The Distance Geometry of Music

We demonstrate relationships between the classic Euclidean algorithm and many other fields of study, particularly in the context of music and distance geometry. Specifically, we show how the structure of the Euclidean algorithm defines a family of rhythms which encompass over forty timelines (\emph{ostinatos}) from traditional world music. We prove that these \emph{Euclidean rhythms} have the mathematical property that their onset patterns are distributed as evenly as possible: they maximize the sum of the Euclidean distances between all pairs of onsets, viewing onsets as points on a circle. Indeed, Euclidean rhythms are the unique rhythms that maximize this notion of \emph{evenness}. We also show that essentially all Euclidean rhythms are \emph{deep}: each distinct distance between onsets occurs with a unique multiplicity, and these multiplicies form an interval $1,2,...,k-1$. Finally, we characterize all deep rhythms, showing that they form a subclass of generated rhythms, which in turn proves a useful property called shelling. All of our results for musical rhythms apply equally well to musical scales. In addition, many of the problems we explore are interesting in their own right as distance geometry problems on the circle; some of the same problems were explored by Erd\H{o}s in the plane.Comment: This is the full version of the paper: "The distance geometry of deep rhythms and scales." 17th Canadian Conference on Computational Geometry (CCCG '05), University of Windsor, Canada, 200

The Gbt 67–93.6 Ghz Spectral Line Survey Of Orion-Kl

We present a 67--93.6 GHz spectral line survey of Orion-KL with the new 4 mm Receiver on the Green Bank Telescope (GBT). The survey reaches unprecedented depths and covers the low-frequency end of the 3 mm atmospheric window which has been relatively unexplored previously. The entire spectral-line survey is published electronically for general use by the astronomical community. The calibration and performance of 4 mm Receiver on the GBT is also summarized

O₂ photoabsorption in the 40 950–41 300 cm⁻¹ region: New Herzberg bands, new absorption lines, and improved spectroscopic data

The technique of cavity ring‐down (CRD) spectroscopy is particularly useful for measuring absorptions of very weak optical transitions. We have in this manner investigated the 40 950–41 300 cm−1 region in O2, where only absorption in the O2(A 3Σ+u–X 3Σ−g) 11‐0 band had been previously identified. Five new bands have been discovered in this range—the A′ 3Δu–X 3Σ−g 12‐0 and 13‐0 bands, the c 1Σ−u–X 3Σ−g 17‐0 and 18‐0 bands, and the A 3Σ+u−X 3Σ−g 12‐0 band. The origins of the F1 and F2 components of the latter lie only 7 cm−1 below the lowest dissociation limit, and 15 lines have been identified. No F3 levels were observed; apparently all are above the dissociation limit. The high instrumental sensitivity of the CRD technique has allowed observation of weak lines of the A–X 11‐0 band, and 12 of the 13 branches have been identified and their intensities measured. A very low upper limit has been set on the intensity of the thirteenth branch, Q13. We find 107 unidentified lines in the region, the stronger ones (19) lying in the vicinity of lines of the A–X 11‐0 band. The weaker ones (88) are spread throughout the spectral region, up to and even beyond the O2dissociation limit, and probably have their origin in transitions to very weakly bound O2 states, which may have atmospheric significance. These weaker lines have intensities that are typically 1%–5% of the strong A–X 11‐0 band lines

Stark shift and field ionization of arsenic donors in 28^{28}Si-SOI structures

We develop an efficient back gate for silicon-on-insulator (SOI) devices operating at cryogenic temperatures, and measure the quadratic hyperfine Stark shift parameter of arsenic donors in isotopically purified $^{28}$Si-SOI layers using such structures. The back gate is implemented using MeV ion implantation through the SOI layer forming a metallic electrode in the handle wafer, enabling large and uniform electric fields up to $\sim$ 2 V/$\mu$m to be applied across the SOI layer. Utilizing this structure we measure the Stark shift parameters of arsenic donors embedded in the $^{28}$Si SOI layer and find a contact hyperfine Stark parameter of $\eta_a=-1.9\pm0.2\times10^{-3} \mu$m$^2$/V$^2$. We also demonstrate electric-field driven dopant ionization in the SOI device layer, measured by electron spin resonance.Comment: 5 pages, 3 figure

Electrostatic trapping of metastable NH molecules

We report on the Stark deceleration and electrostatic trapping of $^{14}$NH ($a ^1\Delta$) radicals. In the trap, the molecules are excited on the spin-forbidden $A ^3\Pi \leftarrow a ^1\Delta$ transition and detected via their subsequent fluorescence to the $X ^3\Sigma^-$ ground state. The 1/e trapping time is 1.4 $\pm$ 0.1 s, from which a lower limit of 2.7 s for the radiative lifetime of the $a ^1\Delta, v=0,J=2$ state is deduced. The spectral profile of the molecules in the trapping field is measured to probe their spatial distribution. Electrostatic trapping of metastable NH followed by optical pumping of the trapped molecules to the electronic ground state is an important step towards accumulation of these radicals in a magnetic trap.Comment: replaced with final version, added journal referenc

Electrical current distribution across a metal-insulator-metal structure during bistable switching

Combining scanning electron microscopy (SEM) and electron-beam-induced current (EBIC) imaging with transport measurements, it is shown that the current flowing across a two-terminal oxide-based capacitor-like structure is preferentially confined in areas localized at defects. As the thin-film device switches between two different resistance states, the distribution and intensity of the current paths, appearing as bright spots, change. This implies that switching and memory effects are mainly determined by the conducting properties along such paths. A model based on the storage and release of charge carriers within the insulator seems adequate to explain the observed memory effect.Comment: 8 pages, 7 figures, submitted to J. Appl. Phy

Effects of hole-doping on the magnetic ground state and excitations in the edge-sharing CuO2_2 chains of Ca2+x_{2+x}Y2−x_{2-x}Cu5_5O10_{10}

Neutron scattering experiments were performed on the undoped and hole-doped Ca$_{2+x}$Y$_{2-x}$Cu$_5$O$_{10}$, which consists of ferromagnetic edge-sharing CuO$_2$ chains. It was previously reported that in the undoped Ca$_2$Y$_2$Cu$_5$O$_{10}$ there is an anomalous broadening of spin-wave excitations along the chain, which is caused mainly by the antiferromagnetic interchain interactions [Matsuda $et$ $al.$, Phys. Rev. B 63, 180403(R) (2001)]. A systematic study of temperature and hole concentration dependencies of the magnetic excitations shows that the magnetic excitations are softened and broadened with increasing temperature or doping holes irrespective of $Q$ direction. The broadening is larger at higher $Q$. A characteristic feature is that hole-doping is much more effective to broaden the excitations along the chain. It is also suggested that the intrachain interaction does not change so much with increasing temperature or doping although the anisotropic interaction and the interchain interaction are reduced. In the spin-glass phase ($x$=1.5) and nearly disordered phase ($x$=1.67) the magnetic excitations are much broadened in energy and $Q$. It is suggested that the spin-glass phase originates from the antiferromagnetic clusters, which are caused by the hole disproportionation.Comment: 8 pages, submitted to Phys. Rev.

A new Stark decelerator based surface scattering instrument for studying energy transfer at the gas-surface interface

We report on the design and characterization of a new apparatus for performing quantum-state resolved surface scattering experiments. The apparatus combines optical state-specific molecule preparation with a compact hexapole and a Stark decelerator to prepare carrier gas-free pulses of quantum-state pure CO molecules with velocities controllable between 33 and 1000 m/s with extremely narrow velocity distributions. The ultrahigh vacuum surface scattering chamber includes homebuilt ion and electron detectors, a closed-cycle helium cooled single crystal sample mount capable of tuning surface temperature between 19 and 1337 K, a Kelvin probe for non-destructive work function measurements, a precision leak valve manifold for targeted adsorbate deposition, an inexpensive quadrupole mass spectrometer modified to perform high resolution temperature programmed desorption experiments and facilities to clean and characterize the surface

DRAM:A three-dimensional analytical model for the mobilisation of root reinforcement in direct shear conditions

Roots can stabilise slopes against shallow landslides by mobilising their mechanical strength. Existing analytical models are highly simplified and typically focus on the ultimate limit state only, thus providing little insight into the underlying mechanism of reinforcement mobilisation. A new analytical model (‘DRAM’) was therefore developed to predict mechanical root reinforcement as a function of direct shear displacements. This model accounts for elasto-plastic root behaviour, three-dimensional root orientations, root failure through breakage or slippage, and a dynamically changing shear zone thickness. Comparison to two independent experimental direct shear data sets showed that the model was able to accurately predict the gradual mobilisation of root strength, the magnitude of peak root reinforcement, as well as the presence of significant root reinforcement at large shear displacements, associated with a relatively large quantity of roots slipping out of the surrounding soil. Because the newly developed model more closely resembles the underlying physics of the mobilisation of root reinforcement in direct shear while still being easy to use, it will be a useful tool for the engineering industry, in terms of quantifying root reinforcement distribution for limit analyses at the ultimate limit state, as well as for directing future research into the drivers of mechanical root reinforcement.</p