Application of energy and angular momentum balance to gravitational radiation reaction for binary systems with spin-orbit coupling

We study gravitational radiation reaction in the equations of motion for binary systems with spin-orbit coupling, at order (v/c)^7 beyond Newtonian gravity, or O(v/c)^2 beyond the leading radiation reaction effects for non-spinning bodies. We use expressions for the energy and angular momentum flux at infinity that include spin-orbit corrections, together with an assumption of energy and angular momentum balance, to derive equations of motion that are valid for general orbits and for a class of coordinate gauges. We show that the equations of motion are compatible with those derived earlier by a direct calculation.Comment: 12 pages, submitted to General Relativity and Gravitatio

The Lennard-Jones-Devonshire cell model revisited

We reanalyse the cell theory of Lennard-Jones and Devonshire and find that in addition to the critical point originally reported for the 12-6 potential (and widely quoted in standard textbooks), the model exhibits a further critical point. We show that the latter is actually a more appropriate candidate for liquid-gas criticality than the original critical point.Comment: 5 pages, 3 figures, submitted to Mol. Phy

The Effects of Caffeinated Gum and Caffeine Capsules on Running Sprint Performance

Use of anhydrous caffeine is an established and widely used ergogenic method. In sprinting events, optimum performance is highly dependent on the simultaneous peak functioning of a host of physiological systems. Therefore, caffeine supplementation protocols need to be perfectly timed in order to achieve culmination in sprint performance parameters within a narrow time window. Typically, caffeine capsules are ingested approximately 1 h before exercise however absorption rates may be highly variable. An alternative mode of ingestion is through caffeinated gum where caffeine is rapidly absorbed through the buccal mucosa. Our aim was to investigate the acute effects of two distinct modes of caffeine ingestion on sprint performance. Following ethics approval, eight trained male sprinters aged 20.2 (±0.8) took part in a screening and familiarisation session before they completed four trials (3x40 m sprints with 4 min recovery between runs) a week apart. A double-blind randomized crossover design was adopted where, during the trials, participants received: 1) Caffeine gum (CAFG, 6 mg.kg-1 of body weight), 2) CAFG placebo (CAFGP), 3) Caffeine capsules (CAFC, mg.kg-1 of body weight), 4) CAFC placebo (CAFCP). General and sport-specific warm-up commenced 15 minutes before sprint one. Capsules were given 45 minutes and chewing gums 15 minutes before sprint one. The gums were chewed for 5 minutes. Blood lactate and glucose concentration, heart rate, arousal and feeling levels were recorded at baseline and different time points during testing. Mean time to complete the three sprints were 5.00(±0.23), 5.03(±0.17), 5.10(±0.15), and 5.10(±0.14) seconds for the CAFG, CAFC, CAFGP and CAFCP conditions respectively. Participants ran significantly faster (p<0.05) during the caffeine compared to the placebo conditions. Additionally, sprint two in the CAFG (2.25±0.45 % faster than CAFGP) was significantly faster (p=0.022) than in the CAFC (1.40±0.32 % faster than CAFCP). Blood glucose and arousal levels were also significantly higher during the caffeine trials. Our data confirms that caffeine is an effective ergogenic strategy for sprinters. Furthermore, the greatest performance gains in sprint two suggests that caffeinated gum may be a more efficacious mode of ingestion than traditional methods of caffeine ingestion

The Physics of Miniature Worlds

This excerpt from a book length work on the history of the methodology of experimental physical models (physically similar systems) interwoven in Ludwig Wittgenstein's life begins in 1913-1914. It also discusses works by physicists around the same time that were thematically related to the philosophical topics he was working on: Ludwig Boltzmann, Wilhelm Ostwald, Edgar Buckingham, James Thomson, D'Arcy Wentworth Thompson, Henry Crew (and his new translation of Galileo's Two New Sciences during this period), Heike Kamerlingh Onnes, Van Der Waals, and Rayleigh (following up on the work of Gabriel Stokes), and Richard C Tolman. The landmark work at Britain's National Physical Laboratory in 1914 on Similar Motions by Stanton and Pannell, following up on Osborne Reynolds' work in Manchester, is also described and discussed. Connections between physics and the history of flight are mentioned, too: Penuad's successes, Boltzmann's relationship with engineer Otto Lilienthal, and the significance that Hermann von Helmholtz's landmark paper in meteorology which addressed the problem of steering aircraft, took on during this period

Metastability of a granular surface in a spinning bucket

The surface shape of a spinning bucket of granular material is studied using a continuum model of surface flow developed by Bouchaud et al. and Mehta et al. An experimentally observed central subcritical region is reproduced by the model. The subcritical region occurs when a metastable surface becomes unstable via a nonlinear instability mechanism. The nonlinear instability mechanism destabilizes the surface in large systems while a linear instability mechanism is relevant for smaller systems. The range of angles in which the granular surface is metastable vanishes with increasing system size.Comment: 8 pages with postscript figures, RevTex, to appear in Phys. Rev.

Coalescence of Two Spinning Black Holes: An Effective One-Body Approach

We generalize to the case of spinning black holes a recently introduced ``effective one-body'' approach to the general relativistic dynamics of binary systems. The combination of the effective one-body approach, and of a Pad\'e definition of some crucial effective radial functions, is shown to define a dynamics with much improved post-Newtonian convergence properties, even for black hole separations of the order of $6 GM / c^2$. We discuss the approximate existence of a two-parameter family of ``spherical orbits'' (with constant radius), and, of a corresponding one-parameter family of ``last stable spherical orbits'' (LSSO). These orbits are of special interest for forthcoming LIGO/VIRGO/GEO gravitational wave observations. It is argued that for most (but not all) of the parameter space of two spinning holes the effective one-body approach gives a reliable analytical tool for describing the dynamics of the last orbits before coalescence. This tool predicts, in a quantitative way, how certain spin orientations increase the binding energy of the LSSO. This leads to a detection bias, in LIGO/VIRGO/GEO observations, favouring spinning black hole systems, and makes it urgent to complete the conservative effective one-body dynamics given here by adding (resummed) radiation reaction effects, and by constructing gravitational waveform templates that include spin effects. Finally, our approach predicts that the spin of the final hole formed by the coalescence of two arbitrarily spinning holes never approaches extremality.Comment: 26 pages, two eps figures, accepted in Phys. Rev. D, minor updating of the text, clarifications added and inclusion of a few new reference