Hydrodynamic Limit of the Gross-Pitaevskii Equation

We study dynamics of vortices in solutions of the Gross-Pitaevskii equation i? _t u = Δu + ?^?2 u(1 ? |u|²) on ?² with nonzero degree at infinity. We prove that vortices move according to the classical Kirchhoff-Onsager ODE for a small but finite coupling parameter ?. By carefully tracking errors we allow for asymptotically large numbers of vortices, and this lets us connect the Gross-Pitaevskii equation on the plane to two dimensional incompressible Euler equations through the work of Schochet [19 Schochet , S. ( 1996 ). The point vortex method for periodic weak solutions of the 2D Euler equations . Comm. Pure Appl. Math. 49 : 911 – 965 .[Crossref], [Web of Science ®] , [Google Scholar]].     

A new approach to the incorporation of servo constraints in multibody dynamics

A new index reduction approach is developed to solve the servo constraint problems [2] in the inverse dynamics simulation of underactuated mechanical systems. The servo constraint problem of underactuated systems is governed by differential algebraic equations (DAEs) with high index. The underlying equations of motion contain both holonomic constraints and servo constraints in which desired outputs (specified in time) are described in terms of state variables. The realization of servo constraints with the use of control forces can range from orthogonal to tangential [3]. Since the (differentiation) index of the DAEs is often higher than three for underactuated systems, in which the number of degrees of freedom is greater than the control outputs/inputs, we propose a new index reduction method [1] which makes possible the stable numerical integration of the DAEs. We apply the proposed method to differentially flat systems, such as cranes [1,4,5], and non-flat underactuated systems. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

PSEUDOHALOGEN CHEMISTRY. PART IV. HETEROLYTIC ADDITION OF THIOCYANOGEN TO ALKENES

Abstract

Thiocyanogen reacts slowly with alkenes, in the presence of a radical inhibitor in benzene or acetic acid in the dark at 25°, to yield α,β-dithiocyanates, α-isothiocyanates-β-thiocyanates and, in acetic acid, α-acetoxy-β-thiocyanates in varying proportions. The additions to alkyl alkenes are trans-stereospecific, and, in the case of the α-isothiocyanato-β-thiocyanates, non-regiospecific. The additions to aryl alkenes are trans-stereoselective and regiospecific, yielding the Markownikov-orientated α-isothiocyanato-β-thiocyanates. A heterolytic mechanism involving a two-step, kinetically controlled addition, with the formation of a cyano-sulfonium ion intermediate, e.g., 35, in the case of alkyl alkenes and an open carbonium ion, e.g., 36, in the case of aryl alkenes, is suggested. The diothiocyanate: isothiocyanato-thiocyanate ratios are discussed in terms of kinetic and steric control of reaction.     

Neutral Hexacoordinate Phosphorus(V) Compounds Containing Tridentate Dianionic Ligands Obtained from Salicylideneamines, 2,2′-Azodiphenol and a Thio(Diphenol)

Abstract

Neutral hexacoordinate phosphorus(V) compounds of a number of univalent bidentate ligands are known.^l,2 The silylated forms of tridentate, dianionic Schiff base ligands: N-(2-hydroxyphenyl)salicylideneamine H₂L^I, N-(4-tert-butyl-2-hydroxyphenyl)-salicylideneamine H₂L^II, N-(2-hydroxy-4-nitrophenyl)salicylidene-amine H₂L^III, and 2,2′-azodiphenol H₂L^IV gave, with halogeno- and (trifluoromethyl)halogenophosphoranes, neutral hexa-coordinate derivatives with bis-chelate structures. The ligands form bicyclic five- and six-membered chelate rings in a meridional conformation, with two P-O bonds and one N→P donor bond. Hexacoordinate structures were evidenced by high-field ³¹P NMR chemical shifts (-136 to -148 ppm), characteristic J _PF coupling patterns and was further substantiated by crystal structures of Cl₃L^II (A) and F₃PL^II (B).     

THE PREPARATION OF TRIALKYL PHOSPHITES DIRECTLY FROM THE ELEMENT

Abstract

The reaction between finely divided white phosphorus and several alkoxide ions in the presence of tetrachloromethane and excess of alcohol has been investigated under a variety of conditions. High yields of trialkylphosphite are obtained when two equivalents of alkoxide are used. With one equivalent of alkoxide, dialkylphosphonate is formed in comparable yield. Maximum yields of triester are obtained within 1–3 h at room temperature. Prolonged treatment results in the conversion of trialkylphosphite to phosphate by reaction with tetrachloromethane. Phenolate ions are unreactive under the same experimental conditions. The mechanism of the reaction is discussed.     

Formation of Chiral β-Silyl-Vinyl Ethers

Chiral formates derived from propane-1,2-diol, 1,2- O -isopropylidene- f - D -xylo- and f - D -gluco-furanoses were subjected to treatment with cyclopentadienyl [tris(trimethylsilylmethyl)] titanium (IV). A mixture of the corresponding ( E )- and ( Z )- g -silylvinyl ethers were obtained with predominance of the former. It was found that in contrast to ( Z )-vinyl ethers, which give g -lactams with chlorosulfonyl isocyanate, the ( E )-vinyl ethers gave unstable cycloadducts which undergo rapid elimination reaction leading to ( E )- f , g -unsaturated amides.     

AN INVESTIGATION OF THE REACTION PRODUCTS OF N3P3CL4(NH2)2 WITH NUCLEOPHILIC REAGENTS. EXAMPLES OF GEMINAL → NON-GEMINAL REARRANGEMENTS

Abstract

Based on its reactions with various nucleophiles both geminal and non-geminal structures have been earlier proposed for N₃P₃Cl₄(NH₂)₂, although its geminal structure is now considered established. The reactions of this compound with alcohols have been investigated and the products examined by NMR spectroscopy and X-ray crystallography. Evidence for both unrearranged as well as geminal → non-geminal rearranged alcoholysis products is presented.     

2-Phospha-Allylic Systems

Abstract

Phosphamethincyanines prepared in 1964 by Dimroth and Hoffmann were among the first compounds with two-coordinate phosphorus. They are special cases of 2-phospha-allylic cations. Simple representatives of this type become available from the reaction of imidoyl chlorides with tris(trimethylsily1)phosphane.