, the final 19 of which comprise an Appendix. 15 figures in main text. A further 14 4-panel greyscale plots and 14 line plots which appear in the Appendix have been reproduced here with reduced quality due to space limitations. A full resolution copy of the manuscript can be obtained via ftp://ftp.roe.ac.uk/pub/jsd/dunlop2002.ps.g