The near-stability of the Lax-Wendroff method

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46325/1/211_2005_Article_BF01397974.pd

Estimates in Beurling--Helson type theorems. Multidimensional case

We consider the spaces $A_p(\mathbb T^m)$ of functions $f$ on the $m$ -dimensional torus $\mathbb T^m$ such that the sequence of the Fourier coefficients $\hat{f}=\{\hat{f}(k), ~k \in \mathbb Z^m\}$ belongs to $l^p(\mathbb Z^m), ~1\leq p<2$. The norm on $A_p(\mathbb T^m)$ is defined by $\|f\|_{A_p(\mathbb T^m)}=\|\hat{f}\|_{l^p(\mathbb Z^m)}$. We study the rate of growth of the norms $\|e^{i\lambda\varphi}\|_{A_p(\mathbb T^m)}$ as $|\lambda|\rightarrow \infty, ~\lambda\in\mathbb R,$ for $C^1$ -smooth real functions $\varphi$ on $\mathbb T^m$ (the one-dimensional case was investigated by the author earlier). The lower estimates that we obtain have direct analogues for the spaces $A_p(\mathbb R^m)$

Transient evolution of C-type shocks in dusty regions of varying density

Outflows of young stars drive shocks into dusty, molecular regions. Most models of such shocks assume that they are steady and propagating perpendicular to the magnetic field. Real shocks often violate both of these assumptions and the media through which they propagate are inhomogeneous. We use the code employed previously to produce the first time-dependent simulations of fast-mode, oblique C-type shocks interacting with density perturbations. We include a self-consistent calculation of the thermal and ionisation balances and a fluid treatment of grains. We identify features that develop when a multifluid shock encounters a density inhomogeneity to investigate whether any part of the precursor region ever behaves in a quasi-steady fashion. If it does the shock may be modelled approximately without solving the time-dependent hydromagnetic equations. Simulations were made for initially steady oblique C-type shocks encountering density inhomogeneities. For a semi-finite inhomogeneity with a density larger than the surrounding medium, a transmitted shock evolves from being J-type to a steady C-type shock on a timescale comparable to the ion-flow time through it. A sufficiently upstream part of the precursor of an evolving J-type shock is quasi-steady. The ion-flow timescale is also relevant for the evolution of a shock moving into a region of decreasing density. The models for shocks propagating into regions in which the density increases and then decreases to its initial value cannot be entirely described in terms of the results obtained for monotonically increasing and decreasing densities. For the latter model, the long-term evolution to a C-type shock cannot be approximated by quasi-steady models.Comment: 11 pages, 9 figure

Absorbing boundary conditions for the Westervelt equation

The focus of this work is on the construction of a family of nonlinear absorbing boundary conditions for the Westervelt equation in one and two space dimensions. The principal ingredient used in the design of such conditions is pseudo-differential calculus. This approach enables to develop high order boundary conditions in a consistent way which are typically more accurate than their low order analogs. Under the hypothesis of small initial data, we establish local well-posedness for the Westervelt equation with the absorbing boundary conditions. The performed numerical experiments illustrate the efficiency of the proposed boundary conditions for different regimes of wave propagation

El chinche apestoso marrón marmolado Halyomorpha halys

El chinche apestoso marrón marmolado (Halyomorpha halys) es un insecto invasor y una amenaza muy grave para la agricultura de Oregon. Se alimenta de más de 100 plantas incluyendo plantas agrícolas y ornamentales de importancia económica. Esta tarjeta presenta con fotos y descripciones para ayudar a identificar el chinche apestoso marrón marmolado y distinguirlos de otros insectos. La tarjeta también incluye fotos de los síntomas de daño en varias plantas.Published January 2013. Facts and recommendations in this publication may no longer be valid. Please look for up-to-date information in the OSU Extension Catalog: http://extension.oregonstate.edu/catalogKeywords: Halyomorpha halys, brown marmorated stink bug, invasive, insecto invasor, el chinche apestoso marrón marmolad

Characteristic Evolution and Matching

I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black hole spacetime. Cauchy codes have now been successful at simulating all aspects of the binary black hole problem inside an artificially constructed outer boundary. A prime application of characteristic evolution is to extend such simulations to null infinity where the waveform from the binary inspiral and merger can be unambiguously computed. This has now been accomplished by Cauchy-characteristic extraction, where data for the characteristic evolution is supplied by Cauchy data on an extraction worldtube inside the artificial outer boundary. The ultimate application of characteristic evolution is to eliminate the role of this outer boundary by constructing a global solution via Cauchy-characteristic matching. Progress in this direction is discussed.Comment: New version to appear in Living Reviews 2012. arXiv admin note: updated version of arXiv:gr-qc/050809

Developmental Expression of Kv Potassium Channels at the Axon Initial Segment of Cultured Hippocampal Neurons

Axonal outgrowth and the formation of the axon initial segment (AIS) are early events in the acquisition of neuronal polarity. The AIS is characterized by a high concentration of voltage-dependent sodium and potassium channels. However, the specific ion channel subunits present and their precise localization in this axonal subdomain vary both during development and among the types of neurons, probably determining their firing characteristics in response to stimulation. Here, we characterize the developmental expression of different subfamilies of voltage-gated potassium channels in the AISs of cultured mouse hippocampal neurons, including subunits Kv1.2, Kv2.2 and Kv7.2. In contrast to the early appearance of voltage-gated sodium channels and the Kv7.2 subunit at the AIS, Kv1.2 and Kv2.2 subunits were tethered at the AIS only after 10 days in vitro. Interestingly, we observed different patterns of Kv1.2 and Kv2.2 subunit expression, with each confined to distinct neuronal populations. The accumulation of Kv1.2 and Kv2.2 subunits at the AIS was dependent on ankyrin G tethering, it was not affected by disruption of the actin cytoskeleton and it was resistant to detergent extraction, as described previously for other AIS proteins. This distribution of potassium channels in the AIS further emphasizes the heterogeneity of this structure in different neuronal populations, as proposed previously, and suggests corresponding differences in action potential regulation

Mechanism of Heparin Acceleration of Tissue Inhibitor of Metalloproteases-1 (TIMP-1) Degradation by the Human Neutrophil Elastase

Heparin has been shown to regulate human neutrophil elastase (HNE) activity. We have assessed the regulatory effect of heparin on Tissue Inhibitor of Metalloproteases-1 [TIMP-1] hydrolysis by HNE employing the recombinant form of TIMP-1 and correlated FRET-peptides comprising the TIMP-1 cleavage site. Heparin accelerates 2.5-fold TIMP-1 hydrolysis by HNE. The kinetic parameters of this reaction were monitored with the aid of a FRET-peptide substrate that mimics the TIMP-1 cleavage site in pre-steady-state conditionsby using a stopped-flow fluorescence system. The hydrolysis of the FRET-peptide substrate by HNE exhibits a pre-steady-state burst phase followed by a linear, steady-state pseudo-first-order reaction. The HNE acylation step (k2 = 21±1 s−1) was much higher than the HNE deacylation step (k3 = 0.57±0.05 s−1). The presence of heparin induces a dramatic effect in the pre-steady-state behavior of HNE. Heparin induces transient lag phase kinetics in HNE cleavage of the FRET-peptide substrate. The pre-steady-state analysis revealed that heparin affects all steps of the reaction through enhancing the ES complex concentration, increasing k1 2.4-fold and reducing k−1 3.1-fold. Heparin also promotes a 7.8-fold decrease in the k2 value, whereas the k3 value in the presence of heparin was increased 58-fold. These results clearly show that heparin binding accelerates deacylation and slows down acylation. Heparin shifts the HNE pH activity profile to the right, allowing HNE to be active at alkaline pH. Molecular docking and kinetic analysis suggest that heparin induces conformational changes in HNE structure. Here, we are showing for the first time that heparin is able to accelerate the hydrolysis of TIMP-1 by HNE. The degradation of TIMP-1is associated to important physiopathological states involving excessive activation of MMPs

Genetic Control of a Central Pattern Generator: Rhythmic Oromotor Movement in Mice Is Controlled by a Major Locus near Atp1a2

Fluid licking in mice is a rhythmic behavior that is controlled by a central pattern generator (CPG) located in a complex of brainstem nuclei. C57BL/6J (B6) and DBA/2J (D2) strains differ significantly in water-restricted licking, with a highly heritable difference in rates (h2≥0.62) and a corresponding 20% difference in interlick interval (mean ± SEM = 116.3±1 vs 95.4±1.1 ms). We systematically quantified motor output in these strains, their F1 hybrids, and a set of 64 BXD progeny strains. The mean primary interlick interval (MPI) varied continuously among progeny strains. We detected a significant quantitative trait locus (QTL) for a CPG controlling lick rate on Chr 1 (Lick1), and a suggestive locus on Chr 10 (Lick10). Linkage was verified by testing of B6.D2-1D congenic stock in which a segment of Chr 1 of the D2 strain was introgressed onto the B6 parent. The Lick1 interval on distal Chr 1 contains several strong candidate genes. One of these is a sodium/potassium pump subunit (Atp1a2) with widespread expression in astrocytes, as well as in a restricted population of neurons. Both this subunit and the entire Na+/K+-ATPase molecule have been implicated in rhythmogenesis for respiration and locomotion. Sequence variants in or near Apt1a2 strongly modulate expression of the cognate mRNA in multiple brain regions. This gene region has recently been sequenced exhaustively and we have cataloged over 300 non-coding and synonymous mutations segregating among BXD strains, one or more of which is likely to contribute to differences in central pattern generator tempo