Supercloseness of Orthogonal Projections onto Nearby Finite Element Spaces

We derive upper bounds on the difference between the orthogonal projections of a smooth function $u$ onto two finite element spaces that are nearby, in the sense that the support of every shape function belonging to one but not both of the spaces is contained in a common region whose measure tends to zero under mesh refinement. The bounds apply, in particular, to the setting in which the two finite element spaces consist of continuous functions that are elementwise polynomials over shape-regular, quasi-uniform meshes that coincide except on a region of measure $O(h^\gamma)$, where $\gamma$ is a nonnegative scalar and $h$ is the mesh spacing. The projector may be, for example, the orthogonal projector with respect to the $L^2$- or $H^1$-inner product. In these and other circumstances, the bounds are superconvergent under a few mild regularity assumptions. That is, under mesh refinement, the two projections differ in norm by an amount that decays to zero at a faster rate than the amounts by which each projection differs from $u$. We present numerical examples to illustrate these superconvergent estimates and verify the necessity of the regularity assumptions on $u$

Comparison of several system identification methods for flexible structures

In the last few years various methods of identifying structural dynamics models from modal testing data have appeared. A comparison is presented of four of these algorithms: the Eigensystem Realization Algorithm (ERA), the modified version ERA/DC where DC indicated that it makes use of data correlation, the Q-Markov Cover algorithm, and an algorithm due to Moonen, DeMoor, Vandenberghe, and Vandewalle. The comparison is made using a five mode computer module of the 20 meter Mini-Mast truss structure at NASA Langley Research Center, and various noise levels are superimposed to produced simulated data. The results show that for the example considered ERA/DC generally gives the best results; that ERA/DC is always at least as good as ERA which is shown to be a special case of ERA/DC; that Q-Markov requires the use of significantly more data than ERA/DC to produce comparable results; and that is some situations Q-Markov cannot produce comparable results

Alcohol-Induced Histone Acetylation Reveals a Gene Network Involved in Alcohol Tolerance

Alfredo Ghezzi, Harish R. Krishnan, Linda Lew, Francisco J. Prado III, Darryl S. Ong, Nigel S. Atkinson, Section of Neurobiology and Waggoner Center for Alcohol and Addiction Research, The University of Texas at Austin, Austin, Texas, United States of AmericaSustained or repeated exposure to sedating drugs, such as alcohol, triggers homeostatic adaptations in the brain that lead to the development of drug tolerance and dependence. These adaptations involve long-term changes in the transcription of drug-responsive genes as well as an epigenetic restructuring of chromosomal regions that is thought to signal and maintain the altered transcriptional state. Alcohol-induced epigenetic changes have been shown to be important in the long-term adaptation that leads to alcohol tolerance and dependence endophenotypes. A major constraint impeding progress is that alcohol produces a surfeit of changes in gene expression, most of which may not make any meaningful contribution to the ethanol response under study. Here we used a novel genomic epigenetic approach to find genes relevant for functional alcohol tolerance by exploiting the commonalities of two chemically distinct alcohols. In Drosophila melanogaster, ethanol and benzyl alcohol induce mutual cross-tolerance, indicating that they share a common mechanism for producing tolerance. We surveyed the genome-wide changes in histone acetylation that occur in response to these drugs. Each drug induces modifications in a large number of genes. The genes that respond similarly to either treatment, however, represent a subgroup enriched for genes important for the common tolerance response. Genes were functionally tested for behavioral tolerance to the sedative effects of ethanol and benzyl alcohol using mutant and inducible RNAi stocks. We identified a network of genes that are essential for the development of tolerance to sedation by alcohol.This work was supported by National Institute of Health grant R01 AA018037 to NSA (http://www.nih.gov/). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.NeuroscienceWaggoner Center for Alcohol and Addiction ResearchEmail: [email protected] (AG)Email: [email protected] (NSA

Optoelectronics of Inverted Type-I CdS/CdSe Core/Crown Quantum Ring

Inverted type-I heterostructure core/crown quantum rings (QRs) are quantum-efficient luminophores, whose spectral characteristics are highly tunable. Here, we study the optoelectronic properties of type-I core/crown CdS/CdSe QRs in the zincblende phase - over contrasting lateral size and crown width. For this we inspect their strain profiles, transition energies, transition matrix elements, spatial charge densities, electronic bandstructure, band-mixing probabilities, optical gain spectra, maximum optical gains and differential optical gains. Our framework uses an effective-mass envelope function theory based on the 8-band k$\cdot$p method employing the valence force field model for calculating the atomic strain distributions. The gain calculations are based on the density-matrix equation and take into consideration the excitonic effects with intraband scattering. Variations in the QR lateral size and relative widths of core and crown (ergo the composition) affect their energy levels, band-mixing probabilities, optical transition matrix elements, emission wavelengths/intensity, etc. The optical gain of QRs is also strongly dimension and composition dependent with further dependency on the injection carrier density causing band-filling effect. They also affect the maximum and differential gain at varying dimensions and compositions.Comment: Published in AIP Journal of Applied Physics (11 pages, 7 figures

Electronic structure of silicon-based nanostructures

We have developed an unifying tight-binding Hamiltonian that can account for the electronic properties of recently proposed Si-based nanostructures, namely, Si graphene-like sheets and Si nanotubes. We considered the $sp^3s^*$ and $sp^{3}$ models up to first- and second-nearest neighbors, respectively. Our results show that the Si graphene-like sheets considered here are metals or zero-gap semiconductors, and that the corresponding Si nanotubes follow the so-called Hamada's rule [Phys. Rev. Lett. {\bf 68}, 1579 1992]. Comparison to a recent {\it ab initio} calculation is made.Comment: 12 pages, 6 Figure