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

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

Relativistic r-modes in Slowly Rotating Neutron Stars: Numerical Analysis in the Cowling Approximation

We investigate the properties of relativistic $r$-modes of slowly rotating neutron stars by using a relativistic version of the Cowling approximation. In our formalism, we take into account the influence of the Coriolis like force on the stellar oscillations, but ignore the effects of the centrifugal like force. For three neutron star models, we calculated the fundamental $r$-modes with $l'=m=2$ and 3. We found that the oscillation frequency $\bar\sigma$ of the fundamental $r$-mode is in a good approximation given by $\bar\sigma\approx \kappa_0 \Omega$, where $\bar\sigma$ is defined in the corotating frame at the spatial infinity, and $\Omega$ is the angular frequency of rotation of the star. The proportional coefficient $\kappa_0$ is only weakly dependent on $\Omega$, but it strongly depends on the relativistic parameter $GM/c^2R$, where $M$ and $R$ are the mass and the radius of the star. All the fundamental $r$-modes with $l'=m$ computed in this study are discrete modes with distinct regular eigenfunctions, and they all fall in the continuous part of the frequency spectrum associated with Kojima's equation (Kojima 1998). These relativistic $r$-modes are obtained by including the effects of rotation higher than the first order of $\Omega$ so that the buoyant force plays a role, the situation of which is quite similar to that for the Newtonian $r$-modes.Comment: 22 pages, 8 figures, accepted for publication in Ap

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

Protective effect of prostacyclin on postischemic acute renal failure in the rat

Protective effect of prostacyclin on postischemic acute renal failure in the rat. Infusion of prostacyclin (PGI2) reportedly attenuates renal ischemic injury in the dog and the rat. In the dog, PGI2 is a potent renal vasodilator; in the rat a direct action on the renal vasculature is not always apparent. To determine whether or not the protective effect of PGI2 on postichemic ARF was hemodynamically mediated, studies were performed in uninephrectomized Sprague–Dawley rats before and after a 40 minute period of complete renal artery occlusion. In response to the preischemic infusion of PGI2 for 30 minutes at 160 ng/kg body wt/min i.v. (N = 7), MAP and RBF fell to 86 ± 7% (P < 0.0001) and 84 ± 9% (P < 0.05) of baseline values, respectively. RVR initially declined to 81 ± 9% of baseline values (P < 0.025) but returned to 102 ± 13% of baseline values prior to the period of ischemia. Following the period of ischemia, reflow of blood in the rats receiving PGI2 was delayed when compared to rats not receiving PGI2 (N = 1). RBF returned to only 76 ± 19% of the initial values in PGI2-treated rats (P < 0.01) but to 90 ± 12% of the initial values in rats receiving buffer alone (NS). Observations made during the ensuing 48 hours in animals treated with either 80 (N = 8) or 160 ng/kg/body wt/min (N = 7) for 30 minutes before and four hours after the period of ischemia indicated that renal function improved to a greater extent in the PGI2-treated animals than in buffer–treated animals (N = 15) as judged by significantly–greater mean values of V, UOsm, UCr and CCr. On the second day after ischemia, CInwas significantly greater in PGI2-treated animals than in the postischemic animals receiving buffer alone (77 ± 45 vs. 33 ± 20 µl/min/100 g body wt; P < 0.05) despite the fact that no differences were found in the mean values of RBF (3.59 ± 1.08 vs. 3.43 ± 0.32 ml/min/100 body wt. Blinded analysis of the histological sections revealed significantly less evidence of tublar epithelial cell necrosis in the PGI2-treated animals (P < 0.005). The data indicate that the protective effect of PGI2 on the renal response to ischemic injury in the Sprague–Dawley rat is not related to changes in RBF or RVR. Instead, the beneficial effect of PGI2may be a result of cytoprotective properties as has been demonstrated in other tissues