Addendum to: Capillary floating and the billiard ball problem

We compare the results of our earlier paper on the floating in neutral equilibrium at arbitrary orientation in the sense of Finn-Young with the literature on its counterpart in the sense of Archimedes. We add a few remarks of personal and social-historical character.Comment: This is an addendum to my article Capillary floating and the billiard ball problem, Journal of Mathematical Fluid Mechanics 14 (2012), 363 -- 38

On recurrence and ergodicity for geodesic flows on noncompact periodic polygonal surfaces

We study the recurrence and ergodicity for the billiard on noncompact polygonal surfaces with a free, cocompact action of $\Z$ or $\Z^2$. In the $\Z$-periodic case, we establish criteria for recurrence. In the more difficult $\Z^2$-periodic case, we establish some general results. For a particular family of $\Z^2$-periodic polygonal surfaces, known in the physics literature as the wind-tree model, assuming certain restrictions of geometric nature, we obtain the ergodic decomposition of directional billiard dynamics for a dense, countable set of directions. This is a consequence of our results on the ergodicity of \ZZ-valued cocycles over irrational rotations.Comment: 48 pages, 12 figure

Relativistic corrections to the Pionium Lifetime

Next to leading order contributions to the pionium lifetime are considered within non-relativistic effective field theory. A more precise determination of the coupling constants is then needed in order to be consistent with the relativistic pion-pion scattering amplitude which can be obtained from chiral perturbation theory. The relativistic correction is found to be 4.1% and corresponds simply to a more accurate value for the non-relativistic decay momentum.Comment: 5 pages, Latex. Includes corrections based on a more precise matching to the pion-pion scattering amplitude from chiral perturbation theor

Binary inspiral, gravitational radiation, and cosmology

Observations of binary inspiral in a single interferometric gravitational wave detector can be cataloged according to signal-to-noise ratio $\rho$ and chirp mass $\cal M$. The distribution of events in a catalog composed of observations with $\rho$ greater than a threshold $\rho_0$ depends on the Hubble expansion, deceleration parameter, and cosmological constant, as well as the distribution of component masses in binary systems and evolutionary effects. In this paper I find general expressions, valid in any homogeneous and isotropic cosmological model, for the distribution with $\rho$ and $\cal M$ of cataloged events; I also evaluate these distributions explicitly for relevant matter-dominated Friedmann-Robertson-Walker models and simple models of the neutron star mass distribution. In matter dominated Friedmann-Robertson-Walker cosmological models advanced LIGO detectors will observe binary neutron star inspiral events with $\rho>8$ from distances not exceeding approximately $2\,\text{Gpc}$, corresponding to redshifts of $0.48$ (0.26) for $h=0.8$ ($0.5$), at an estimated rate of 1 per week. As the binary system mass increases so does the distance it can be seen, up to a limit: in a matter dominated Einstein-deSitter cosmological model with $h=0.8$ ($0.5$) that limit is approximately $z=2.7$ (1.7) for binaries consisting of two $10\,\text{M}_\odot$ black holes. Cosmological tests based on catalogs of the kind discussed here depend on the distribution of cataloged events with $\rho$ and $\cal M$. The distributions found here will play a pivotal role in testing cosmological models against our own universe and in constructing templates for the detection of cosmological inspiraling binary neutron stars and black holes.Comment: REVTeX, 38 pages, 9 (encapsulated) postscript figures, uses epsf.st

Extreme morning chronotypes are often familial and not exceedingly rare: the estimated prevalence of advanced sleep phase, familial advanced sleep phase, and advanced sleep-wake phase disorder in a sleep clinic population.

Study objectivesReport the first prevalence estimates of advanced sleep phase (ASP), familial advanced sleep phase (FASP), and advanced sleep-wake phase disorder (ASWPD). This can guide clinicians on the utility of screening for extreme chronotypes both for clinical decision-making and to flag prospective participants in the study of the genetics and biology of FASP.MethodsData on morning or evening sleep schedule preference (chronotype) were collected from 2422 new patients presenting to a North American sleep center over 9.8 years. FASP was determined using a severity criterion that has previously identified dominant circadian mutations in humans. All patients were personally seen and evaluated by one of the authors (C.R.J.).ResultsOur results demonstrate an ASP prevalence of 0.33%, an FASP prevalence of 0.21%, and an ASWPD prevalence of at least 0.04%. Most cases of young-onset ASP were familial.ConclusionsAmong patients presenting to a sleep clinic, conservatively 1 out of every 300 patients will have ASP, 1 out of every 475 will have FASP, and 1 out of every 2500 will have ASWPD. This supports obtaining a routine circadian history and, for those with extreme chronotypes, obtaining a family history of circadian preference. This can optimize treatment for evening sleepiness and early morning awakening and lead to additional circadian gene discovery. We hope these findings will lead to improved treatment options for a wide range of sleep and medical disorders in the future

Entropy of Thermally Excited Black Rings

A string theory description of near extremal black rings is proposed. The entropy is computed and the thermodynamic properties are derived for a large family of black rings that have not yet been constructed in supergravity. It is also argued that the most general black ring in N=8 supergravity has 21 parameters up to duality.Comment: 17 pages; v2: minor edits and refs adde

Lateral Pile Response from Model Tests in a Large Centrifuge

Lateral loading tests on instrumented model piles in saturated sand in a centrifuge are described. Piles were tested in isolation and in groups of two, three and six piles. Data were obtained on deflections and bending moments in single piles and on interaction factors between piles. Response of single piles compared favourably with data from Mustang Island field tests. Experimental interaction factors generally differed from those commonly used which are derived from elastic theory. The difference depends on pile spacing