Slow motion in the gradient theory of phase transitions via energy and spectrum

We describe some aspects of the Cahn-Hilliard and related equations. In particular we consider the dynamics of almost spherical interfaces and establish that almost spherical interfaces either persist forever or until they reach the boundary, a phenomenon which happens superslowly. Received June 23, 1996 / Accepted October 28, 1996     

Sobolev imbedding theorems in borderline cases

An imbedding theorem is given for functions whose gradient belongs to a class slightly larger than , .

     

On the investigation of the low-energy conformational space of molecules

A new perspective on traditional energy minimization problems is provided by a connection between statistical thermodynamics and combinatorial optimization (finding the minimum of a function depending on many variables). The joint use of a new method for uncovering the global minimum of intramolecular potential energy functions, based on following the asymptotic behavior of a system of stochastic differential equations, and an iterative-improvement technique, whereby a search for relative minima is made by carrying out local quasi-Newton minimizations starting from many distinct points of the energy hypersurface, proved most effective for investigating the low-energy conformational space of molecules.     

Continued Progress towards Efficient Functionalization of Natural and Non-natural Targets under Mild Conditions: Oxygenation by C−H Bond Activation with Dioxirane

The successful isolation and characterization of a dioxirane species in 1988 opened up one of the most attractive methods for the efficient oxidation of simple and/or structurally complex molecules. Dioxirane today rank among the most powerful tools in organic chemistry, with numerous applications in commercially important processes. They were quickly recognized as efficient oxygen transfer agents, especially for epoxidations and for a wide range of O-insertion reactions into C−H bonds. Dioxirane possess catalytic activity and appear as highly (chemo-, regio-, and stereo-) selective oxidants, despite their reactivity under mild and strictly neutral conditions being controlled by a combination of steric and electronic factors. In this review, we discuss some of the most recent and significant developments in the selective homogeneous and heterogeneous oxyfunctionalization of non-activated C−H bonds in hydrocarbons of natural and non-natural targets by using isolated dioxirane or, more generally, by using the ketones (i.e., the dioxirane precursors) as organocatalysts.     

Experimental verification of thin-beam wandering dependence on distance in strong indoor turbulence

Abstract

The dependence of beam wandering (random lateral displacement) on distance of a thin beam propagating through strong indoor turbulence is investigated experimentally. In the case of small fluctuations and within the limits of the geometrical-optics approximation, the transverse displacement variance is expected to follow a third-power law dependence on distance. Here we present the results of measurements made over paths of a few metres, both in the laboratory and in a large corridor. Inner scale measured values are also reported.     

Acetone‐induced polymerisation of 3‐aminopropyltrimethoxysilane (APTMS) as revealed by NMR spectroscopy

We followed the reactivity of acetone with 3‐aminopropyltrimethoxysilane, a potential organosilane coupling agent, by ¹H, ¹³C and ²⁹Si NMR spectroscopy. Selective 1D and 2D‐edited NMR experiments significantly contributed to simplify the spectral complexity of reaction solution and elucidated molecular structures within progressive reaction phases. The course of the 3‐aminopropyltrimethoxysilane reaction with acetone was shown by a progressive decrease of both reactants, and a concomitant appearance of water and methanol, due to formation of imine and hydrolysis of alkoxysilane groups, respectively. The occurrence of multiple siloxane linkages in a progressively larger cross‐linked macromolecular structure was revealed by DOSY‐NMR experiments and new signals in ²⁹Si‐NMR spectra at different reaction times. The NMR approach described here may be applied to investigate the reactivity of other γ‐aminopropylalkoxysilanes and contribute to define procedures for the preparation of silica‐based materials. Copyright © 2014 John Wiley & Sons, Ltd.