Sweeping preconditioner for the Helmholtz equation: Hierarchical matrix representation

The paper introduces the sweeping preconditioner, which is highly efficient for iterative solutions of the variable‐coefficient Helmholtz equation including very‐high‐frequency problems. The first central idea of this novel approach is to construct an approximate factorization of the discretized Helmholtz equation by sweeping the domain layer by layer, starting from an absorbing layer or boundary condition. Given this specific order of factorization, the second central idea is to represent the intermediate matrices in the hierarchical matrix framework. In two dimensions, both the construction and the application of the preconditioners are of linear complexity. The generalized minimal residual method (GMRES) solver with the resulting preconditioner converges in an amazingly small number of iterations, which is essentially independent of the number of unknowns. This approach is also extended to the three‐dimensional case with some success. Numerical results are provided in both two and three dimensions to demonstrate the efficiency of this new approach. © 2011 Wiley Periodicals, Inc.     

Anyons,deformed oscillator algebras and projectors

We initiate an algebraic approach to the many-anyon problem based on deformed oscillator algebras. The formalism utilizes a generalization of the deformed Heisenberg algebras underlying the operator solution of the Calogero problem. We define a many-body Hamiltonian and an angular momentum operator which are relevant for a linearized analysis in the statistical parameter ν. There exists a unique ground state and, in spite of the presence of defect lines, the anyonic weight lattices are completely connected by the application of the oscillators of the algebra. This is achieved by supplementing the oscillator algebra with a certain projector algebra.     

Redox freezing temperature and Bartenev equation in a 25Na2O-15B2O3-60SiO2 glass doped with chromium and manganese

In a melt with the base mol% composition 25Na₂O-15B₂O₃-60SiO₂, doped with chromium and manganese, a redox reaction takes place during cooling the melt. This reaction was studied using high temperature UV-vis spectroscopy. Above 600 °C, the reaction is in equilibrium and shifted during cooling to the Cr³⁺ and Mn³⁺ species. At temperatures between 500 and 600 °C, the kinetics of the redox reaction is decisive and the cooling rate plays an important part. At temperatures < 500 °C, the reaction is frozen in. The smaller the cooling rate, the smaller is the Cr⁶⁺ concentration and the lower is the fictive redox temperature.The kinetics of the reaction was described by a differential equation assuming Arrhenian behaviour. The equation was numerically solved and fictive temperatures were calculated. These temperatures depended on cooling rate similar to Bartenev equation. Activation energies calculated hereof were around 38 kJ?mol⁻¹ larger than those inserted into the kinetic equation. The experimentally determined activation energy is 565 kJ?mol⁻¹, a value much larger than the activation energies of diffusion of the polyvalent elements. The rate determining step in the case of the Cr³⁺/Cr⁶⁺/Mn²⁺/Mn³⁺ system is the electron transfer reaction, because a notable structural rearrangement is necessary during the course of the electron transfer reaction (Cr³⁺ and Cr⁶⁺ occur in octahedral and tetrahedral coordination, respectively). The latter leads to a large inner reorganisation energy and to an activation energy similar to that of the viscous flow. In the case of the redox reaction between copper and arsenic, the activation energy is much smaller (210 kJ?mol⁻¹), because here the coordination numbers do not change during the course of the redox reaction.     

Spatial control of p-n junction in an organic light-emitting electrochemical transistor

Low-voltage-operating organic electrochemical light-emitting cells (LECs) and transistors (OECTs) can be realized in robust device architectures, thus enabling easy manufacturing of light sources using printing tools. In an LEC, the p-n junction, located within the organic semiconductor channel, constitutes the active light-emitting element. It is established and fixated through electrochemical p- and n-doping, which are governed by charge injection from the anode and cathode, respectively. In an OECT, the electrochemical doping level along the organic semiconducting channel is controlled via the gate electrode. Here we report the merger of these two devices: the light-emitting electrochemical transistor, in which the location of the emitting p-n junction and the current level between the anode and cathode are modulated via a gate electrode. Light emission occurs at 4 V, and the emission zone can be repeatedly moved back and forth within an interelectrode gap of 500 μm by application of a 4 V gate bias. In transistor operation, the estimated on/off ratio ranges from 10 to 100 with a gate threshold voltage of -2.3 V and transconductance value between 1.4 and 3 μS. This device structure opens for new experiments tunable light sources and LECs with added electronic functionality.     

New labeling procedures for the basis graph in generalized networks

Labeling procedures for the basis graph of a generalized network are introduced which build on procedures designed for pure networks. Computational results are presented which show that a primal simplex code which uses these procedures is about 60 times faster than a general purpose linear programming code.     

An optical model for exchange reactions

An optical model or complex potential has been used in a relatively simple fashion to provide an interpretation of several molecular dynamics experiments. Rather than attempting a quantitative curve fit to the available data using a phenomenological optical potential (which is certainly possible) we have correlated certain physically reasonable features of the complex potential with general trends in the reaction dynamics. As an explicit example, the relationship between the range characteristics of the optical potential and the dependence of the reaction probability upon the kinetic energy of the reactants is derived. Other correlations are also presented, such as the dependence of the reaction probability upon impact parameter and degree of rotational excitation. The power of such a treatment obviously lies in its general applicability to complex systems as well as in its ability to often provide a simple physical understanding of some rather anomalous features of the reaction dynamics.     

Nachweis der Poly?thylenglykole mit Hilfe von Chromperoxid

Zusammenfassung Polyäthylenglykole vermögen die Existenz von Chromperoxid zu stabilisieren. Dabei wird die Oktettlücke des in freiem Zustande äußerst unbeständigen CrO₅ durch das freie Elektronenpaar der Äthersauerstoffatome der Polyäthylenglykole besetzt. Auf dieser Stabilisierung des tiefblauen CrO₅ basiert der hier beschriebene Nachweis der Polyäthylenglykole.

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Summary Polyethylene glycols have the ability to stabilize chromium peroxide. The octet gap of CrO₅ (which is extremely unstable in the free state) is filled up by the free electron pair of the ether oxygen atoms of the polyethylene glycols. The described detection of polyethylene glycols is based on this stabilisation of the dark blue CrO₅.

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9. Mitteilung: Springer, R., u. H. Isak: Dtsch. Apotheker-Ztg. 103, 525 (1963).