Maximum norms of random sums and transient pattern formation

Many interesting and complicated patterns in the applied sciences are formed through transient pattern formation processes. In this paper we concentrate on the phenomenon of spinodal decomposition in metal alloys as described by the Cahn-Hilliard equation. This model depends on a small parameter, and one is generally interested in establishing sharp lower bounds on the amplitudes of the patterns as the parameter approaches zero. Recent results on spinodal decomposition have produced such lower bounds. Unfortunately, for higher-dimensional base domains these bounds are orders of magnitude smaller than what one would expect from simulations and experiments. The bounds exhibit a dependence on the dimension of the domain, which from a theoretical point of view seemed unavoidable, but which could not be observed in practice.

In this paper we resolve this apparent paradox. By employing probabilistic methods, we can improve the lower bounds for certain domains and remove the dimension dependence. We thereby obtain optimal results which close the gap between analytical methods and numerical observations, and provide more insight into the nature of the decomposition process. We also indicate how our results can be adapted to other situations.

     

The Neumann problem,cylindrical outlets and Sobolev spaces

The Neumann problem is crucial in mathematical physics. Nevertheless, as far as cylindrical domains are concerned there is still the open question how to construct solutions to data in usual Sobolev spaces since the standard Kondratiev theory does not apply. In this paper that unsatisfactory gap is filled and moreover, data with polynomial asymptotic behaviour are considered. As interesting special case we find solutions with bounded Dirichlet integral. Copyright © 2002 John Wiley & Sons, Ltd.     

Orientation and relaxation of polymer–clay solutions studied by rheology and small-angle neutron scattering

The influence of shear on viscoelastic solutions of poly(ethylene oxide) (PEO) and clay [montmorillonite, i.e., Cloisite NA+ (CNA)] was investigated with rheology and small-angle neutron scattering (SANS). The steady-state viscosity and SANS were used to measure the shear-induced orientation and relaxation of the polymer and clay platelets. Anisotropic scattering patterns developed at much lower shear rates than in pure clay solutions. The scattering anisotropy saturated at low shear rates, and the CNA clay platelets aligned with the flow, with the surface normal parallel to the gradient direction. The cessation of shear led to partial and slow randomization of the CNA platelets, whereas extremely fast relaxation was observed for laponite (LRD) platelets. These PEO–CNA networklike solutions were compared with previously reported PEO–LRD networks, and the differences and similarities, with respect to the shear orientation, relaxation, and polymer–clay interactions, were examined. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3102–3112, 2004     

4-Amino-imidazole durchThorpe-Cyclisierung

The alkylation of arylaminomethylenecyanamides1 or cyano-imidothiocarbamates2 with -halogen carbonyl compounds followed by base catalysed cyclization yields substituted 4-amino-imidazoles4. Imidazo[4,5-d]pyrimidones5, 6 and imidazo[4,5-b]pyridines7 can be obtained from4.     

An integrated console for capsule-based,automated organic synthesis

The current laboratory practices of organic synthesis are labor intensive, impose safety and environmental hazards, and hamper the implementation of artificial intelligence guided drug discovery. Using a combination of reagent design, hardware engineering, and a simple operating system we provide an instrument capable of executing complex organic reactions with prepacked capsules. The machine conducts coupling reactions and delivers the purified products with minimal user involvement. Two desirable reaction classes – the synthesis of saturated N-heterocycles and reductive amination – were implemented, along with multi-step sequences that provide drug-like organic molecules in a fully automated manner. We envision that this system will serve as a console for developers to provide synthetic methods as integrated, user-friendly packages for conducting organic synthesis in a safe and convenient fashion.

Using a combination of reagent design, hardware engineering, and a simple operating system we provide an instrument capable of executing complex organic reactions using prepacked capsules with minimal user involvement.     

PHOTOSENSITIZATION OF MELANIN: AN ELECTRON SPIN RESONANCE STUDY OF SENSITIZED RADICAL PRODUCTION AND OXYGEN CONSUMPTION

Abstract Rose Bengal is shown to photosensitize free-radical production and oxygen consumption in solutions of melanin from autooxidation of 3,4-dihydroxyphenylalanine (DOPA). In anaerobic solutions the sensitizer enhances rates of free-radical production by up to a factor of 20. In aerobic solutions, rates of oxygen consumption can be increased by a factor of several hundred. The reactions appear to involve the triplet state of the sensitizer. The effect of the sensitizer in increasing oxygen consumption is quenched by low concentrations of azide and enhanced by D₂O, suggesting that a singlet oxygen mechanism is involved.     

A convenient synthesis of 1,3-oxazolidin-4-ones and 1,3-oxazin-4-ones

1,3-Oxazolidin-4-ones and 1,3-oxazin-4-ones were synthesized by formal cyclocondensation of imines with α- or β-hydroxy acids.