Synthesis of a Chiral Hexane-1,6-Dinitrile from D-Glucose

Abstract

Using well-established methodology, D-glucose was transformed into a tribenzoyloxy cyclohexanone oxime derivative. Sodium azide treatment permitted the regiospecific exchange of the benzoyloxy group at a α-position relative to ketone oxime. Under standard Beckmann conditions the α-azido was oxime cleaved to provide an ω-dicyano compound.     

Hopf Bifurcations,Drops in the Lid-Driven Square Cavity Flow

The lid-driven square cavity flow is investigated by numerical experiments. It is found that from $ \mathrm{Re} $$=$ $5,000 $ to $ \mathrm{Re} $$=$$ 7,307.75 $ the solution is stationary, but at $ \mathrm{Re}$$=$$7,308 $ the solution is time periodic. So the critical Reynolds number for the first Hopf bifurcation localizes between $ \mathrm{Re} $$=$$ 7,307.75 $ and $ \mathrm{Re} $$=$$ 7,308 $. Time periodical behavior begins smoothly, imperceptibly at the bottom left corner at a tiny tertiary vortex; all other vortices stay still, and then it spreads to the three relevant corners of the square cavity so that all small vortices at all levels move periodically. The primary vortex stays still. At $ \mathrm{Re} $$=$$ 13,393.5 $ the solution is time periodic; the long-term integration carried out past $ t_{\infty} $$=$$ 126,562.5 $ and the fluctuations of the kinetic energy look periodic except slight defects. However, at $ \mathrm{Re} $$=$$ 13,393.75 $ the solution is not time periodic anymore: losing unambiguously, abruptly time periodicity, it becomes chaotic. So the critical Reynolds number for the second Hopf bifurcation localizes between $ \mathrm{Re} $$=$$ 13,393.5 $ and $ \mathrm{Re} $$=$$ 13,393.75 $. At high Reynolds numbers $ \mathrm{Re} $$=$$ 20,000 $ until $ \mathrm{Re} $$=$$ 30,000 $ the solution becomes chaotic. The long-term integration is carried out past the long time $ t_{\infty} $$=$$ 150,000 $, expecting the time asymptotic regime of the flow has been reached. The distinctive feature of the flow is then the appearance of drops: tiny portions of fluid produced by splitting of a secondary vortex, becoming loose and then fading away or being absorbed by another secondary vortex promptly. At $ \mathrm{Re} $$=$$ 30,000 $ another phenomenon arises—the abrupt appearance at the bottom left corner of a tiny secondary vortex, not produced by splitting of a secondary vortex.     

Theoretical description of ultrafast phenomena in clusters

A theoretical study of different ultrafast nonequilibrium processes taking place during and after ultrashort excitation of clusters is presented. We discuss similarities and differences for several processes involving nonequilibrium ultrafast motion of atoms and electrons. We study ultrashort relaxation of clusters in response to excitations produced by femtosecond laser pulses of different intensities. We show how different relaxation processes, such as bond breaking, melting, fragmentation, emission of atoms, or Coulomb explosion, can be induced, depending on the laser intensity and laser pulse duration. We also discuss processes involving nonequilibrium electron dynamics, such as intraband Auger decay in clusters and ultrafast electronic motion during collisions between clusters and surfaces. We show that this electron dynamics leads to Stückelberg-like oscillations of measurable quantities, such as the electron emission yield. Received: 4 April 2000 / Accepted: 6 November 2000 / Published online: 9 February 2001