Analysis of and workarounds for element reversal for a finite element-based algorithm for warping triangular and tetrahedral meshes

We consider an algorithm called FEMWARP for warping triangular and tetrahedral finite element meshes that computes the warping using the finite element method itself. The algorithm takes as input a two- or three-dimensional domain defined by a boundary mesh (segments in one dimension or triangles in two dimensions) that has a volume mesh (triangles in two dimensions or tetrahedra in three dimensions) in its interior. It also takes as input a prescribed movement of the boundary mesh. It computes as output updated positions of the vertices of the volume mesh. The first step of the algorithm is to determine from the initial mesh a set of local weights for each interior vertex that describes each interior vertex in terms of the positions of its neighbors. These weights are computed using a finite element stiffness matrix. After a boundary transformation is applied, a linear system of equations based upon the weights is solved to determine the final positions of the interior vertices. The FEMWARP algorithm has been considered in the previous literature (e.g., in a 2001 paper by Baker). FEMWARP has been succesful in computing deformed meshes for certain applications. However, sometimes FEMWARP reverses elements; this is our main concern in this paper. We analyze the causes for this undesirable behavior and propose several techniques to make the method more robust against reversals. The most successful of the proposed methods includes combining FEMWARP with an optimization-based untangler.Comment: Revision of earlier version of paper. Submitted for publication in BIT Numerical Mathematics on 27 April 2010. Accepted for publication on 7 September 2010. Published online on 9 October 2010. The final publication is available at http://www.springerlink.co

VEGFA, B, C: Implications of the C-Terminal Sequence Variations for the Interaction with Neuropilins

Vascular endothelial growth factors (VEGFs) are the key regulators of blood and lymphatic vessels’ formation and function. Each of the proteins from the homologous family VEGFA, VEGFB, VEGFC and VEGFD employs a core cysteine-knot structural domain for the specific interaction with one or more of the cognate tyrosine kinase receptors. Additional diversity is exhibited by the involvement of neuropilins–transmembrane co-receptors, whose b1 domain contains the binding site for the C-terminal sequence of VEGFs. Although all relevant isoforms of VEGFs that interact with neuropilins contain the required C-terminal Arg residue, there is selectivity of neuropilins and VEGF receptors for the VEGF proteins, which is reflected in the physiological roles that they mediate. To decipher the contribution made by the C-terminal sequences of the individual VEGF proteins to that functional differentiation, we determined structures of molecular complexes of neuropilins and VEGFderived peptides and examined binding interactions for all neuropilin-VEGF pairs experimentally and computationally. While X-ray crystal structures and ligand-binding experiments highlighted similarities between the ligands, the molecular dynamics simulations uncovered conformational preferences of VEGF-derived peptides beyond the C-terminal arginine that contribute to the ligand selectivity of neuropilins. The implications for the design of the selective antagonists of neuropilins’ functions are discussed

Peptides Derived from Vascular Endothelial Growth Factor B Show Potent Binding to Neuropilin-1

Vascular endothelial growth factors (VEGFs) regulate significant pathways in angiogenesis, myocardial and neuronal protection, metabolism, and cancer progression. The VEGF-B isoform is involved in cell survival, anti-apoptotic and antioxidant mechanisms, through binding to VEGF receptor 1 and neuropilin-1 (NRP-1). We employed surface plasmon resonance technology and X-ray crystallography to analyse the molecular basis of the interaction between VEGF-B and the b1 domain of NRP-1, and developed VEGF-B - C-terminus derived peptides to be used as chemical tools for studying VEGF-B - NRP-1 related pathways. Peptide lipidation was used as a means to stabilise the peptides. VEGF-B - derived peptides containing a C-terminal arginine show potent binding to NRP1-b1. Peptide lipidation increased binding residence time and improved plasma stability. A crystal structure of a peptide with NRP-1 demonstrated that VEGF-B peptides bind at the canonical C-terminal Arginine binding site. VEGF-B C-terminus imparts higher affinity for NRP-1 than the corresponding VEGF-A_{165} region. This tight binding may impact on the activity and selectivity of the full-length protein. The VEGF-B_{167} derived peptides were more effective than VEGF-A_{165} peptides in blocking functional phosphorylation events. Blockers of VEGF-B function have potential applications in diabetes and non-alcoholic fatty liver disease

Doping effects in the coupled, two-leg spin ladder BiCu2PO6

We report preparation, x-ray diffraction, magnetic susceptibility chi(T) and heat capacity Cp(T) measurements on the undoped samples as also samples with Zn-doped (S = 0) at Cu site, Ni doped (S = 1) at Cu site, and Ca-doped (holes) at Bi site in the coupled two-leg spin ladder system BiCu2PO6. While, Zn shows complete solid solubility, Ni could be doped to about 20% and Ca to about 15%. Magnetization and heat capacity data in the undoped compound point towards the existence of frustration effects. In all the samples, the chi(T) at low temperature increases with doping content. The Zn-induced susceptibility is smaller than that due to effective S=1/2 moments possibly due to frustrating next-nearest-neighbor interactions along the leg. For Zn content x > 0.01, chi(T) deviates from the Curie-law at low temperatures. The magnetic specific heat data Cm(T) for the Zn-doped samples show weak anomalies at low temperature in agreement with chi(T) behavior. The anomalies are suggestive of spin freezing at low-T. In contrast, prominent effects are observed in chi(T) and Cm(T) on Ni-doped samples. The zero-field-cooled (ZFC) and field-cooled (FC) chi(T) data are different from each other at low temperature unlike that for Zn doped samples, clearly indicating a transition to a spin-glass like phase. No anomalies were found in Ca- or Pb-doped samples.Comment: 16 pages, 9 figures, Submitted to J. Phy. Cond. Matte

On the Spiral Structure of the Milky Way Galaxy

We consider the possible pattern of the overall spiral structure of the Galaxy, using data on the distribution of neutral (atomic), molecular, and ionized hydrogen, on the base of the hypothesis of the spiral structure being symmetric, i.e. the assumption that spiral arms are translated into each other for a rotation around the galactic center by 180{\deg} (a two-arm pattern) or by 90{\deg} (a four-arm pattern). We demonstrate that, for the inner region, the observations are best represented with a four-arm scheme of the spiral pattern, associated with all-Galaxy spiral density waves. The basic position is that of the Carina arm, reliably determined from distances to HII regions and from HI and H2 radial velocities. This pattern is continued in the quadrants III and IV with weak outer HI arms; from their morphology, the Galaxy should be considered an asymmetric multi-arm spiral. The kneed shape of the outer arms that consist of straight segments can indicate that these arms are transient formations that appeared due to a gravitational instability in the gas disk. The distances between HI superclouds in the two arms that are the brightest in neutral hydrogen, the Carina arm and the Cygnus (Outer) arm, concentrate to two values, permitting to assume the presence of a regular magnetic field in these arms.Comment: 21 pages, 14 fugures; accepted for publication in Astronomichesky Journal (Astron. Rep.

High resolution global climate modelling; the UPSCALE project, a large simulation campaign

The UPSCALE (UK on PRACE: weather-resolving Simulations of Climate for globAL Environmental risk) project constructed and ran an ensemble of HadGEM3 (Hadley Centre Global Environment Model 3) atmosphere only global climate simulations over the period 1985–2011, at resolutions of N512 (25 km), N216 (60 km) and N96 (130 km) as used in current global weather forecasting, seasonal prediction and climate modelling respectively. Alongside these present climate simulations a parallel ensemble looking at extremes of future climate was run, using a timeslice methodology to consider conditions at the end of this century. These simulations were primarily performed using a 144 million core hour, single year grant of computing time from PRACE (the Partnership for Advanced Computing in Europe) in 2012, with additional resources supplied by the Natural Environment Research Council (NERC) and the Met Office. Almost 400 terabytes of simulation data were generated on the HERMIT supercomputer at the High Performance Computing Center Stuttgart (HLRS), and transferred to the JASMIN super-data cluster provided by the Science and Technology Facilities Council Centre for Data Archival (STFC CEDA) for analysis and storage. In this paper we describe the implementation of the project, present the technical challenges in terms of optimisation, data output, transfer and storage that such a project involves and include details of the model configuration and the composition of the UPSCALE data set. This data set is available for scientific analysis to allow assessment of the value of model resolution in both present and potential future climate conditions

Magnetic behavior of Ba_{3}Cu_{3}Sc_{4}O_{12}

The chain-like system Ba_{3}Cu_{3}Sc_4O_{12} has potentially interesting magnetic properties due to the presence of Cu^{2+} and a structure-suggested low-dimensionality. We present magnetization M versus magnetic field H and temperature T, T- and H-dependent heat-capacity C_{p}, ^{45}Sc nuclear magnetic resonance (NMR), muon spin rotation ({\mu}SR), neutron diffraction measurements and electronic structure calculations for Ba_{3}Cu_{3}Sc_{4}O_{12}. The onset of magnetic long-range antiferromagnetic order at T_{N} ~16 K is consistently evidenced from the whole gamut of our data. A significant sensitivity of T_{N} to the applied magnetic field H (T_{N}~0 K for H=70 kOe) is also reported. Coupled with a ferromagnetic Curie-Weiss temperature ({\theta}_{CW}~65 K) in the susceptibility (from a 100 K-300 K fit), it is indicative of competing ferromagnetic and antiferromagnetic interactions. These indications are corroborated by our density functional theory based electronic structure calculations where we find the presence of significant ferromagnetic couplings between some copper ions whereas AF couplings were present between some others. Our experimental data, backed by our theoretical calculations, rule out one-dimensional magnetic behaviour suggested by the structure and the observed long-range order is due to the presence of non-negligible magnetic interactions between adjacent as well as next-nearest chains.Comment: 37 pages, 15 figure

Effects of boundary conditions on magnetization switching in kinetic Ising models of nanoscale ferromagnets

Magnetization switching in highly anisotropic single-domain ferromagnets has been previously shown to be qualitatively described by the droplet theory of metastable decay and simulations of two-dimensional kinetic Ising systems with periodic boundary conditions. In this article we consider the effects of boundary conditions on the switching phenomena. A rich range of behaviors is predicted by droplet theory: the specific mechanism by which switching occurs depends on the structure of the boundary, the particle size, the temperature, and the strength of the applied field. The theory predicts the existence of a peak in the switching field as a function of system size in both systems with periodic boundary conditions and in systems with boundaries. The size of the peak is strongly dependent on the boundary effects. It is generally reduced by open boundary conditions, and in some cases it disappears if the boundaries are too favorable towards nucleation. However, we also demonstrate conditions under which the peak remains discernible. This peak arises as a purely dynamic effect and is not related to the possible existence of multiple domains. We illustrate the predictions of droplet theory by Monte Carlo simulations of two-dimensional Ising systems with various system shapes and boundary conditions.Comment: RevTex, 48 pages, 13 figure