Nonlinear Galerkin methods and mixed finite elements: two-grid algorithms for the Navier-Stokes equations

Summary. A nonlinear Galerkin method using mixed finite elements is presented for the two-dimensional incompressible Navier-Stokes equations. The scheme is based on two finite element spaces and for the approximation of the velocity, defined respectively on one coarse grid with grid size and one fine grid with grid size and one finite element space for the approximation of the pressure. Nonlinearity and time dependence are both treated on the coarse space. We prove that the difference between the new nonlinear Galerkin method and the standard Galerkin solution is of the order of $H^2$, both in velocity ( and pressure norm). We also discuss a penalized version of our algorithm which enjoys similar properties. Received October 5, 1993 / Revised version received November 29, 1993     

Cyclometalated Iridium(III) Complexes Containing Semicarbazone Ligands: Synthesis,Characterization, Photophysical and Biological Studies

The synthesis, crystal structure, photophysical properties, and biological activity of the novel bis‐cyclometalated complexes [Ir(ptpy)₂(vnsc)] ( 2 ) and [Ir(ptpy)₂(acsc)] ( 3 ) [ptpy = 2‐(p‐tolyl)pyridinato, vnsc = vanillin semicarbazone, acsc = acetone semicarbazone] are described. The new compounds were prepared by the reaction of [{Ir(μ‐Cl)(ptpy)₂}₂] ( 1 ) with the corresponding semicarbazone ligands under basic conditions. The molecular structure of compound 3 was confirmed by a single‐crystal X‐ray diffraction study. The complex crystallized from chloroform as a mono‐ solvate in the orthorhombic space group Pcab with eight molecules in the unit cell.     

Approximate inertial manifolds for reaction-diffusion equations in high space dimension

The concept of approximate inertial manifolds was introduced by Foiaset al. (1987) in the case of the two-dimensional Navier-Stokes equations. These manifolds are finite dimensional smooth manifolds such that the orbits enter a very thin neighborhood of the manifold after a transient time; this concept replaces the one of inertial manifold when either an inertial manifold does not exist or its existence is not known. Our aim in this paper is to prove that approximate inertial manifolds exist for reaction-diffusion equations in high space dimension by opposition with exact inertial manifolds whose existence has only been proved in low dimension and for which nonexistence results have been obtained in space dimensionn=4.     

Interaction between inner and outer layer in drag-reduced turbulent flows

Effects of wall-based skin-friction drag reduction strategies on the statistical properties of large-scale motions in moderate Reynolds number turbulent flows have been investigated by exploiting Direct Numerical Simulation of turbulent channels. To educe large scales, a new efficient parallel distributed memory algorithm has been implemented which delivers data-driven modes of increasing characteristic lengthscales: the Fast and Adaptive Bidimensional Empirical Mode Decomposition (FABEMD). The influence of wall-based skin friction reduction on large scales is studied by comparing single point statistics, such as r.m.s. fluctuations, and two-point statistics, as cross-correlation functions in controlled and uncontrolled channel flow fields at constant friction Reynolds number. The traditional way of observing large-scale footprinting at the wall, as cross-correlation of the streamwise velocity components at different wall distances, has been found to be unreliable when comparing drag-reduced flows, due to the arbitrary choice of a reference plane in the logarithmic layer. A more sound way of observing the footprinting via the correlation of the streamwise velocity with the friction velocity is addressed and shows an increase of the footprinting in drag-reduced flows. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Preparation and characterization of cellulose microspheres

The aim of this work was to synthesize and characterize cellulose microspheres with a particle size below 5 μm and narrow size distribution. After activation and functionalization with antibodies, these particles shall be applied as adsorbents in suspension-based extracorporeal blood purification systems, such as the Microspheres-Based Detoxification System. In the frame of this work such microspheres were developed and synthesized with reproducible properties. Besides using well-established methods for characterization of this kind of bead cellulose, additional procedures for the examination of its properties were developed and applied.     

New chiral cyclooctatriene-based polycyclic architectures

The synthesis and properties of new chiral polycyclic architectures that display both helicity and a saddle-type shape are described. The enantiomers have been separated, and their absolute configuration was determined by VCD and ECD. The unprecedented molecular architecture is based on a cyclooctatriene core surrounded by an association of benzo[c]fluorene and ortho-phenylene units.     

Development of an online SPE�CLC�CMS-based assay using endogenous substrate for investigation of soluble epoxide hydrolase (sEH) inhibitors

Soluble epoxide hydrolase (sEH) is a promising therapeutic target for the treatment of hypertension, pain, and inflammation-related diseases. In order to enable the development of sEH inhibitors (sEHIs), assays are needed for determination of their potency. Therefore, we developed a new method utilizing an epoxide of arachidonic acid (14(15)-EpETrE) as substrate. Incubation samples were directly injected without purification into an online solid phase extraction (SPE) liquid chromatography electrospray ionization tandem mass spectrometry (LC-ESI-MS-MS) setup allowing a total run time of only 108 s for a full gradient separation. Analytes were extracted from the matrix within 30 s by turbulent flow chromatography. Subsequently, a full gradient separation was carried out on a 50X2.1 mm RP-18 column filled with 1.7 μm core-shell particles. The analytes were detected with high sensitivity by ESI-MS-MS in SRM mode. The substrate 14(15)-EpETrE eluted at a stable retention time of 96 ± 1 s and its sEH hydrolysis product 14,15-DiHETrE at 63 ± 1 s with narrow peak width (full width at half maximum height: 1.5 ± 0.1 s). The analytical performance of the method was excellent, with a limit of detection of 2 fmol on column, a linear range of over three orders of magnitude, and a negligible carry-over of 0.1% for 14,15-DiHETrE. The enzyme assay was carried out in a 96-well plate format, and near perfect sigmoidal dose-response curves were obtained for 12 concentrations of each inhibitor in only 22 min, enabling precise determination of IC(50) values. In contrast with other approaches, this method enables quantitative evaluation of potent sEHIs with picomolar potencies because only 33 pmol L(-1) sEH were used in the reaction vessel. This was demonstrated by ranking ten compounds by their activity; in the fluorescence method all yielded IC(50) ≤ 1 nmol L(-1). Comparison of 13 inhibitors with IC(50) values >1 nmol L(-1) showed a good correlation with the fluorescence method (linear correlation coefficient 0.9, slope 0.95, Spearman's rho 0.9). For individual compounds, however, up to eightfold differences in potencies between this and the fluorescence method were obtained. Therefore, enzyme assays using natural substrate, as described here, are indispensable for reliable determination of structure-activity relationships for sEH inhibition.     

Development of highly potent inhibitors of the ras-targeting human acyl protein thioesterases based on substrate similarity design

A matter of common sense: A common recognition motif consisting of a negatively charged group five to six bonds away (red) from the (thio)ester functionality (green) and a positively charged tail group ten to twelve bonds away (blue) was identified in two native acyl protein thioesterase?1 (APT1) substrates. This similarity led to the design of potent inhibitors of the Ras-depalmitoylating enzyme APT1.