James Mills Peirce and the cult of quaternions

Quaternions furnish an example of the rise and fall in popularity of a mathematical theory. Without attempting to trace its mathematical and sociological causes, this note highlights some moments in the history, of this phenomenon, as well as some of the scientists involved, especially the neglected mathematician, James Mills Peirce.     

Droplet streams for serial crystallography of proteins

Serial diffraction of proteins requires an injection method to deliver analyte molecules—preferably uncharged, fully hydrated, spatially oriented, and with high flux—into a focused probe beam of electrons or X-rays that is only a few tens of microns in diameter. This work examines conventional Rayleigh sources and electrospray-assisted Rayleigh sources as to their suitability for this task. A comparison is made and conclusions drawn on the basis of time-resolved optical images of the droplet streams produced by these sources. Straight-line periodic streams of monodisperse droplets were generated with both sources, achieving droplet diameters of 4 and 1 micrometer, respectively, for the conventional and electrospray-assisted versions. Shrinkage of droplets by evaporation is discussed and quantified. It is shown experimentally that proteins pass undamaged through a conventional Rayleigh droplet source.     

Isomeric icosaboranes B20H26: the synchrotron structure of 1,1′‐bis(nido‐decaboranyl)

An isomer of B₂₀H₂₆, isolated from the autolysis of nido‐B₁₀H₁₄ in a silent electrical discharge, is shown to be the title compound 1,1′‐bis(nido‐decaboranyl). The mol­ecule has crystallographic inversion symmetry and a long intercage B—B bond of 1.704 (3) Å.     

Dynamic stiffness method for inplane free vibration of rotating beams including Coriolis effects

The paper addresses the in-plane free vibration analysis of rotating beams using an exact dynamic stiffness method. The analysis includes the Coriolis effects in the free vibratory motion as well as the effects of an arbitrary hub radius and an outboard force. The investigation focuses on the formulation of the frequency dependent dynamic stiffness matrix to perform exact modal analysis of rotating beams or beam assemblies. The governing differential equations of motion, derived from Hamilton's principle, are solved using the Frobenius method. Natural boundary conditions resulting from the Hamiltonian formulation enable expressions for nodal forces to be obtained in terms of arbitrary constants. The dynamic stiffness matrix is developed by relating the amplitudes of the nodal forces to those of the corresponding responses, thereby eliminating the arbitrary constants. Then the natural frequencies and mode shapes follow from the application of the Wittrick–Williams algorithm. Numerical results for an individual rotating beam for cantilever boundary condition are given and some results are validated. The influences of Coriolis effects, rotational speed and hub radius on the natural frequencies and mode shapes are illustrated.     

A small angle neutron scattering (SANS) experiment using very cold neutrons (VCN)

This paper describes the results of SANS measurements of small samples using the very cold neutron (VCN) beam of the PF2 instrument at the Institut Laue Langevin (ILL), France. In addition to a classical SANS pinhole collimation, the experiment used a polarizing supermirror as a monochromator and a magnetic sextupole lens to focus the neutron beam in order to gain intensity and avoid any material in the neutron beam besides the sample.     

Coherent control of optical emission from a conjugated polymer

We have observed that resonant Rayleigh scattering dominates the emission from poly(p-phenylene vinylene) excited with photons at energies below the threshold at which excitonic migration is reduced. The intensity of the resonant emission decays exponentially with a lifetime of up to 450 fs after pulsed excitation. The coherent nature of the emission was confirmed by angular variations in the far-field emission intensity-bright and dark speckles. Persistence of a coherent polarization was demonstrated by coherent control using phase-locked pulses.     

20-kW peak power all-fiber 1.57-microm source based on compression in air-core photonic bandgap fiber, its frequency doubling, and broadband generation from 430 to 1450 nm

We demonstrate an ultrashort all-fiber-integrated chirped-pulse amplification system yielding 1-ps pulses with 20 kW of peak power. 40-ps initial pulses generated by an externally modulated laser diode are chirped by self-phase modulation in a conventional fiber, amplified, and compressed in 110 m of air-core photonic bandgap fiber. The compressed pulses are frequency doubled in a periodically poled KTP crystal with up to 48% efficiency and applied to supercontinuum generation in a holey fiber, resulting in a high-power uniform continuum that stretches from 430 to 1450 nm.     

Quantum telecommunication based on atomic cascade transitions

A quantum repeater at telecommunications wavelengths with long-lived atomic memory is proposed, and its critical elements are experimentally demonstrated using a cold atomic ensemble. Via atomic cascade emission, an entangled pair of 1.53 microm and 780 nm photons is generated. The former is ideal for long-distance quantum communication, and the latter is naturally suited for mapping to a long-lived atomic memory. Together with our previous demonstration of photonic-to-atomic qubit conversion, both of the essential elements for the proposed telecommunications quantum repeater have now been realized.     

Spin–spin interaction in magnetic semiconductor quantum dots

Self-assembled Cd(Mn)Se/Zn(Mn)Se quantum dots have been investigated by means of spatially and time-resolved magneto-optical spectroscopy. In such quasi zero-dimensional diluted magnetic semiconductors, the exchange interaction couples the spins of optically generated charge carriers with localized magnetic ion spins. We demonstrate that this can be used on the one hand to monitor nanoscale magnetization with a resolution of <100 μ_B by a purely optical technique and on the other hand to optically manipulate the magnetization in a semiconductor quantum dot.