Ordering and finite-size effects in the dynamics of one-dimensional transient patterns

We introduce and analyze a general one-dimensional model for the description of transient patterns which occur in the evolution between two spatially homogeneous states. This phenomenon occurs, for example, during the Freedericksz transition in nematic liquid crystals.The dynamics leads to the emergence of finite domains which are locally periodic and independent of each other. This picture is substantiated by a finite-size scaling law for the structure factor. The mechanism of evolution towards the final homogeneous state is by local roll destruction and associated reduction of local wavenumber. The scaling law breaks down for systems of size comparable to the size of the locally periodic domains. For systems of this size or smaller, an apparent nonlinear selection of a global wavelength holds, giving rise to long lived periodic configurations which do not occur for large systems. We also make explicit the unsuitability of a description of transient pattern dynamics in terms of a few Fourier mode amplitudes, even for small systems with a few linearly unstable modes.Comment: 18 pages (REVTEX) + 10 postscript figures appende

The forgotten drought of 1765–1768: Reconstructing and re-evaluating historical droughts in the British and Irish Isles

Historical precipitation records are fundamental for the management of water resources, yet rainfall observations typically span 100–15 0 years at most, with considerable uncertainties surrounding earlier records. Here, we analyse some of the longest a vailabl e precipitation records globally, for England and Wales, Scotland and Ireland. To assess the credibility of these records and extend them further back in time, we statistically reconstruct (using independent predictors) monthly precipitation series representing these regions for the period 1748–2000. By applying the Standardized Precipi- tation Index at 12-month accumulations (SPI-12) to the observed and our reconstructed series we re-evaluate historical meteorological droughts. We find strong agreement between observed and reconstructed drought chronol- ogies in post-1870 records, but divergence in e arlier series due to biases in early precipitation observations. Hence, the 1800s decade was less drought prone in our reconstructions relative to observations. Overall, the drought of 1834–1836 was the most intense SPI-12 event in our reconstruction for England and Wales. Newspaper accounts and documentary sources confirm the extent of impacts across England in particular. We also identify a major, “forgotten” drought in 1765–1768 that affected the British-Irish Isles. This was the most intense event in our reconstructions for Ireland and Scotland, and ranks first for accumulated deficits a cross all three regional series. Moreover, the 1765–1768 event was also the most extreme multi-year drought across all regional series when considering 36-month a ccumulations (SPI-36). Newspaper and other sources confirm the occurrence and major socio- economic impact of this drought, such as major rivers like the Shannon being fordable by foot. Our results provide new insights into historical droughts across the British Irish Isles. Given the importance of historical droughts for stress-testing the resilience of water resources, drought plans and supply sys- tems, the forgotten drought of 1765–1 768 offers perhaps the most extreme benchmark scenario in more than 250-years

Making Almost Commuting Matrices Commute

Suppose two Hermitian matrices $A,B$ almost commute ($\Vert [A,B] \Vert \leq \delta$). Are they close to a commuting pair of Hermitian matrices, $A',B'$, with $\Vert A-A' \Vert,\Vert B-B'\Vert \leq \epsilon$? A theorem of H. Lin shows that this is uniformly true, in that for every $\epsilon>0$ there exists a $\delta>0$, independent of the size $N$ of the matrices, for which almost commuting implies being close to a commuting pair. However, this theorem does not specify how $\delta$ depends on $\epsilon$. We give uniform bounds relating $\delta$ and $\epsilon$. We provide tighter bounds in the case of block tridiagonal and tridiagonal matrices and a fully constructive method in that case. Within the context of quantum measurement, this implies an algorithm to construct a basis in which we can make a {\it projective} measurement that approximately measures two approximately commuting operators simultaneously. Finally, we comment briefly on the case of approximately measuring three or more approximately commuting operators using POVMs (positive operator-valued measures) instead of projective measurements.Comment: 22 pages; tighter bounds; Note: fixed mistake in proof pointed out by Filonov and Kachkovski

The Drosophila melanogaster Genetic Reference Panel

A major challenge of biology is understanding the relationship between molecular genetic variation and variation in quantitative traits, including fitness. This relationship determines our ability to predict phenotypes from genotypes and to understand how evolutionary forces shape variation within and between species. Previous efforts to dissect the genotype-phenotype map were based on incomplete genotypic information. Here, we describe the Drosophila melanogaster Genetic Reference Panel (DGRP), a community resource for analysis of population genomics and quantitative traits. The DGRP consists of fully sequenced inbred lines derived from a natural population. Population genomic analyses reveal reduced polymorphism in centromeric autosomal regions and the X chromosome, evidence for positive and negative selection, and rapid evolution of the X chromosome. Many variants in novel genes, most at low frequency, are associated with quantitative traits and explain a large fraction of the phenotypic variance. The DGRP facilitates genotype-phenotype mapping using the power of Drosophila genetics

Energetic particle influence on the Earth's atmosphere

This manuscript gives an up-to-date and comprehensive overview of the effects of energetic particle precipitation (EPP) onto the whole atmosphere, from the lower thermosphere/mesosphere through the stratosphere and troposphere, to the surface. The paper summarizes the different sources and energies of particles, principally galactic cosmic rays (GCRs), solar energetic particles (SEPs) and energetic electron precipitation (EEP). All the proposed mechanisms by which EPP can affect the atmosphere are discussed, including chemical changes in the upper atmosphere and lower thermosphere, chemistry-dynamics feedbacks, the global electric circuit and cloud formation. The role of energetic particles in Earth’s atmosphere is a multi-disciplinary problem that requires expertise from a range of scientific backgrounds. To assist with this synergy, summary tables are provided, which are intended to evaluate the level of current knowledge of the effects of energetic particles on processes in the entire atmosphere

Generator Life and Power Electronics

The deleterious effect of full bridge rectifiers on the output of an AC generator deserves attention from the Naval community. The harmonics observed at the stator of the generator not only introduce hysteresis and eddy current losses, but voltage spikes that impact the life of the generator. The two primary factors compromising life are localized heating due to harmonics and voltage spikes that cause insulation failure through partial discharge. Induced eddy currents are proportional to frequency squared.Center for Electromechanic