Plane wave discontinuous Galerkin methods: exponential convergence of the hp-version

We consider the two-dimensional Helmholtz equation with constant coefficients on a domain with piecewise analytic boundary, modelling the scattering of acoustic waves at a sound-soft obstacle. Our discretisation relies on the Trefftz-discontinuous Galerkin approach with plane wave basis functions on meshes with very general element shapes, geometrically graded towards domain corners. We prove exponential convergence of the discrete solution in terms of number of unknowns.

Response of the North Atlantic wave climate to atmospheric modes of variability

This study investigates the relationship between the wind wave climate and the main climate modes of atmospheric variability in the North Atlantic Ocean. The modes considered are the North Atlantic Oscillation (NAO), the East Atlantic (EA) pattern, the East Atlantic Western Russian (EA/WR) pattern and the Scandinavian (SCAN) pattern. The wave dataset consists of buoys records, remote sensing altimetry observations and a numerical hindcast providing significant wave height (SWH), mean wave period (MWP) and mean wave direction (MWD) for the period 1989–2009. After evaluating the reliability of the hindcast, we focus on the impact of each mode on seasonal wave parameters and on the relative importance of wind-sea and swell components. Results demonstrate that the NAO and EA patterns are the most relevant, whereas EA/WR and SCAN patterns have a weaker impact on the North Atlantic wave climate variability. During their positive phases, both NAO and EA patterns are related to winter SWH at a rate that reaches 1 m per unit index along the Scottish coast (NAO) and Iberian coast (EA) patterns. In terms of winter MWD, the two modes induce a counterclockwise shift of up to 65° per negative NAO (positive EA) unit over west European coasts. They also increase the winter MWP in the North Sea and in the Bay of Biscay (up to 1 s per unit NAO) and along the western coasts of Europe and North Africa (1 s per unit EA). The impact of winter EA pattern on all wave parameters is mostly caused through the swell wave component.

Easterly wave disturbances over Northeast Brazil: an observational analysis

This paper aims to identify the circulation associated with Easterly Wave Disturbances (EWDs) that propagate toward the Eastern Northeast Brazil (ENEB) and their impact on the rainfall over ENEB during 2006 and 2007 rainy seasons (April–July). The EWDs identification and trajectory are analyzed using an automatic tracking technique (TracKH). The EWDs circulation patterns and their main features were obtained using the composite technique. To evaluate the TracKH efficiency, a validation was done by comparing the EWDs number tracked against observed cases obtained from an observational analysis. The mean characteristics of EWDs are 5.5-day period, propagation speed of ~9.5 m·s−1, and a 4500 km wavelength. A synoptic analysis shows that between days −2 d and 0 d, the low level winds presented cyclonic relative vorticity and convergence anomalies both in 2006 and 2007. The EWDs signals are strongest at low levels. The EWDs propagation is associated with relative humidity and precipitation positive anomalies and OLR and omega negative anomalies. The EWDs tracks are seen over all ENEB and their lysis occurs between the ENEB and marginally inside the continent. The tracking captured 71% of EWDs in all periods, indicating that an objective analysis is a promising method for EWDs detection.

Pseudopod growth and evolution during cell movement is controlled through SCAR/WAVE dephosphorylation

Regulated dephosphorylation of a fraction of the cellular SCAR pool is a key step in SCAR activation during pseudopod growth. Phosphorylation increases autoinhibition of the intact complex. Dephosphorylation weakens this interaction and facilitates SCAR activation but also destabilizes the protein. We show that SCAR is specifically dephosphorylated in pseudopods, increasing activation by Rac and lipids and supporting positive feedback of pseudopod growth.

Abi mutants in Dictyostelium reveal specific roles for the SCAR/WAVE complex in cytokinesis.

Actin polymerization drives multiple cell processes involving movement and shape change. SCAR/WAVE proteins connect signaling to actin polymerization through the activation of the Arp2/3 complex. SCAR/WAVE is normally found in a complex with four other proteins: PIR121, Nap1, Abi2,and HSPC300 (Figure S1A available online) [1-3]. However,there is no consensus as to whether the complex functions as an unchanging unit or if it alters its composition in response to stimulation, as originally proposed by Edenet al. [1]. It also is unclear whether complex members exclusively regulate SCAR/WAVEs or if they have additional targets [4-6]. Here, we analyze the roles of the unique Dictyostelium Abi. We find that abiA null mutants show less severe defects in motility than do scar null cells, indicating--unexpectedly--that SCAR retains partial activity in the absence of Abi. Furthermore, abiA null mutants have a serious defect in cytokinesis, which is not seen in other SCAR complex mutants and is seen only when SCAR itself is present. Detailed examination reveals that normal cytokinesis requires SCAR activity, apparently regulated through multiple pathways.

Regulation of actin assembly by SCAR/WAVE proteins.

Actin reorganization is a tightly regulated process that co-ordinates complex cellular events, such as cell migration, chemotaxis, phagocytosis and adhesion, but the molecular mechanisms that underlie these processes are not well understood. SCAR (suppressor of cAMP receptor)/WAVE [WASP (Wiskott-Aldrich syndrome protein)-family verprolin homology protein] proteins are members of the conserved WASP family of cytoskeletal regulators, which play a critical role in actin dynamics by triggering Arp2/3 (actin-related protein 2/3)-dependent actin nucleation. SCAR/WAVEs are thought to be regulated by a pentameric complex which also contains Abi (Abl-interactor), Nap (Nck-associated protein), PIR121 (p53-inducible mRNA 121) and HSPC300 (haematopoietic stem progenitor cell 300), but the structural organization of the complex and the contribution of its individual components to the regulation of SCAR/WAVE function remain unclear. Additional features of SCAR/WAVE regulation are highlighted by the discovery of other interactors and distinct complexes. It is likely that the combinatorial assembly of different components of SCAR/WAVE complexes will prove to be vital for their roles at the centre of dynamic actin reorganization.

A priori error analysis of space–time Trefftz discontinuous Galerkin methods for wave problems

We present and analyse a space–time discontinuous Galerkin method for wave propagation problems. The special feature of the scheme is that it is a Trefftz method, namely that trial and test functions are solution of the partial differential equation to be discretised in each element of the (space–time) mesh. The method considered is a modification of the discontinuous Galerkin schemes of Kretzschmar et al. (2014) and of Monk & Richter (2005). For Maxwell’s equations in one space dimension, we prove stability of the method, quasi-optimality, best approximation estimates for polynomial Trefftz spaces and (fully explicit) error bounds with high order in the meshwidth and in the polynomial degree. The analysis framework also applies to scalar wave problems and Maxwell’s equations in higher space dimensions. Some numerical experiments demonstrate the theoretical results proved and the faster convergence compared to the non-Trefftz version of the scheme.

The solsticial pause on Mars: 1. A planetary wave reanalysis

Large-scale planetary waves are diagnosed from an analysis of profiles retrieved from the Thermal Emission Spectrometer aboard the Mars Global Surveyor spacecraft during its scientific mapping phase. The analysis is conducted by assimilating thermal profiles and total dust opacity retrievals into a Mars global circulation model. Transient waves are largest throughout the northern hemisphere autumn, winter and spring period and almost absent during the summer. The southern hemisphere exhibits generally weaker transient wave behaviour. A striking feature of the low-altitude transient waves in the analysis is that they show a broad subsidiary minimum in amplitude centred on the winter solstice, a period when the thermal contrast between the summer hemisphere and the winter pole is strongest and baroclinic wave activity might be expected to be strong. This behaviour, here called the ‘solsticial pause,’ is present in every year of the analysis. This strong pause is under-represented in many independent model experiments, which tend to produce relatively uniform baroclinic wave activity throughout the winter. This paper documents and diagnoses the transient wave solsticial pause found in the analysis; a companion paper investigates the origin of the phenomenon in a series of model experiments.

Activation of p21-activated protein kinase alpha (alpha PAK) by hyperosmotic shock in neonatal ventricular myocytes.

The p21-activated protein kinases (PAKs) may participate in signalling from Cdc42/Rac1 to the stress-regulated MAPKs (SAPKs/JNKs and p38-/HOG-1-related-MAPKs). We characterized the expression and regulation of alpha PAK in cultured ventricular myocytes. alpha PAK was specifically immunoprecipitated from myocyte extracts. High basal alpha PAK activity was detected in unstimulated myocytes. Its activity was increased rapidly (<30 s) by hyperosmotic shock in the presence of okadaic acid, and was maximal by 3 min (187 +/- 7% relative to unstimulated cells). Endothelin-1 and interleukin-1beta, which also activate SAPKs/JNKs, did not increase alpha PAK activity and presumably act through different PAK isoforms or other mechanisms.

Stimulation of multiple mitogen-activated protein kinase sub-families by oxidative stress and phosphorylation of the small heat shock protein, HSP25/27, in neonatal ventricular myocytes.

We investigated the activation of three subfamilies of mitogen-activated protein kinases (MAPKs), namely the stress-activated protein kinases/c-Jun N-terminal kinases (SAPKs/JNKs), the extracellularly responsive kinases (ERKs) and p38-MAPK, by oxidative stress as exemplified by H2O2 in primary cultures of neonatal rat ventricular myocytes. The 46 and 54 kDa species of SAPKs/JNKs were activated 5- and 10-fold, respectively, by 0.1 mM H2O2 (the maximally effective concentration). Maximal activation occurred at 15-30 min, but was still detectable after 2 h. Both ERK1 and ERK2 were activated 16-fold by 0.1 mM H2O2 with a similar time course to the SAPKs/JNKs, and this was comparable with their activation by 1 microM PMA, the most powerful activator of ERKs that we have so far identified in these cells. The activation of ERKs by H2O2 was inhibited by PD98059, which inhibits the activation of MAPK (or ERK) kinases, and by the protein kinase C (PKC) inhibitor, GF109203X. ERK activation was also inhibited by down-regulation of PMA-sensitive PKC isoforms. p38-MAPK was activated by 0.1 mM H2O2 as shown by an increase in its phosphorylation. However, maximal phosphorylation (activation) was more rapid (<5 min) than for the SAPKs/JNKs or the ERKs. We studied the downstream consequences of p38-MAPK activation by examining activation of MAPK-activated protein kinase 2 (MAPKAPK2) and phosphorylation of the MAPKAPK2 substrate, the small heat shock protein HSP25/27. As with p38-MAPK, MAPKAPK2 was rapidly activated (maximal within 5 min) by 0.1 mM H2O2. This activation was abolished by 10 microM SB203580, a selective inhibitor of certain p38-MAPK isoforms. The phosphorylation of HSP25/27 rapidly followed activation of MAPKAPK2 and was also inhibited by SB203580. Phosphorylation of HSP25/27 was associated with a decrease in its aggregation state. These data indicate that oxidative stress is a powerful activator of all three MAPK subfamilies in neonatal rat ventricular myocytes. Activation of all three MAPKs has been associated with the development of the hypertrophic phenotype. However, stimulation of p38-MAPK and the consequent phosphorylation of HSP25/27 may also be important in cardioprotection.

Effects of oxidative stress on the cardiac myocyte proteome: modifications to peroxiredoxins and small heat shock proteins

Endogenous oxidative stress is a likely cause of cardiac myocyte death in vivo. We examined the early (0-2 h) changes in the proteome of isolated cardiac myocytes from neonatal rats exposed to H2O2 (0.1 mM), focussing on proteins with apparent molecular masses of between 20 and 30 kDa. Proteins were separated by two-dimensional gel electrophoresis (2DGE), located by silver-staining and identified by mass spectrometry. Incorporation of [35S]methionine or 32Pi was also studied. For selected proteins, transcript abundance was examined by reverse transcriptase-polymerase chain reaction. Of the 38 protein spots in the region, 23 were identified. Two families showed changes in 2DGE migration or abundance with H2O2 treatment: the peroxiredoxins and two small heat shock protein (Hsp) family members: heat shock 27 kDa protein 1 (Hsp25) and alphaB-crystallin. Peroxiredoxins shifted to lower pI values and this was probably attributable to 'over-oxidation' of active site Cys-residues. Hsp25 also shifted to lower pI values but this was attributable to phosphorylation. alphaB-crystallin migration was unchanged but its abundance decreased. Transcripts encoding peroxiredoxins 2 and 5 increased significantly. In addition, 10 further proteins were identified. For two (glutathione S-transferase pi, translationally-controlled tumour protein), we could not find any previous references indicating their occurrence in cardiac myocytes. We conclude that exposure of cardiac myocytes to oxidative stress causes post-translational modification in two protein families involved in cytoprotection. These changes may be potentially useful diagnostically. In the short term, oxidative stress causes few detectable changes in global protein abundance as assessed by silver-staining.

Geometric polarimetry − part I: spinors and wave states

A new formal approach for representation of polarization states of coherent and partially coherent electromagnetic plane waves is presented. Its basis is a purely geometric construction for the normalised complex-analytic coherent wave as a generating line in the sphere of wave directions, and whose Stokes vector is determined by the intersection with the conjugate generating line. The Poincare sphere is now located in physical space, simply a coordination of the wave sphere, its axis aligned with the wave vector. Algebraically, the generators representing coherent states are represented by spinors, and this is made consistent with the spinor-tensor representation of electromagnetic theory by means of an explicit reference spinor we call the phase flag. As a faithful unified geometric representation, the new model provides improved formal tools for resolving many of the geometric difficulties and ambiguities that arise in the traditional formalism.

Rossby wave propagation on potential vorticity fronts with finite width

The horizontal gradient of potential vorticity (PV) across the tropopause typically declines with lead time in global numerical weather forecasts and tends towards a steady value dependent on model resolution. This paper examines how spreading the tropopause PV contrast over a broader frontal zone affects the propagation of Rossby waves. The approach taken is to analyse Rossby waves on a PV front of finite width in a simple single-layer model. The dispersion relation for linear Rossby waves on a PV front of infinitesimal width is well known; here an approximate correction is derived for the case of a finite width front, valid in the limit that the front is narrow compared to the zonal wavelength. Broadening the front causes a decrease in both the jet speed and the ability of waves to propagate upstream. The contribution of these changes to Rossby wave phase speeds cancel at leading order. At second order the decrease in jet speed dominates, meaning phase speeds are slower on broader PV fronts. This asymptotic phase speed result is shown to hold for a wide class of single-layer dynamics with a varying range of PV inversion operators. The phase speed dependence on frontal width is verified by numerical simulations and also shown to be robust at finite wave amplitude, and estimates are made for the error in Rossby wave propagation speeds due to the PV gradient error present in numerical weather forecast models.