Family of cofacial bimetallic complexes of a hexaanionic carboxamide cryptand

A series of coordination compounds has been prepared comprising manganese, iron, nickel, and zinc bound by a hexaanionic cryptand where carboxamides are anionic N-donors. The metal complexes have been investigated by X-ray crystallography, and possess metal centers in trigonal monopyramidal geometries with intermetallic distances spanning d(Mn,avg) = 6.080 ? to d(Ni,avg) = 6.495 ?. All complexes featuring trigonal monopyramidal metal(II) ions crystallize in Cc, and feature extended three-dimensional networks composed of cryptate anions linked by bridging potassium countercations. We also report the first solid state structure of the free cryptand ligand, which features no guest in its cavity and which possesses an extended hydrogen-bonding network. SQuID magnetometry data of the metal complexes reveal weak antiferromagnetic coupling of the metal centers. Only the diiron(II) complex exhibits reversible electrochemistry, and correspondingly, its chemical oxidation yields a powder formulated as the diiron(III) congener. The insertion of cyanide into the intermetallic cleft of the diiron(II) complex has been achieved, and comparisons of its solid state structure to the recently reported dicobalt(II) analogue are made. The antiferromagnetic coupling between the diiron(II) and the dicobalt(II) centers when bridged by cyanide does not increase significantly relative to the unbridged congeners. A one-site model satisfactorily fits Mo?ssbauer spectra of unbridged diiron(II) and diiron(III) complexes whereas a two site fit was needed to model the iron(II) centers that are bridged by cyanide.     

Planar Steering of a Single Ferrofluid Drop by Optimal Minimum Power Dynamic Feedback Control of Four Electromagnets at a Distance

Any single permanent magnet or electromagnet will always attract a magnetic fluid. For this reason it is difficult to precisely position and manipulate ferrofluid at a distance from magnets. We develop and experimentally demonstrate optimal (minimum electrical power) 2-dimensional manipulation of a single droplet of ferrofluid by feedback control of 4 external electromagnets. The control algorithm we have developed takes into account, and is explicitly designed for, the nonlinear (fast decay in space, quadratic in magnet strength) nature of how the magnets actuate the ferrofluid, and it also corrects for electromagnet charging time delays. With this control, we show that dynamic actuation of electromagnets held outside a domain can be used to position a droplet of ferrofluid to any desired location and steer it along any desired path within that domain—an example of precision control of a ferrofluid by magnets acting at a distance.     

Nuclear magnetic resonance: A quantum technology for computation and spectroscopy

In this article we consider nuclear magnetic resonance (NMR) as an example of a quantum technology; we consider in particular detail the implementation of quantum computers using NMR. We begin by outlining the physical principles underlying NMR, and give an introduction to the quantum mechanics involved. We next discuss the general characteristics of quantum technologies and the ways and extent to which these characteristics are expressed in NMR. We then give an introduction to the subject of quantum computation and its implementation using NMR. Finally, we describe some spectroscopy techniques which also exploit the quantum nature of NMR.     

Approximate quantum cloning with nuclear magnetic resonance

Here we describe a nuclear magnetic resonance (NMR) experiment that uses a three qubit NMR device to implement the one-to-two approximate quantum cloning network of Buzek et al. [Phys. Rev. A 56, 3446 (1997)]. As expected the experimental results indicate that the network clones all input states with similar fidelities, but as a result of decoherence and incoherent evolution arising from B(1) inhomogeneity the total fidelity achieved does not exceed the measurement bound.     

Elliptic curves with nonsplit mod representations

We calculate explicitly the -invariants of the elliptic curves corresponding to rational points on the modular curve by giving an expression defined over of the -function in terms of the function field generators and of the elliptic curve . As a result we exhibit infinitely many elliptic curves over with nonsplit mod representations.

     

The formation of cobalt acetylides by direct reaction at cobalt(III)

A new method is described for the preparation of cobalt(III) acetylides, in which monosubstituted alkynes are treated directly with cobalt(III) forms of quadridentate Schiff base compounds in methanol.     

Nonlinear limits on bandwidth at the minimum dispersion in optical fibres

High bit rate systems can be achieved by operating at the wavelength of zero second order dispersion in optical fibres. The bandwidth is then limited by higher order dispersion terms. We consider the propagation of high intensity pulses in such a system, where the Kerr effect cannot be ignored. It is shown that the bandwidth is further limited by the optical nonlinearity.