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

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

Mechanistic mathematical model of polarity in yeast

The establishment of cell polarity involves positive-feedback mechanisms that concentrate polarity regulators, including the conserved GTPase Cdc42p, at the “front” of the polarized cell. Previous studies in yeast suggested the presence of two parallel positive-feedback loops, one operating as a diffusion-based system, and the other involving actin-directed trafficking of Cdc42p on vesicles. F-actin (and hence directed vesicle traffic) speeds fluorescence recovery of Cdc42p after photobleaching, suggesting that vesicle traffic of Cdc42p contributes to polarization. We present a mathematical modeling framework that combines previously developed mechanistic reaction-diffusion and vesicle-trafficking models. Surprisingly, the combined model recapitulated the observed effect of vesicle traffic on Cdc42p dynamics even when the vesicles did not carry significant amounts of Cdc42p. Vesicle traffic reduced the concentration of Cdc42p at the front, so that fluorescence recovery mediated by Cdc42p flux from the cytoplasm took less time to replenish the bleached pool. Simulations in which Cdc42p was concentrated into vesicles or depleted from vesicles yielded almost identical predictions, because Cdc42p flux from the cytoplasm was dominant. These findings indicate that vesicle-mediated delivery of Cdc42p is not required to explain the observed Cdc42p dynamics, and raise the question of whether such Cdc42p traffic actually contributes to polarity establishment

Interaction between bud-site selection and polarity-establishment machineries in budding yeast

Saccharomyces cerevisiae yeast cells polarize in order to form a single bud in each cell cycle. Distinct patterns of bud-site selection are observed in haploid and diploid cells. Genetic approaches have identified the molecular machinery responsible for positioning the bud site: during bud formation, specific locations are marked with immobile landmark proteins. In the next cell cycle, landmarks act through the Ras-family GTPase Rsr1 to promote local activation of the conserved Rho-family GTPase, Cdc42. Additional Cdc42 accumulates by positive feedback, creating a concentrated patch of GTP-Cdc42, which polarizes the cytoskeleton to promote bud emergence. Using time-lapse imaging and mathematical modelling, we examined the process of bud-site establishment. Imaging reveals unexpected effects of the bud-site-selection system on the dynamics of polarity establishment, raising new questions about how that system may operate. We found that polarity factors sometimes accumulate at more than one site among the landmark-specified locations, and we suggest that competition between clusters of polarity factors determines the final location of the Cdc42 cluster. Modelling indicated that temporally constant landmark-localized Rsr1 would weaken or block competition, yielding more than one polarity site. Instead, we suggest that polarity factors recruit Rsr1, effectively sequestering it from other locations and thereby terminating landmark activity

Spin orbit torque induced asymmetric depinning of chiral Néel domain wall in Co/Ni heterostructures

In this letter, we report on distinct depinning of a chiral Néel domain wall (DW) driven by spin-orbit torque (SOT) in Co/Ni nanowires with symmetric potential barriers. In these structures, DW propagation was shown to be in the opposite direction to the electron flow as evidenced from current assisted DW depinning measurements. A transition from field dominated DW depinning to SOT dominated DW depinning was observed as the bias current was increased. For SOT dominated DW depinning, the Up-Down DW exhibits a larger depinning field as compared to the Down-Up DW. This is attributed to the interplay between the SOT and Dzyaloshinskii-Moriya interaction in the structure

Asymmetrical domain wall propagation in bifurcated PMA wire structure due to the Dzyaloshinskii-Moriya interaction

Controlling domain wall (DW) motion in complex magnetic network structures is of paramount significance for the development of spin-based devices. Here, we report on the dynamics of a propagating DW in a bifurcated ferromagnetic wire with perpendicular magnetic anisotropy (PMA). The Dzyaloshinskii-Moriya interaction (DMI) in the wire structure induces a tilt angle to the injected DW, which leads to a quasi-selective propagation through the network branch. The DW tilting causes a field interval between DWs to arrive at Hall bars in the individual branches. Micromagnetic results further show that by tailoring the strength of the DMI, the control of DW dynamics in the PMA complex network structures can be achieved

Formulation and performance of variational integrators for rotating bodies

Variational integrators are obtained for two mechanical systems whose configuration spaces are, respectively, the rotation group and the unit sphere. In the first case, an integration algorithm is presented for Euler’s equations of the free rigid body, following the ideas of Marsden et al. (Nonlinearity 12:1647–1662, 1999). In the second example, a variational time integrator is formulated for the rigid dumbbell. Both methods are formulated directly on their nonlinear configuration spaces, without using Lagrange multipliers. They are one-step, second order methods which show exact conservation of a discrete angular momentum which is identified in each case. Numerical examples illustrate their properties and compare them with existing integrators of the literature