Efficient linear solvers for incompressible flow simulations using Scott‐Vogelius finite elements

Recent research has shown that in some practically relevant situations like multiphysics flows (Galvin et al., Comput Methods Appl Mech Eng, to appear) divergence‐free mixed finite elements may have a significantly smaller discretization error than standard nondivergence‐free mixed finite elements. To judge the overall performance of divergence‐free mixed finite elements, we investigate linear solvers for the saddle point linear systems arising in ((P_k)^d,P _k‐1^disc) Scott‐Vogelius finite element implementations of the incompressible Navier–Stokes equations. We investigate both direct and iterative solver methods. Due to discontinuous pressure elements in the case of Scott‐Vogelius (SV) elements, considerably more solver strategies seem to deliver promising results than in the case of standard mixed finite elements such as Taylor‐Hood elements. For direct methods, we extend recent preliminary work using sparse banded solvers on the penalty method formulation to finer meshes and discuss extensions. For iterative methods, we test augmented Lagrangian and \begin{align*}\mathcal{H}\end{align*} ‐LU preconditioners with GMRES, on both full and statically condensed systems. Several numerical experiments are provided that show these classes of solvers are well suited for use with SV elements and could deliver an interesting overall performance in several applications.© 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

On nonlinear boundary value problems in the discrete setting

ABSTRACT

Results appearing in this paper can be used to establish the solvability of nonlinear discrete time systems subject to generalized nonlinear boundary conditions. Two separate sets of results are established, each of which can be used to establish existence of solutions to problems for which previous related work proves inconclusive. The first set of results imposes conditions on the sizes of nonlinearities, while the second framework requires geometric properties of the nonlinearity in the dynamics.     

Crystal growth,crystal structure and physical properties of polar orthorhombic tris(glycine) zinc chloride

Large single crystals of the polar (point group mm 2) compound tris(glycine) zinc chloride, (NH₃CH₂COO)₃ · ZnCl₂, were grown from aqueous solutions. The refractive indices were measured in the wavelength region from 365 nm to 1083 nm and an unpolarised absorption spectrum was recorded (transparency range from 260 to 1550nm). The phase matching conditions for second harmonic generation were analysed: both, type I (ss‐f) and type II (sf‐f) are possible in the red and near IR region. All five components of the piezoelectric tensor [d_ijk ] were determined; the maximum values of longitudinal and transverse piezoelectric effects are less than one half of d₁₁₁ of α‐quartz. In addition, a redetermination of the crystal structure (including location of H atoms) is presented. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear optical properties of strontium tartrato‐antimonate(III) dihydrate,Sr[Sb2{(+)‐C4H2O6}2]·2H2O

The tensor of nonlinear optical susceptibility for second harmonic generation [d^SHG _ijk ] of hexagonal (point group 6) strontium tartrato‐antimonate(III) dihydrate, Sr[Sb₂{(+)‐C₄H₂O₆}₂]·2H₂O, was determined using the Maker fringes method and a Nd:YAG laser with a wavelength of 1064 nm. The largest component of the tensor d^SHG ₃₃₃ amounts two times d^SHG ₁₁₁ of α‐quartz. Effective nonlinear optical susceptibility d^SHG _eff is given for phase matching type I for several wavelengths (for type II d^SHG _eff is nearly zero). The thermal stability of crystals of Sr[Sb₂{(+)‐C₄H₂O₆}₂]·2H₂O was determined in the temperature range from 153 K to 573 K by means of thermal expansion measurements and thermogravimetry. The temperature dependence of thermal expansion coefficients is given in the range from 153 K to 293 K. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Evidence for an isomeric 3/2- state in 53Co

The fragmentation of a 550MeV/u primary beam of ⁵⁸Ni on a ⁹Be target has been used to measure time- and energy-correlated γ decays following the implantation of event-by-event discriminated secondary fragments into a ⁹Be stopper plate. A new isomeric γ decay with T _1/2 = 14( ) ns and E _γ = 646.2(2) keV is observed and attributed to the decay of the yrast 3/2^- state in ⁵³ ₂₇Co₂₆ . This short-lived isomeric state has been populated by means of nuclear reactions during the stopping process of the secondary fragments. The experimental findings are discussed in the framework of large-scale spherical shell model calculations in conjunction with isospin symmetry-breaking residual interactions for the A = 53 , T _z = ±1/2 mirror nuclei ⁵³Co and ⁵³Fe .     

The function of Shp2 tyrosine phosphatase in the dispersal of acetylcholine receptor clusters

Background

Tone languages such as Thai and Mandarin Chinese use differences in fundamental frequency (F₀, pitch) to distinguish lexical meaning. Previous behavioral studies have shown that native speakers of a non-tone language have difficulty discriminating among tone contrasts and are sensitive to different F₀ dimensions than speakers of a tone language. The aim of the present ERP study was to investigate the effect of language background and training on the non-attentive processing of lexical tones. EEG was recorded from 12 adult native speakers of Mandarin Chinese, 12 native speakers of American English, and 11 Thai speakers while they were watching a movie and were presented with multiple tokens of low-falling, mid-level and high-rising Thai lexical tones. High-rising or low-falling tokens were presented as deviants among mid-level standard tokens, and vice versa. EEG data and data from a behavioral discrimination task were collected before and after a two-day perceptual categorization training task.

Results

Behavioral discrimination improved after training in both the Chinese and the English groups. Low-falling tone deviants versus standards elicited a mismatch negativity (MMN) in all language groups. Before, but not after training, the English speakers showed a larger MMN compared to the Chinese, even though English speakers performed worst in the behavioral tasks. The MMN was followed by a late negativity, which became smaller with improved discrimination. The High-rising deviants versus standards elicited a late negativity, which was left-lateralized only in the English and Chinese groups.

Conclusion

Results showed that native speakers of English, Chinese and Thai recruited largely similar mechanisms when non-attentively processing Thai lexical tones. However, native Thai speakers differed from the Chinese and English speakers with respect to the processing of late F₀ contour differences (high-rising versus mid-level tones). In addition, native speakers of a non-tone language (English) were initially more sensitive to F₀ onset differences (low-falling versus mid-level contrast), which was suppressed as a result of training. This result converges with results from previous behavioral studies and supports the view that attentive as well as non-attentive processing of F₀ contrasts is affected by language background, but is malleable even in adult learners.     

Electrochemical and photochemical approaches for the synthesis of the C28–C38 fragment of okadaic acid

Okadaic acid, a potent and selective inhibitor of Protein Phosphatases 1 and 2A (PP1 and PP2A), is widely used as a probe for various biochemical processes. We describe herein two innovative methods for the synthesis of the terminal C28–C38 fragment of the natural polyether. Suárez photochemical oxidative cyclization and electrochemical oxidation of malonates to their ketals equivalents have been successfully applied for the assembly of the key spiroketal core.     

Synthesis of Plasmonic Group‐4 Nitride Nanocrystals by Solid‐State Metathesis

Ceramic nanoparticles that exhibit a plasmonic response are promising next‐generation photonic materials. In this contribution, a solid‐state metathesis method has been reported for the synthesis of Group 4 nitride (TiN, ZrN, and HfN) nanocrystals. A high‐temperature (1000 °C) reaction between Group 4 metal oxide (TiO₂, ZrO₂, and HfO₂) nanoparticles and magnesium nitride powder yielded nitride nanocrystals that were dispersible in water. A localized surface plasmonic resonance was observed in the near‐infrared region for TiN and in the visible region of light for ZrN and HfN nanocrystals. The frequency of the plasmon resonance was dependent on the refractive index of the solvent and the nanocrystal size.     

Nonlinear Optical Switching in Regioregular Porphyrin Covalent Organic Frameworks

Covalent organic frameworks (COFs) have garnered immense scientific interest among porous materials because of their structural tunability and diverse properties. However, the response of such materials toward laser‐induced nonlinear optical (NLO) applications is hardly understood and demands prompt attention. Three novel regioregular porphyrin (Por)‐based porous COFs—Por‐COF‐HH and its dual metalated congeners Por‐COF‐ZnCu and Por‐COF‐ZnNi—have been prepared and present excellent NLO properties. Notably, intensity‐dependent NLO switching behavior was observed for these Por‐COFs, which is highly desirable for optical switching and optical limiting devices. Moreover, the efficient π‐conjugation and charge‐transfer transition in ZnCu‐Por‐COF enabled a high nonlinear absorption coefficient (β=4470 cm/GW) and figure of merit (FOM=σ₁/σ_o, 3565) value compared to other state‐of‐the‐art materials, including molecular porphyrins (β≈100–400 cm/GW), metal–organic frameworks (MOFs; β≈0.3–0.5 cm/GW), and graphene (β=900 cm/GW).