Characteristic temperatures and electron number densities in an R.F. capacitively coupled plasma

The excitation temperatures of Ar and Fe, the ionization temperatures of Ar and Ca and the electron number densities have been determined for a radiofrequency capacitively coupled plasma in the tip-ring electrode geometry. The temperatures and the electron number densities possess their maximum value close to the electrodes.     

Stress communication and filtering of viscoelastic layers in oscillatory shear

We revisit a classical topic: response functions of viscoelastic layers in large amplitude oscillatory shear. Motivated by questions concerning protective biological layers, we focus on boundary stresses in a parallel plate geometry with imposed oscillatory strain or stress. These features are gleaned from resolution and analysis of coupled standing waves of deformation and stress. We identify a robust non-monotone variation in boundary stress signals with respect to all experimental controls: viscoelastic moduli of the layer, layer thickness, and driving frequency. This structure of peaks and valleys in boundary values of shear and normal stress indicates redundant mechanisms for stress communication (by tuning to the peaks) and stress filtering (by tuning to the valleys). In this paper, we first restrict to a single-mode non-linear Maxwell model for the viscoelastic layer, where analysis renders a transparent explanation of the phenomena. We then consider a Giesekus constitutive model of the layer, where analysis is supplanted by numerical simulations of coupled non-linear partial differential equations. Parametric studies of wall stress values from standing waves confirm persistence of the Maxwell model phenomena. The analysis and simulations rely on and extend our recent studies of shear waves in a micro parallel plate rheometer [S.M. Mitran, M.G. Forest, L. Yao, B. Lindley, D. Hill, Extenstions of the Ferry shear wave model for active linear and nonlinear microrheology, J. Non-Newtonian Fluid Mech. 154 (2008) 120–135; D.B. Hill, B. Lindley, M.G. Forest, S.M. Mitran, R. Superfine, Experimental and modeling protocols from a micro-parallel plate rheometer, UNC Preprint, 2008].     

Coordination Behavior of Acetoacetate Ligands with Attached Methacrylate Groups Containing Alkyl-Spacers of Different Length to Titanium and Zirconium Alkoxides

Summary. Metal-alkoxides containing polymerizable groups are regularly used as precursors for inorganic–organic hybrid materials applying the combination of the sol–gel process and organic polymerizations. Here we report the synthesis of acetoacetoxy derivatives that are linked to methacrylate groups via alkyl chains of different chain length. The coordination of the resulting molecules to titanium- and zirconium-alkoxides (M(OR)₄; M = Ti, Zr; R = ethyl, butyl, isopropyl) was investigated applying NMR and FT-IR measurements. The results were related to structural data of the dinuclear complex [Ti(O ⁱ Pr)₃(EAA)]₂ (HEAA: ethyl acetoacetate) which was obtained by single crystal X-ray diffraction. The study revealed that the β-keto ester groups acted as chelating ligands in all cases and thus polymerizable coordination compounds were formed. However, NMR analyses in solution showed that transesterification of the methacrylic-type monomers occurred even at mild conditions as a side reaction in a ratio which was found to be dependent on the type of metal alkoxide used.     

Asymptotic behaviour of the Stokes problem in cylinders becoming unbounded in one direction

We study the asymptotics of the Stokes problem in cylinders becoming unbounded in the direction of their axis. First we assume that the applied forces are independent of the axis coordinate, then we assume that they are periodic along the axis of the cylinder. Finally in Section 4, we make an asymptotic analysis under much more general assumptions on the applied forces.     

A Grüss Type Discrete Inequality in Inner Product Spaces and Applications

A Grüss type inequality in inner product spaces and applications for the discrete Fourier transform, Mellin transform of sequences, polynomials with coefficients in Hilbert spaces, and Lipschitzian vector valued mappings are given.     

On the homogenization of the Buckley-Leverett equation including trapping effects at the micro scale

We consider a simplified, one dimensional model for two-phase (oil/water) flow in a porous medium. The medium consist of alternating homogeneous blocks separated by interfaces, where trapping effects may occur. Two effective models are derived in [2] and [7]. In this paper we show that the two models are equivalent. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Pharmacophore-based screening and drug repurposing exemplified on glycogen synthase kinase-3 inhibitors

The current study was conducted to elaborate a novel pharmacophore model to accurately map selective glycogen synthase kinase-3 (GSK-3) inhibitors, and perform virtual screening and drug repurposing. Pharmacophore modeling was developed using PHASE on a data set of 203 maleimides. Two benchmarking validation data sets with focus on selectivity were assembled using ChEMBL and PubChem GSK-3 confirmatory assays. A drug repurposing experiment linking pharmacophore matching with drug information originating from multiple data sources was performed. A five-point pharmacophore model was built consisting of a hydrogen bond acceptor (A), hydrogen bond donor (D), hydrophobic (H), and two rings (RR). An atom-based 3D quantitative structure–activity relationship (QSAR) model showed good correlative and satisfactory predictive abilities (training set \({R}^{2}= 0.904\); test set: \({Q}^{2}= 0.676\); whole data set: stability \(s = 0.803\)). Virtual screening experiments revealed that selective GSK-3 inhibitors are ranked preferentially by Hypo-1, but fail to retrieve nonselective compounds. The pharmacophore and 3D QSAR models can provide assistance to design novel, potential GSK-3 inhibitors with high potency and selectivity pattern, with potential application for the treatment of GSK-3-driven diseases. A class of purine nucleoside antileukemic drugs was identified as potential inhibitor of GSK-3, suggesting the reassessment of the target range of these drugs.     

Branched polymeric labels used as drag-tags in free-solution electrophoresis of ssDNA

In the framework of the classical blob theory of end-labeled free-solution electrophoresis of ssDNA, and based on recent experimental data with linear and branched polymeric labels (or drag-tags), the present study puts forward design principles for the optimal type of branching that would give, for a given total number of monomers, the highest effective frictional drag for ssDNA sequencing purposes. The hydrodynamic radii of the linear and branched labels are calculated using standard models like the freely jointed chain model and the Kratky-Porod worm-like chain model. Based on comparisons of the theory with the experimental data, we propose that the design of new branched labels should use either side chains whose length is comparable to the distance between the branching points or two long branches located near the ends of the molecule's backbone.     

The N = 2 Supersymmetric Unconstrained Matrix GNLS Hierarchies

The generalization of the N = 2 supersymmetric chiral matrix (k | n,m)-GNLS hierarchy (Lett. Math. Phys. 45 (1998) 63, solv-int/9711009) to the case when matrix entries are bosonic and fermionic unconstrained N = 2 superfields is proposed. This is done by exhibiting the corresponding matrix Lax-pair representation in terms of N = 2 unconstrained superfields. It is demonstrated that when matrix entries are chiral and antichiral N = 2 superfields, it reproduces the N = 2 chiral matrix (k | n,m)-GNLS hierarchy, while in the scalar case, k = 1, it is equivalent to the N = 2 supersymmetric multicomponent hierarchy (J. Phys. A 29 (1996) 1281, hep-th/9510185). The simplest example—the N = 2 unconstrained (1 | 1,0)-GNLS hierarchy—and its reduction to the N = 2 supersymmetric = 1 KdV hierarchy are discussed in more detail, and its rich symmetry structure is uncovered.