42,833 research outputs found
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 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 . 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
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