Optimization of graded multilayer designs for astronomical x-ray telescopes

We developed a systematic method for optimizing the design of depth-graded multilayers for astronomical hard-x-ray and soft-γ-ray telescopes based on the instrument’s bandpass and the field of view. We apply these methods to the design of the conical-approximation Wolter I optics employed by the balloon-borne High Energy Focusing Telescope, using W/Si as the multilayer materials. In addition, we present optimized performance calculations of mirrors, using other material pairs that are capable of extending performance to photon energies above the W K-absorption edge (69.5 keV), including Pt/C, Ni/C, Cu/Si, and Mo/Si

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

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

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

How leisure activities affect health: a narrative review and multi-level theoretical framework of mechanisms of action

There is a large and growing body of evidence on the health benefits of engagement in leisure activities (voluntary, enjoyable non-work activities, such as hobbies, arts, volunteering, community group membership, sports, and socialising). However, there is no unifying framework explaining how leisure activities affect health: what the mechanisms of action are by which engagement with leisure activities leads to the prevention, management, or treatment of mental and physical illness. In this Review, we identify and map over 600 mechanisms of action. These mechanisms can be categorised as psychological, biological, social, and behavioural processes that operate at individual (micro), group (meso), and societal (macro) levels, and are synthesised into a new theoretical framework: the Multi-level Leisure Mechanisms Framework. This framework situates understanding of leisure activities within the theoretical lens of complex adaptive systems and aims to support the design of more theory-driven, cross-disciplinary studies

Optimizations of Pt/SiC and W/Si multilayers for the Nuclear Spectroscopic Telescope Array

The Nuclear Spectroscopic Telescope Array, NuSTAR, is a NASA funded Small Explorer Mission, SMEX, scheduled for launch in mid 2011. The spacecraft will fly two co-aligned conical approximation Wolter-I optics with a focal length of 10 meters. The mirrors will be deposited with Pt/SiC and W/Si multilayers to provide a broad band reflectivity from 6 keV up to 78.4 keV. To optimize the mirror coating we use a Figure of Merit procedure developed for gazing incidence optics, which averages the effective area over the energy range, and combines an energy weighting function with an angular weighting function to control the shape of the desired effective area. The NuSTAR multilayers are depth graded with a power-law, d_i = a/(b + i)^c, and we optimize over the total number of bi-layers, N, c, and the maximum bi-layer thickness, d_(max). The result is a 10 mirror group design optimized for a flat even energy response both on and off-axis

Optimal detection of burst events in gravitational wave interferometric observatories

We consider the problem of detecting a burst signal of unknown shape. We introduce a statistic which generalizes the excess power statistic proposed by Flanagan and Hughes and extended by Anderson et al. The statistic we propose is shown to be optimal for arbitrary noise spectral characteristic, under the two hypotheses that the noise is Gaussian, and that the prior for the signal is uniform. The statistic derivation is based on the assumption that a signal affects only affects N samples in the data stream, but that no other information is a priori available, and that the value of the signal at each sample can be arbitrary. We show that the proposed statistic can be implemented combining standard time-series analysis tools which can be efficiently implemented, and the resulting computational cost is still compatible with an on-line analysis of interferometric data. We generalize this version of an excess power statistic to the multiple detector case, also including the effect of correlated noise. We give full details about the implementation of the algorithm, both for the single and the multiple detector case, and we discuss exact and approximate forms, depending on the specific characteristics of the noise and on the assumed length of the burst event. As a example, we show what would be the sensitivity of the network of interferometers to a delta-function burst.Comment: 21 pages, 5 figures in 3 groups. Submitted for publication to Phys.Rev.D. A Mathematica notebook is available at http://www.ligo.caltech.edu/~avicere/nda/burst/Burst.nb which allows to reproduce the numerical results of the pape

Gravitational radiation from a particle in circular orbit around a black hole. VI. Accuracy of the post-Newtonian expansion

A particle of mass $\mu$ moves on a circular orbit around a nonrotating black hole of mass $M$. Under the assumption $\mu \ll M$ the gravitational waves emitted by such a binary system can be calculated exactly numerically using black-hole perturbation theory. If, further, the particle is slowly moving, then the waves can be calculated approximately analytically, and expressed in the form of a post-Newtonian expansion. We determine the accuracy of this expansion in a quantitative way by calculating the reduction in signal-to-noise ratio incurred when matched filtering the exact signal with a nonoptimal, post-Newtonian filter.Comment: 5 pages, ReVTeX, 1 figure. A typographical error was discovered in the computer code used to generate the results presented in the paper. The corrected results are presented in an Erratum, which also incorporates new results, obtained using the recently improved post-Newtonian calculations of Tanaka, Tagoshi, and Sasak

Development of thermally formed glass optics for astronomical hard x-ray telescopes

The next major observational advance in hard X-ray/soft gamma-ray astrophysics will come with the implementation of telescopes capable of focusing 10-200 keV radiation. Focusing allows high signal-to-noise imaging and spectroscopic observations of many sources in this band for the first time. The recent development of depth-graded multilayer coatings has made the design of telescopes for this bandpass practical, however the ability to manufacture inexpensive substrates with appropriate surface quality and figure to achieve sub-arcminute performance has remained an elusive goal. In this paper, we report on new, thermally-formed glass micro-sheet optics capable of meeting the requirements of the next-generation of astronomical hard X-ray telescopes

Magnetic Energy and Helicity Budgets in the Active-Region Solar Corona. I. Linear Force-Free Approximation

We self-consistently derive the magnetic energy and relative magnetic helicity budgets of a three-dimensional linear force-free magnetic structure rooted in a lower boundary plane. For the potential magnetic energy we derive a general expression that gives results practically equivalent to those of the magnetic Virial theorem. All magnetic energy and helicity budgets are formulated in terms of surface integrals applied to the lower boundary, thus avoiding computationally intensive three-dimensional magnetic field extrapolations. We analytically and numerically connect our derivations with classical expressions for the magnetic energy and helicity, thus presenting a so-far lacking unified treatment of the energy/helicity budgets in the constant-alpha approximation. Applying our derivations to photospheric vector magnetograms of an eruptive and a noneruptive solar active regions, we find that the most profound quantitative difference between these regions lies in the estimated free magnetic energy and relative magnetic helicity budgets. If this result is verified with a large number of active regions, it will advance our understanding of solar eruptive phenomena. We also find that the constant-alpha approximation gives rise to large uncertainties in the calculation of the free magnetic energy and the relative magnetic helicity. Therefore, care must be exercised when this approximation is applied to photospheric magnetic field observations. Despite its shortcomings, the constant-alpha approximation is adopted here because this study will form the basis of a comprehensive nonlinear force-free description of the energetics and helicity in the active-region solar corona, which is our ultimate objective.Comment: 44 pages, 8 figures, 2 tables. The Astrophysical Journal, in pres