A dual graph-norm refinement indicator for finite volume approximations of the Euler equations

Summary. We generalise and apply a refinement indicator of the type originally designed by Mackenzie, Süli and Warnecke in [15] and [16] for linear Friedrichs systems to the Euler equations of inviscid, compressible fluid flow. The Euler equations are symmetrized by means of entropy variables and locally linearized about a constant state to obtain a symmetric hyperbolic system to which an a posteriori error analysis of the type introduced in [15] can be applied. We discuss the details of the implementation of the refinement indicator into the DLR--Code which is based on a finite volume method of box type on an unstructured grid and present numerical results. Received May 15, 1995 / Revised version received April 17, 1996     

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Rodlike bimetallic ruthenium and osmium complexes bridged by phenylene spacers. Synthesis, electrochemistry, and photophysics

In the search for light-addressable nanosized compounds we have synthesized 10 dinuclear homometallic trisbipyridyl complexes of linear structure with the general formula [M(bpy)3-BL-M(bpy)3]4+ [M = Ru(II) or Os(II); BL = polyphenylenes (2, 3, 4, or 5 units) or indenofluorene; bpy = 2,2'-bipyridine]. By using a "chemistry on the complex" approach, different sizes of rodlike systems have been obtained with a length of 19.8 and 32.5 A for the shortest and longest complex, respectively. For one of the ruthenium precursors, [Rubpy-ph2-Si(CH3)3][PF6]2, single crystals were obtained by recrystallization from methanol. Their photophysical and electrochemical properties are reported. All the compounds are luminescent both at room and low temperature with long excited-state lifetimes due to an extended delocalization. Nanosecond transient absorption showed that the lowest excited state involves the chelating unit attached to the bridging ligand. Electrochemical data indicated that the first reduction is at a slightly more positive potential than for the reference complexes [M(bpy)3]2+ (M = Ru, Os). This result confirms that the best acceptor is the bipyridine moiety connected to the conjugated spacers. The role of the tilt angle between the phenylene units, in the two series of complexes, for the ground and excited states is discussed.     

(E)‐3‐(Benzo[b]thiophen‐2‐yl)‐2‐(3,4,5‐trimethoxyphenyl)acrylonitrile and (Z)‐3‐(benzo[b]thiophen‐2‐yl)‐2‐(3,4‐dimethoxyphenyl)acrylonitrile

The title compounds, C₂₀H₁₇NO₃S, (I), and C₁₉H₁₅NO₂S, (II), were prepared by the reaction of benzo[b]thiophene‐2‐carbaldehyde with (3,4,5‐trimethoxyphenyl)acetonitrile and (3,4‐dimethoxyphenyl)acetonitrile, respectively, in the presence of methanolic potassium hydroxide. In (I), the C=C bond linking the benzo[b]thiophene and the 3,4,5‐trimethoxyphenyl units has E geometry, with dihedral angles between the plane of the bridging unit and the planes of the two adjacent ring systems of 5.2 (3) and 13.1 (2)°, respectively. However, in (II), the C=C bond has Z geometry, with dihedral angles between the plane of the bridging unit and the planes of the adjacent benzo[b]thiophene and 3,4‐dimethoxyphenyl units of 4.84 (17) and 76.09 (7)°, respectively. There are no significant intermolecular hydrogen‐bonding interactions in the packing of (I) and (II). The packing is essentially stabilized via van der Waals forces.     

Untersuchung von Kobalt(II)-Komplexen mit N-Arylthioharnstoffen

The complexes of cobalt(II) chloride with o, m, p-tolyl thiourea (I–III); m, p-nitrophenyl thiourea (IV, V); o, m, p-hydroxy phenyl thiourea (VI–VIII); m, p-bromophenyl thiourea (IX, X); p-iodophenyl thiourea (XI) and o-bromo-p-methyl phenyl thiourea (XII) have been synthesised. The elemental analysis reveals that ligands (I–V) form bis and the rest forms tris complexes with cobalt(II). Infrared and farinfrared spectral measurements prove that sulphur is taking part in co-ordination. All complexes are nonelectrolytes in acetone as revealed by conductivity measurements. The data obtained from magnetic susceptibility measurements, electronic spectra in solution are consistant with a practically tetrahedral symmetry.     

A comparison of the Discontinuous-Galerkin- and Spectral-Difference-Method on triangulations using PKD polynomials

This paper gives a first numerical comparison of the Discontinuous-Galerkin-(DG) and Spectral-Difference-Method (SD) under almost equivalent conditions for smooth test cases.     

Kinetic and thermodynamic study of adsorption of methylene blue and rhodamine B on adsorbent prepared from Hyptis suaveolens (Vilayti Tulsi)

In the present study adsorption behavior of methylene blue and rhodamine B from aqueous solution using adsorbent prepared from “Hyptis suaveolens” (Vilayti Tulsi) was investigated as a function of parameters such as initial concentration, adsorbent dose, pH, contact time and temperature. The adsorption process was pH dependent. The thermodynamic parameters such as $ {{\Updelta}}G,{{\Updelta}}H \,{\text{and}} \,{{\Updelta}}S $ were calculated to investigate the nature of adsorption, their values indicate that the adsorption process is favorable. The first-order, second-order and intra-particle diffusion models were used to describe the kinetic parameter. The Freundlich and Langmuir adsorption models were applied to describe the adsorption equilibrium. Column study was conducted for both dyes.