Incremental unknowns preconditioning for solving the Helmholtz equation

An efficient preconditioner is developed for solving the Helmholtz problem in both high and low frequency (wavenumber) regimes. The preconditioner is based on hierarchical unknowns on nested grids, known as incremental unknowns (IU). The motivation for the IU preconditioner is provided by an eigenvalue analysis of a simplified Helmholtz problem. The performance of our preconditioner is tested on the iterative solution of two‐dimensional electromagnetic scattering problems. When compared with other well‐known methods, our technique is shown to often provide a better numerical efficacy and, most importantly, to be more robust. Moreover, for the best performance, the number of IU levels used in the preconditioner should be designed for the coarsest grid to have roughly two points per linear wavelength. This result is consistent with the conventional sampling criteria for wave phenomena in contrast with existing IU applications for solving the Laplace/Poisson problem, where the coarsest grid comprises just one interior point. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Diverse redox-active molecules bearing O-, S-, or Se-terminated tethers for attachment to silicon in studies of molecular information storage

A molecular approach to information storage employs redox-active molecules tethered to an electroactive surface. Attachment of the molecules to electroactive surfaces requires control over the nature of the tether (linker and surface attachment group). We have synthesized a collection of redox-active molecules bearing different linkers and surface anchor groups in free or protected form (hydroxy, mercapto, S-acetylthio, and Se-acetylseleno) for attachment to surfaces such as silicon, germanium, and gold. The molecules exhibit a number of cationic oxidation states, including one (ferrocene), two [zinc(II)porphyrin], three [cobalt(II)porphyrin], or four (lanthanide triple-decker sandwich compound). Electrochemical studies of monolayers of a variety of the redox-active molecules attached to Si(100) electrodes indicate that molecules exhibit a regular mode of attachment (via a Si-X bond, X = O, S, or Se), relatively homogeneous surface organization, and robust reversible electrochemical behavior. The acetyl protecting group undergoes cleavage during the surface deposition process, enabling attachment to silicon via thio or seleno groups without handling free thiols or selenols.     

Polarographic microdetermination of sulphur in organic compounds after oxygen flask combustion

Summary Three polarographic micro-methods are described for the determination of sulphur in organic compounds after oxygen-flask combustion. The products are converted into sulphuric acid by oxidation with hydrogen peroxide, the excess of which is expelled through boiling. The methods are based upon allowing the sulphuric acid to react with an excess of barium iodate or bromate, then recording polarographically the cathodic reduction wave of the iodate or bromate ion. The bromate methods are superior to the iodate method being simpler and more rapid, and the results are correct to within ca. ±0.5%.

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Zusammenfassung Drei polarographische Mikromethoden zur Bestimmung von Schwefel in organischen Verbindungen nach deren Verbrennung im Sauerstoffkolben wurden beschrieben. Die Verbrennungsprodukte werden durch Oxydation mit Wasserstoffperoxid in Schwefelsäure umgesetzt. Der Überschuß des Oxydationsmittels wird durch Kochen zerstört. Die Schwefelsäure läßt man mit überschüssigem Bariumjodat oder -bromat reagieren und mißt dann polarographisch die kathodische Reduktionswelle des Jodats oder Bromats. Die Bromatmethode ist der Jodatmethode überlegen, da sie einfacher und rascher zu Resultaten führt, die innerhalb ±0,5% korrekt sind.

     

Efficient and practical Ag-catalyzed cycloadditions between arylimines and the Danishefsky diene

An efficient Ag-catalyzed method for asymmetric addition of the Danishefsky diene to various aryl imines to afford cycloadducts in > or =89% ee and > or =85% isolated yield is reported. Reactions are effected with 0.1-1 mol % catalyst (4 degrees C), and the chiral ligand is readily prepared from commercially available materials, including the inexpensive i-Leu. These catalytic asymmetric cycloadditions can be carried out without the use of solvent or with undistilled THF in air. A first generation supported chiral catalyst that effectively promotes the cycloaddition reaction and can be recycled (five cycles) is described.     

An Accelerated Coordinate Gradient Descent Algorithm for Non-separable Composite Optimization

Journal of Optimization Theory and Applications - Coordinate descent algorithms are popular in machine learning and large-scale data analysis problems due to their low computational cost iterative...     

Development of a ~3He Gas Filling Station at the China Spallation Neutron Source

At the China Spallation Neutron Source(CSNS), we have developed a custom gas-filling station, a glassblowing workshop, and a spin-exchange optical pumping(SEOP) system for producing high-quality ~3He-based neutron spin filter(NSF) cells. The gas-filling station is capable of routinely filling ~3He cells made from GE180 glass of various dimensions, to be used as neutron polarizers and analyzers on beamlines at the CSNS. Performance tests on cells fabricated at our gas-filling station are conducted via neutron transmission and nuclear-magneticresonance measurements, revealing nominal filling pressures, and a saturated ~3He polarization in the region of 80%, with a lifetime of approximately 240 hours. These results demonstrate our ability to produce competitive NSF cells to meet the ever-increasing research needs of the polarized neutron research community.     

Linker engineering in metal–organic frameworks for dark photocatalysis

Dark reactions featuring continuous activity under light off conditions play a critical role in natural photosynthesis. However, most artificial photocatalysts are inactive upon the removal of the light source, and the artificial photocatalysts with dark photocatalysis abilities have been rarely explored. Herein, we report a Ti-based metal–organic framework (MOF), MIL-125, exhibiting the capability of dark photocatalytic hydrogen production. Remarkably, the introduction of different functional groups onto the linkers enables distinctly different activities of the resulting MOFs (MIL-125-X, X = NH₂, NO₂, Br). Dynamic and thermodynamic investigations indicate that the production and lifetime of the Ti³⁺ intermediate are the key factors, due to the electron-donating/-withdrawing effect of the functional groups. As far as we know, this is the first report on dark photocatalysis over MOFs, providing new insights into the storage of irradiation energy and demonstrating their great potential in dark photocatalysis due to the great MOF diversity.

A Ti-based MOF with long-lived Ti³⁺ can achieve dark photocatalysis. The different groups on the organic linker modulate electron storage ability and the lifetime of Ti³⁺, significantly regulating dark photocatalytic activity in H₂ production.     

Gamow Temperature in Tsallis and Kaniadakis Statistics

Relying on the quantum tunnelling concept and Maxwell–Boltzmann–Gibbs statistics, Gamow shows that the star-burning process happens at temperatures comparable to a critical value, called the Gamow temperature (T) and less than the prediction of the classical framework. In order to highlight the role of the equipartition theorem in the Gamow argument, a thermal length scale is defined, and then the effects of non-extensivity on the Gamow temperature have been investigated by focusing on the Tsallis and Kaniadakis statistics. The results attest that while the Gamow temperature decreases in the framework of Kaniadakis statistics, it can be bigger or smaller than T when Tsallis statistics are employed.     

Inplace 2D matching in compressed images

The compressed matching problem is the problem of finding all occurrences of a pattern in a compressed text. In this paper we discuss the 2-dimensional compressed matching problem in Lempel–Ziv compressed images. Given a pattern P of (uncompressed) size m×m, and a text T of (uncompressed) size n×n, both in 2D-LZ compressed form, our algorithm finds all occurrences of P in T. The algorithm is strongly inplace, that is, the amount of extra space used is proportional to the best possible compression of a pattern of size m². The best compression that the 2D-LZ technique can obtain for a file of size m² is O(m). The time for performing the search is O(n²) and the preprocessing time is O(m³). Our algorithm is general in the sense that it can be used for any 2D compression which can be sequentially decompressed in small space.