Optical imaging and magnetophoresis of nanorods

Peclet number analysis is performed to probe the convective motion of nanospheres and nanorods under the influence of magnetophoresis and diffusion. Under most circumstances, magnetophoretic behaviour dominates diffusion for nanorods, as the magnetic field lines tend to align the magnetic moment along the rod axis. The synthesis and dispersion of fluorophore-tagged nanorods are described. Fluorescence microscopy is employed to image the nanorod motion in a magnetic field gradient. The preliminary experimental data are consistent with the Peclet number analysis.     

Implicit QR algorithms for palindromic and even eigenvalue problems

In the spirit of the Hamiltonian QR algorithm and other bidirectional chasing algorithms, a structure-preserving variant of the implicit QR algorithm for palindromic eigenvalue problems is proposed. This new palindromic QR algorithm is strongly backward stable and requires less operations than the standard QZ algorithm, but is restricted to matrix classes where a preliminary reduction to structured Hessenberg form can be performed. By an extension of the implicit Q theorem, the palindromic QR algorithm is shown to be equivalent to a previously developed explicit version. Also, the classical convergence theory for the QR algorithm can be extended to prove local quadratic convergence. We briefly demonstrate how even eigenvalue problems can be addressed by similar techniques. D. S. Watkins partly supported by Deutsche Forschungsgemeinschaft through Matheon, the DFG Research Center Mathematics for key technologies in Berlin.     

Where are the large and difficult datasets?

A great many comparative performance assessments of classification rules have been undertaken, ranging from small ones involving just one or two methods, to large ones involving many tens of methods. We are undertaking a meta-analytic study of these studies, attempting to distil some overall conclusions. This paper describes just one of our observations. The dataset analysed in this paper contains 5,203 error rates taken from 45 articles and describing 146 datasets. One curious general relationship which was persistent in our data, despite the fact that we were looking at results mixed between distributions rather than conditional on distributions, was that error rate decreased with increasing dataset size. We believe this to be an artefact of the way datasets are collected by the research community.     

Accelerating electromagnetic magic field from the C-metric

Various aspects of the C-metric representing two rotating charged black holes accelerated in opposite directions are summarized and its limits are considered. A particular attention is paid to the special-relativistic limit in which the electromagnetic field becomes the “magic field” of two oppositely accelerated rotating charged relativistic discs. When the acceleration vanishes the usual electromagnetic magic field of the Kerr–Newman black hole with gravitational constant set to zero arises. Properties of the accelerated discs and the fields produced are studied and illustrated graphically. The charges at the rim of the accelerated discs move along spiral trajectories with the speed of light. If the magic field has some deeper connection with the field of the Dirac electron, as is sometimes conjectured because of the same gyromagnetic ratio, the “accelerating magic field” represents the electromagnetic field of a uniformly accelerated spinning electron. It generalizes the classical Born’s solution for two uniformly accelerated monopole charges.     

A rapid boundary perturbation algorithm for scattering by families of rough surfaces

In this paper we describe a novel algorithm for the computation of scattering returns by families of rough surfaces. This algorithm makes explicit use of the fact that some scattering profiles of engineering interest (e.g., traveling ocean waves) come in branches parameterized analytically by a bifurcation quantity. Our approach delivers recursions which not only can be implemented to yield a rapid, robust and high-order numerical scheme, but also give a new proof of analyticity of scattering quantities with respect to the bifurcation parameter of the surface family. The real advantage of this new approach is that it computes, in one step, the scattered field for all possible members of the family of surfaces. By contrast, other state-of-the-art schemes must restart when the returns from a new surface are desired, so that the cost of our new approach is greatly advantaged when the number of samples of the family reaches even modest values. Numerical results which verify the accuracy of our approach and demonstrate their utility in computing grating efficiencies scattered by traveling surface ocean waves are presented.     

Inter-particle interaction induced by broadband radiation

The recent fabrication of optical traps using super-continuum light impresses the need for a theory of inter-particle interactions under such conditions. Development of the theory provides a basis for calculation of the observations expected under experimental conditions. An expression for the inter-particle potential energy induced by continuum states of light is first derived using quantum electrodynamics. This energy expression is cast as a function of the spectral irradiance of the light, and the electric susceptibility of the interacting particles. Specific results are derived for light with a Lorentzian spectrum. It is shown that by filtering part of the spectrum, it is possible to exert control over the length of linear particle chains organized along the Poynting vector. The results exhibit scope for the optical fabrication of moldable structures using broadband light.     

Synthesis and palladium-catalysed isomerisation of fused polycyclic tetrahydrofurans: efficient and stereoselective one-pot domino construction of functionalised bridged bicyclo[n.2.1] ring systems

A new one-pot domino reaction for a general entry to functionalised bridged bicyclo[n.2.1] ring systems from α ,α’-diactivated cyclic ketones and trans-1,4-dihalides is described. The sequence combines a base promoted C–O cycloalkylation reaction leading to fused polycyclic enol ethers and their in situ palladium-catalysed isomerisation.