Spherical Harmonic Decomposition on a Cubic Grid

A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to the treatment of boundary conditions imposed at radii larger than the size of the grid, following Abrahams, Rezzola, Rupright et al.(gr-qc/9709082}. In the method described here, the interpolation of the grid data to the integration 2-sphere is combined in the same step as the integrations to extract the spherical harmonic amplitudes, which become sums over grid points. Coordinates adapted to the integration sphere are not needed.Comment: 5 pages, LaTeX uses cjour.cls (supplied

Levels of genetic polymorphism: marker loci versus quantitative traits

Species are the units used to measure ecological diversity and alleles are the units of genetic diversity. Genetic variation within and among species has been documented most extensively using allozyme electrophoresis. This reveals wide differences in genetic variability within, and genetic distances among, species, demonstrating that species are not equivalent units of diversity. The extent to which the pattern observed for allozymes can be used to infer patterns of genetic variation in quantitative traits depends on the forces generating and maintaining variability. Allozyme variation is probably not strictly neutral but, nevertheless, heterozygosity is expected to be influenced by population size and genetic distance will be affected by time since divergence. The same is true for quantitative traits influenced by many genes and under weak stabilizing selection. However, the limited data available suggest that allozyme variability is a poor predictor of genetic variation in quantitative traits within populations. It is a better predictor of general phenotypic divergence and of postzygotic isolation between populations or species, but is only weakly correlated with prezygotic isolation. Studies of grasshopper and planthopper mating signal variation and assortative mating illustrate how these characters evolve independently of general genetic and morphological variation. The role of such traits in prezygotic isolation, and hence speciation, means that they will contribute significantly to the diversity of levels of genetic variation within and among species

On the magnetospheric ULF wave counterpart of substorm onset

One near‐ubiquitous signature of substorms observed on the ground is the azimuthal structuring of the onset auroral arc in the minutes prior to onset. Termed auroral beads, these optical signatures correspond to concurrent exponential increases in ground ultralow frequency (ULF) wave power and are likely the result of a plasma instability in the magnetosphere. Here, we present a case study showing the development of auroral beads from a Time History of Events and Macroscale Interactions during Substorms (THEMIS) all‐sky camera with near simultaneous exponential increases in auroral brightness, ionospheric and conjugate magnetotail ULF wave power, evidencing their intrinsic link. We further present a survey of magnetic field fluctuations in the magnetotail around substorm onset. We find remarkably similar superposed epoch analyses of ULF power around substorm onset from space and conjugate ionospheric observations. Examining periods of exponential wave growth, we find the ground‐ and space‐based observations to be consistent, with average growth rates of ∼0.01 s−1, lasting for ∼4 min. Cross‐correlation suggests that the space‐based observations lead those on the ground by approximately 1–1.5 min. Meanwhile, spacecraft located premidnight and ∼10 RE downtail are more likely to observe enhanced wave power. These combined observations lead us to conclude that there is a magnetospheric counterpart of auroral beads and exponentially increasing ground ULF wave power. This is likely the result of the linear phase of a magnetospheric instability, active in the magnetotail for several minutes prior to auroral breakup

Mapping and explaining the productivity of Pinus radiata in New Zealand

Mapping Pinus radiata productivity for New Zealand not only provides useful information for forest owners, industry stakeholders and policy managers, but also enables current and future plantations to be visualised, quantified, and planned. Using an extensive set of permanent sample plots, split into fitting (n = 1,146) and validation (n = 618) datasets, models of P. radiata 300 Index (an index of volume mean annual increment) and Site Index (an index of height growth) were developed using a regression kriging technique. Spatial predictions were accurate and accounted for 61% and 70% of the variance for 300 Index and Site Index, respectively. Productivity predicted from these surfaces for the entire plantation estate averaged 27.4 m³ ha⁻¹ yr⁻¹ for the 300 Index and 30.4 m for Site Index. Surfaces showed wide regional variation in this productivity, which was attributable mainly to variation in air temperature and root-zone water storage from site to site

On a hybrid fourth moment involving the Riemann zeta-function

We provide explicit ranges for $\sigma$ for which the asymptotic formula \begin{equation*} \int_0^T|\zeta(1/2+it)|^4|\zeta(\sigma+it)|^{2j}dt \;\sim\; T\sum_{k=0}^4a_{k,j}(\sigma)\log^k T \quad(j\in\mathbb N) \end{equation*} holds as $T\rightarrow \infty$, when $1\leq j \leq 6$, where $\zeta(s)$ is the Riemann zeta-function. The obtained ranges improve on an earlier result of the authors [Annales Univ. Sci. Budapest., Sect. Comp. {\bf38}(2012), 233-244]. An application to a divisor problem is also givenComment: 21 page

Competing associations in six-species predator-prey models

We study a set of six-species ecological models where each species has two predators and two preys. On a square lattice the time evolution is governed by iterated invasions between the neighboring predator-prey pairs chosen at random and by a site exchange with a probability Xs between the neutral pairs. These models involve the possibility of spontaneous formation of different defensive alliances whose members protect each other from the external invaders. The Monte Carlo simulations show a surprisingly rich variety of the stable spatial distributions of species and subsequent phase transitions when tuning the control parameter Xs. These very simple models are able to demonstrate that the competition between these associations influences their composition. Sometimes the dominant association is developed via a domain growth. In other cases larger and larger invasion processes preceed the prevalence of one of the stable asociations. Under some conditions the survival of all the species can be maintained by the cyclic dominance occuring between these associations.Comment: 8 pages, 9 figure