An Expansion Term In Hamilton's Equations

For any given spacetime the choice of time coordinate is undetermined. A particular choice is the absolute time associated with a preferred vector field. Using the absolute time Hamilton's equations are $- (\delta H_{c})/(\delta q)=\dot{\pi}+\Theta\pi,$+ (\delta H_{c})/(\delta \pi)=\dot{q}$, where$\Theta = V^{a}_{.;a}$is the expansion of the vector field. Thus there is a hitherto unnoticed term in the expansion of the preferred vector field. Hamilton's equations can be used to describe fluid motion. In this case the absolute time is the time associated with the fluid's co-moving vector. As measured by this absolute time the expansion term is present. Similarly in cosmology, each observer has a co-moving vector and Hamilton's equations again have an expansion term. It is necessary to include the expansion term to quantize systems such as the above by the canonical method of replacing Dirac brackets by commutators. Hamilton's equations in this form do not have a corresponding sympletic form. Replacing the expansion by a particle number$N\equiv exp(-\int\Theta d \ta)$and introducing the particle numbers conjugate momentum$\pi^{N}$the standard sympletic form can be recovered with two extra fields N and$\pi^N$. Briefly the possibility of a non-standard sympletic form and the further possibility of there being a non-zero Finsler curvature corresponding to this are looked at.Comment: 10 page

Exploring Halo Substructure with Giant Stars IV: The Extended Structure of the Ursa Minor Dwarf Spheroidal

We present a large area photometric survey of the Ursa Minor dSph. We identify UMi giant star candidates extending to ~3 deg from the center of the dSph. Comparison to previous catalogues of stars within the tidal radius of UMi suggests that our photometric luminosity classification is 100% accurate. Over a large fraction of the survey area, blue horizontal branch stars associated with UMi can also be identified. The spatial distribution of both the UMi giant stars and the BHB stars are remarkably similar, and a large fraction of both samples of stars are found outside the tidal radius of UMi. An isodensity contour map of the stars within the tidal radius of UMi reveals two morphological peculiarities: (1) The highest density of dSph stars is offset from the center of symmetry of the outer isodensity contours. (2) The overall shape of the outer contours appear S-shaped. We find that previously determined King profiles with ~50' tidal radii do not fit well the distribution of our UMi stars. A King profile with a larger tidal radius produces a reasonable fit, however a power law with index -3 provides a better fit for radii > 20'. The existence of UMi stars at large distances from the core of the galaxy, the peculiar morphology of the dSph within its tidal radius, and the shape of its surface density profile all suggest that UMi is evolving significantly due to the tidal influence of the Milky Way. However, the photometric data on UMi stars alone does not allow us to determine if the candidate extratidal stars are now unbound or if they remain bound to the dSph within an extended dark matter halo. (Abridged)Comment: accepted by AJ, 32 pages, 15 figures, emulateapj5 styl

'It's a Form of Freedom': The experiences of people with disabilities within equestrian sport

This paper explores the embodied, gendered experiences of disabled horse‐riders. Drawing on data from five in‐depth interviews with paradressage riders, the ways in which their involvement in elite disability sport impacts upon their sense of identity and confidence are explored, as well as the considerable health and social benefits that this involvement brings. Social models of disability are employed and the shortcomings of such models, when applied to disability sport, are highlighted. The data presented here demonstrates the necessity of seeing disability sport as an embodied experience and acknowledging the importance of impairment to the experiences of disabled athletes. Living within an impaired body is also a gendered experience and the implications of this when applied to elite disability sport are considered

A study of 15N14N isotopic exchange over cobalt molybdenum nitrides

The 14N/15N isotopic exchange pathways over Co3Mo3N, a material of interest as an ammonia synthesis catalyst and for the development of nitrogen transfer reactions, have been investigated. Both the homomolecular and heterolytic exchange processes have been studied, and it has been shown that lattice nitrogen species are exchangeable. The exchange behavior was found to be a strong function of pretreatment with ca. 25% of lattice N atoms being exchanged after 40 min at 600 °C after N2 pretreatment at 700 °C compared to only 6% following similar Ar pretreatment. This observation, for which the potential contribution of adsorbed N species can be discounted, is significant in terms of the application of this material. In the case of the Co6Mo6N phase, regeneration to Co3Mo3N under 15N2 at 600 °C occurs concurrently with 14N15N formation. These observations demonstrate the reactivity of nitrogen in the Co–Mo–N system to be a strong function of pretreatment and worthy of further consideration

Diffusion of particles in an expanding sphere with an absorbing boundary

We study the problem of particles undergoing Brownian motion in an expanding sphere whose surface is an absorbing boundary for the particles. The problem is akin to that of the diffusion of impurities in a grain of polycrystalline material undergoing grain growth. We solve the time dependent diffusion equation for particles in a d-dimensional expanding sphere to obtain the particle density function (function of space and time). The survival rate or the total number of particles per unit volume as a function of time is evaluated. We have obtained particular solutions exactly for the case where d=3 and a parabolic growth of the sphere. Asymptotic solutions for the particle density when the sphere growth rate is small relative to particle diffusivity and vice versa are derived.Comment: 12 pages. To appear in J. Phys. A: Math. Theor. 41 (2008

The Metamorphosis of Tidally Stirred Dwarf Galaxies

We present results from high-resolution N-Body/SPH simulations of rotationally supported dwarf irregular galaxies moving on bound orbits in the massive dark matter halo of the Milky Way.The dwarf models span a range in disk surface density and the masses and sizes of their dark halos are consistent with the predictions of cold dark matter cosmogonies. We show that the strong tidal field of the Milky Way determines severe mass loss in their halos and disks and induces bar and bending instabilities that transform low surface brightness dwarfs (LSBs) into dwarf spheroidals (dSphs) and high surface brightness dwarfs (HSBs) into dwarf ellipticals (dEs) in less than 10 Gyr. The final central velocity dispersions of the remnants are in the range 8-30 km/s and their final $v/\sigma$ falls to values $< 0.5$, matching well the kinematics of early-type dwarfs. The transformation requires the orbital time of the dwarf to be \simlt 3-4 Gyr, which implies a halo as massive and extended as predicted by hierarchical models of galaxy formation to explain the origin of even the farthest dSph satellites of the Milky Way, Leo I and Leo II. Only dwarfs with central dark matter densities as high as those of Draco and Ursa Minor can survive for 10 Gyr in the proximity of the Milky Way: this is naturally achieved within hierarchical models, where the densest objects should have small orbital times due to their early formation epochs. Part of the gas is stripped and part is funneled to the center due to the bar, generating one strong burst of star formation in HSBs and smaller, multiple bursts in LSBs. Extended low-surface brightness stellar and gaseous streams originate from LSBs and, when projected along the line of sight, can lead to overestimate the mass-to-light ratio of the bound remnant by a factor \simlt 2,Comment: 29 pages, 34 figures, submitted to ApJ. Figures 5,11 and 32 are given as separate GIF files. Other figures and the movies of the simulations can be found at http://pcblu.mib.infn.it/~lucio/LG/LG.htm

On the state dependency of fast feedback processes in (palaeo) climate sensitivity

Palaeo data have been frequently used to determine the equilibrium (Charney) climate sensitivity $S^a$, and - if slow feedback processes (e.g. land ice-albedo) are adequately taken into account - they indicate a similar range as estimates based on instrumental data and climate model results. Most studies implicitly assume the (fast) feedback processes to be independent of the background climate state, e.g., equally strong during warm and cold periods. Here we assess the dependency of the fast feedback processes on the background climate state using data of the last 800 kyr and a conceptual climate model for interpretation. Applying a new method to account for background state dependency, we find $S^a=0.61\pm0.06$ K(Wm$^{-2}$)$^{-1}$ using the latest LGM temperature reconstruction and significantly lower climate sensitivity during glacial climates. Due to uncertainties in reconstructing the LGM temperature anomaly, $S^a$ is estimated in the range $S^a=0.55-0.95$ K(Wm$^{-2}$)$^{-1}$.Comment: submitted to Geophysical Research Letter

Testing the Hypothesis of Modified Dynamics with Low Surface Brightness Galaxies and Other Evidence

The rotation curves of low surface brightness galaxies provide a unique data set with which to test alternative theories of gravitation over a large dynamic range in size, mass, surface density, and acceleration. Many clearly fail, including any in which the mass discrepancy appears at a particular length-scale. One hypothesis, MOND [Milgrom 1983, ApJ, 270, 371], is consistent with the data. Indeed, it accurately predicts the observed behavior. We find no evidence on any scale which clearly contradicts MOND, and a good deal which supports it.Comment: Accepted for publication in the Astrophysical Journal. 35 pages AAStex + 9 figures. This result surprised the bejeepers out of us, to

Polarization correlations for electron-impact excitation of the resonant transitions of Ne and Ar at low incident energies

The electron-polarized-photon coincidence method is used to determine linear and circular polarization correlations in vacuum ultraviolet (VUV) for the differential electron-impact excitation of neon and argon resonance transitions at impact energies of 25 and 30 eV at small scattering angles up to 40. The circular polarization correlation is found to be positive in the case of Ne at 25 eV and supports the prediction of the present B-spline R-matrix theory concerning the violation of a long-established propensity rule regarding angular momentum transfer in electron-impact excitation of S→P transitions. Comparisons with the results from the present relativistic distorted-wave approximation and an earlier semirelativistic distorted-wave Born model are also made. For the case of Ar, at 25 and 30 eV, the circular polarization measurements remain in agreement with theory, but provide limited evidence as to whether or not the circular polarization at small scattering angles is also positive. For the linear polarizations, much better agreement with theory is obtained than in earlier measurements carried out by S. H. Zheng and K. Becker

Perceived importance of components of asynchronous music in circuit training

This study examined regular exercisers’ perceptions of specific components of music during circuit training. Twenty-four men (38.8 years, s = 11.8 years) and 31 women (32.4 years, s = 9.6 years) completed two questionnaires immediately after a circuit training class. Participants rated the importance of 13 components of music (rhythm, melody, etc.) in relation to exercise enjoyment, and each completed the Affect Intensity Measure (Larsen, 1984) to measure emotional reactivity. Independent t tests were used to evaluate gender differences in perceptions of musical importance. Pearson correlations were computed to evaluate the relationships between affect intensity, age and importance of musical components. Consistent with previous research and theoretical predictions, rhythm response components (rhythm, tempo, beat) were rated as most important. Women rated the importance of melody significantly higher than did men, while men gave more importance to music associated with sport. Affect intensity was found to be positively and significantly related to the perceived importance of melody, lyrical content, musical style, personal associations and emotional content. Results suggest that exercise leaders need to be sensitive to personal factors when choosing music to accompany exercise. Qualitative research that focuses on the personal meaning of music is encouraged