Galerkin‐type space‐time finite elements for volumetrically coupled problems

The study focuses on error estimation techniques for a coupled problem with two constituents based on the Theory of Porous Media. After developing space‐time finite elements for this mixed problem, we extend the numerical scheme to a coupled space‐time adaptive strategy. Therefore, an adjoint or dual problem is formulated and discussed, which is solved lateron numerically. One advantage of the presented technique is the high flexibility of the error indicator with respect to the error measure.     

Republication of: Exact solutions of the field equations of the general theory of relativity

This is an English translation of a paper by Pascual Jordan, Jürgen Ehlers and Wolfgang Kundt, first published in 1960. The original paper was part 1 of a five-part series of articles containing the first summary of knowledge about exact solutions of Einstein’s equations found until then. (The other parts of the series will be printed as Golden Oldies in the future.) The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. It is accompanied by an editorial note written by G. F. R. Ellis, and by the biographies of the authors: P. Jordan (written by A. Krasiński) and W. Kundt (written by himself). The biography of J. Ehlers is contained elsewhere in the same issue of GRG, which is devoted to his memory. An editorial note to this paper and a biography can be found in this issue preceding this Golden Oldie and online via doi:. Original paper: Pascual Jordan, Jürgen Ehlers, Wolfgang Kundt, Strenge L?sungen der Feldgleichungen der Allgemeinen Relativit?tstheorie. Akademie der Wissenschaften und der Literatur, Abhandlungen der Mathematisch-naturwissenschaftliche Klasse Nr 2S (1960), pp. 21–105. Reprinted with the kind permission of the Academy of Sciences and Literature, Mainz, and of the authors: Jürgen Ehlers and Wolfgang Kundt. Translated by Anita Ehlers, Anita.Ehlers@t-online.de, and by Manfred Trümper, manfred@truemper.fr, with ample help from Wolfgang Kundt. P. Jordan (Deceased July 31, 1980) J. Ehlers (Deceased May 20, 2008)

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On the Newtonian limit of the Weyl tensor

In this note we wish to complement some recent work in the cosmological literature concerning the Weyl conformal curvature tensor and its parts. In particular, we shall give a clear-cut definition of the Newtonian limits of electric and magnetic parts of the Weyl tensor. We also discuss that only a subset of the relativistic equations is needed to obtain a closed system of equations in the Newtonian limit.     

Bisphosphine‐Functionalized Cyclic Decapeptides Based on the Natural Product Gramicidin S: A Potential Scaffold for Transition‐Metal Coordination

The natural product Gramicidin S is a promising scaffold for novel oligopeptide‐based bisphosphine ligands, combining the advantageous rigid chiral backbone with the close proximity of phosphine substituents. The required unnatural, phosphine‐containing, amino acid building blocks were synthesized by means of a novel protocol that involves the enantioselective alkylation of a chiral nickel Schiff base template. Three Ni complexes were prepared with different alkyl chains between the phosphine group and the α‐carbon atom of the incorporated glycine; the absolute stereochemistry of two of them was determined by single‐crystal X‐ray structure analysis. By detaching the template, enantiopure L ‐phosphine amino acids resulted enabling the solid‐phase, stepwise construction of a linear sequence of the phosphine‐modified oligopeptides. On cyclization three bisphosphine‐substituted Gramicidin S analogues resulted, differing only in the size and shape of the linkage between the phosphine groups and the oligopeptides backbone. Their crystal structures suggest these species to have potential as chelating ligands.     

η3‐Diphosphavinylcarbene: A P2 Analogue of the Dötz Intermediate

Do the twist : The reaction of in situ generated phosphinidenes with phosphaalkynes is a facile route to the new metal‐coordinated η³‐diphosphavinylcarbene 1 , which shows facile ligand‐exchange reactions and undergoes an unprecedented rearrangement that involves phosphinidene complex 2 and η³‐phosphaalkenylphosphinidene complex 3 , the 1,3 isomer of 1 .

     

Cover Picture: A Phosphorus Analogue of Bis(η4‐cyclobutadiene)iron(0) (Angew. Chem. Int. Ed. 17/2009)

A rare phosphorus analogue of the elusive complex bis(η⁴‐cyclobutadiene)iron(0) is reported by K. Lammertsma et al. in their Communication on page 3104 ff. The background of the cover picture shows John Montagu (1718–1792), 4th Earl of Sandwich and 1st Lord of the Admiralty, who certainly would not have dreamt that an important class of organometallic compounds, sandwich complexes, would bear his name one day. The synthesis of [Fe(P₂C₂tBu₂)₂] shows that sandwich complexes are still topical objects of research.

     

Bidentate phosphorus baskets by intramolecular phosphinidene addition

Intramolecular phosphinidene addition to the C==C bond of Mo-complexed, seven-membered phosphorus heterocycles affords three novel [(diphos)Mo(CO)(4)] complexes (18-20). The three bidentate phosphorus baskets differ in the composition of the seven-membered ring: one of the phosphorus atoms is flanked by CH(2), NCH(3), or O. The unsaturated tetrahydrophosphepine precursors are synthesized by either ring-closing metathesis (C and N derivatives) or by a cyclization sequence (O derivative). The crystal structures of the nitrogen- (19) and oxygen-containing (20) baskets have relatively small P-Mo-P angles of 76.240(13) degrees and 77.626(12) degrees , respectively, and complex 20 has slightly shortened Mo--P bond lengths.     

Fabrication and Investigation of Photovoltaic Converters Based on Polycrystalline Silicon Grown on Borosilicate Glass

The microcrystalline Si layers with grain sizes of up to several tens of micrometers were grown. The physical vapor deposition (PVD), amorphous–liquid–crystalline (ALC) transition technique and a steady-state liquid phase epitaxy (SSLPE) are used for the fabrication of three different samples. The first sample under consideration was prepared first by deposition of a-Si onto glass substrates by PVD at room temperature, followed by heating from the front side to ~300°C and deposition of an indium metallic solvent. At the preparation of the second sample, an additional silicon layer with the thickness of 400 nm was deposited. A sample, when after that a c-Si was grown on the seed layer by SSLPE from indium solution is referred as a third sample. The resulting samples have a strong absorption edge in the mid-infrared region around 1960 cm^?1. Six well-resolved oscillations with an average period of δB = 0.1214 T are revealed on the third sample’s magnetoresistance curve at gradually increasing of the magnetic field from zero up to 1.6 T. It is assumed that either Aharonov–Bohm effect or kinetic phenomena taking place in the grains boundaries at lateral current flow are responsible for those oscillations. Quantitative evaluations show that due to the strong absorption in mid-infrared region, enlargement of the photoresponse spectrum will occur and the efficiency of solar and other thermal energy conversion should be around ~10–15% higher than that of traditional PV cells based on silicon on glass structures.     

Stability Analysis of Decoupled Solution Strategies for Coupled Multi-field Problems – A General Framework

A coupled partial differential equation (PDE) system, stemming from the mathematical modelling of a coupled phenomenon, is usually solved numerically following a monolithic or a decoupled solution method. In spite of the potential unconditional stability offered by monolithic solvers, their usage for solving complex problems sometimes proves cumbersome. This has motivated the development of various partitioned and staggered solution strategies, generally known as decoupled solution schemes. To this end, the problem is broken down into several isolated yet communicating sub-problems that are independently advanced in time, possibly by different integrators. Nevertheless, using a decoupled solver introduces additional errors to the system and, therefore, may jeopardise the stability of the solution [1]. Consequently, to scrutinise the stability of the solution scheme becomes a pertinent step in proposing decoupled solution strategies. Here, we endeavour to present a practical stability analysis algorithm, which can readily be used to reveal the stability condition of numerical solvers. To illustrate its capabilities, the algorithm is then utilised for the stability analysis of solution schemes applied to multi variate coupled PDE systems resulting from the mathematical modelling of surface- and volume-coupled multi-field problems. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)