Keeping your eye on the rail: gaze behaviour of horse riders approaching a jump

The gaze behaviour of riders during their approach to a jump was investigated using a mobile eye tracking device (ASL Mobile Eye). The timing, frequency and duration of fixations on the jump and the percentage of time when their point of gaze (POG) was located elsewhere were assessed. Fixations were identified when the POG remained on the jump for 100 ms or longer. The jumping skill of experienced but non-elite riders (n=10) was assessed by means of a questionnaire. Their gaze behaviour was recorded as they completed a course of three identical jumps five times. The speed and timing of the approach was calculated. Gaze behaviour throughout the overall approach and during the last five strides before take-off was assessed following frame-by-frame analyses. Differences in relation to both round and jump number were found. Significantly longer was spent fixated on the jump during round 2, both during the overall approach and during the last five strides (p , 0.05). Jump 1 was fixated on significantly earlier and more frequently than jump 2 or 3 (p , 0.05). Significantly more errors were made with jump 3 than with jump 1 (p=0.01) but there was no difference in errors made between rounds

Eigenvalue bounds for a class of singular potentials in N dimensions

The eigenvalue bounds obtained earlier [J. Phys. A: Math. Gen. 31 (1998) 963] for smooth transformations of the form V(x) = g(x^2) + f(1/x^2) are extended to N-dimensions. In particular a simple formula is derived which bounds the eigenvalues for the spiked harmonic oscillator potential V(x) = x^2 + lambda/x^alpha, alpha > 0, lambda > 0, and is valid for all discrete eigenvalues, arbitrary angular momentum ell, and spatial dimension N.Comment: 10 pages (plain tex with 2 ps figures). J.Phys.A:Math.Gen.(In Press

The status of traditional Scottish animal breeds and plant varieties and the implications for biodiversity

The aim of this scoping study was to evaluate the effects on Scottish biodiversity of changes in the use of traditional breeds and varieties. The overall objectives were: a) The evaluation of the importance of genetic loss from the reduction in use of these breeds and varieties, for example, the loss of unusual characteristics that might have been of particular local use. b) An assessment of the impacts of reduction in the ability to conduct further breeding or research on rare and traditional varieties and breeds. c) Identification of the loss of certain farming techniques associated with particular varieties and breeds. d) An assessment of possible losses of biodiversity associated with reduction in the use of these breeds and varieties and the farming systems associated with them

Condensate splitting in an asymmetric double well for atom chip based sensors

We report on the adiabatic splitting of a BEC of $^{87}$Rb atoms by an asymmetric double-well potential located above the edge of a perpendicularly magnetized TbGdFeCo film atom chip. By controlling the barrier height and double-well asymmetry the sensitivity of the axial splitting process is investigated through observation of the fractional atom distribution between the left and right wells. This process constitutes a novel sensor for which we infer a single shot sensitivity to gravity fields of $\delta g/g\approx2\times10^{-4}$. From a simple analytic model we propose improvements to chip-based gravity detectors using this demonstrated methodology.Comment: 4 pages, 5 figure

Coherent states and the quantization of 1+1-dimensional Yang-Mills theory

This paper discusses the canonical quantization of 1+1-dimensional Yang-Mills theory on a spacetime cylinder, from the point of view of coherent states, or equivalently, the Segal-Bargmann transform. Before gauge symmetry is imposed, the coherent states are simply ordinary coherent states labeled by points in an infinite-dimensional linear phase space. Gauge symmetry is imposed by projecting the original coherent states onto the gauge-invariant subspace, using a suitable regularization procedure. We obtain in this way a new family of "reduced" coherent states labeled by points in the reduced phase space, which in this case is simply the cotangent bundle of the structure group K. The main result explained here, obtained originally in a joint work of the author with B. Driver, is this: The reduced coherent states are precisely those associated to the generalized Segal-Bargmann transform for K, as introduced by the author from a different point of view. This result agrees with that of K. Wren, who uses a different method of implementing the gauge symmetry. The coherent states also provide a rigorous way of making sense out of the quantum Hamiltonian for the unreduced system. Various related issues are discussed, including the complex structure on the reduced phase space and the question of whether quantization commutes with reduction

Variational analysis for a generalized spiked harmonic oscillator

A variational analysis is presented for the generalized spiked harmonic oscillator Hamiltonian operator H, where H = -(d/dx)^2 + Bx^2+ A/x^2 + lambda/x^alpha, and alpha and lambda are real positive parameters. The formalism makes use of a basis provided by exact solutions of Schroedinger's equation for the Gol'dman and Krivchenkov Hamiltonian (alpha = 2), and the corresponding matrix elements that were previously found. For all the discrete eigenvalues the method provides bounds which improve as the dimension of the basis set is increased. Extension to the N-dimensional case in arbitrary angular-momentum subspaces is also presented. By minimizing over the free parameter A, we are able to reduce substantially the number of basis functions needed for a given accuracy.Comment: 15 pages, 1 figur

An effective singular oscillator for Duffin-Kemmer-Petiau particles with a nonminimal vector coupling: a two-fold degeneracy

Scalar and vector bosons in the background of one-dimensional nonminimal vector linear plus inversely linear potentials are explored in a unified way in the context of the Duffin-Kemmer-Petiau theory. The problem is mapped into a Sturm-Liouville problem with an effective singular oscillator. With boundary conditions emerging from the problem, exact bound-state solutions in the spin-0 sector are found in closed form and it is shown that the spectrum exhibits degeneracy. It is shown that, depending on the potential parameters, there may or may not exist bound-state solutions in the spin-1 sector.Comment: 1 figure. arXiv admin note: substantial text overlap with arXiv:1009.159

Semiclassical energy formulas for power-law and log potentials in quantum mechanics

We study a single particle which obeys non-relativistic quantum mechanics in R^N and has Hamiltonian H = -Delta + V(r), where V(r) = sgn(q)r^q. If N \geq 2, then q > -2, and if N = 1, then q > -1. The discrete eigenvalues E_{n\ell} may be represented exactly by the semiclassical expression E_{n\ell}(q) = min_{r>0}\{P_{n\ell}(q)^2/r^2+ V(r)}. The case q = 0 corresponds to V(r) = ln(r). By writing one power as a smooth transformation of another, and using envelope theory, it has earlier been proved that the P_{n\ell}(q) functions are monotone increasing. Recent refinements to the comparison theorem of QM in which comparison potentials can cross over, allow us to prove for n = 1 that Q(q)=Z(q)P(q) is monotone increasing, even though the factor Z(q)=(1+q/N)^{1/q} is monotone decreasing. Thus P(q) cannot increase too slowly. This result yields some sharper estimates for power-potential eigenvlaues at the bottom of each angular-momentum subspace.Comment: 20 pages, 5 figure

Effect of Magnetization Inhomogeneity on Magnetic Microtraps for Atoms

We report on the origin of fragmentation of ultracold atoms observed on a permanent magnetic film atom chip. A novel technique is used to characterize small spatial variations of the magnetic field near the film surface using radio frequency spectroscopy of the trapped atoms. Direct observations indicate the fragmentation is due to a corrugation of the magnetic potential caused by long range inhomogeneity in the film magnetization. A model which takes into account two-dimensional variations of the film magnetization is consistent with the observations.Comment: 4 pages, 4 figure