Dynamics of the trade balance and the terms of trade: the S-curve

We provide a theoretical interpretation of two features of international data: the countercyclical movements in net exports and the tendency for the trade balance to be negatively correlated with current and future movements in the terms of trade, but positively correlated with past movements. We document these same properties in a two-country stochastic growth model in which trade fluctuations reflect, in large part, the dynamics of capital formation. We find that the general equilibrium perspective is essential: The relation between the trade balance and the terms of trade depends critically on the source of fluctuations.Balance of trade

Relative price movements in dynamic general equilibrium models of international trade

We examine the behavior of international relative prices from the perspective of dynamic general equilibrium theory, with particular emphasis on the variability of the terms of trade and the relation between the terms of trade and net exports. We highlight aspects of the theory that are critical in determining these properties, contrast our perspective with those associated with the Marshall-Lerner condition and the Harberger-Laursen-Metzler effect, and point out features of the data that have proved difficult to explain within existing dynamic general equilibrium models.International trade

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

The Cosmological Constant and Advanced Gravitational Wave Detectors

Interferometric gravitational wave detectors could measure the frequency sweep of a binary inspiral [characterized by its chirp mass] to high accuracy. The observed chirp mass is the intrinsic chirp mass of the binary source multiplied by $(1+z)$, where $z$ is the redshift of the source. Assuming a non-zero cosmological constant, we compute the expected redshift distribution of observed events for an advanced LIGO detector. We find that the redshift distribution has a robust and sizable dependence on the cosmological constant; the data from advanced LIGO detectors could provide an independent measurement of the cosmological constant.Comment: 13 pages plus 5 figure, LaTeX. Revised and final version, to appear in Phys. Rev.

Maximum Entropy for Gravitational Wave Data Analysis: Inferring the Physical Parameters of Core-Collapse Supernovae

The gravitational wave signal arising from the collapsing iron core of a Type II supernova progenitor star carries with it the imprint of the progenitor's mass, rotation rate, degree of differential rotation, and the bounce depth. Here, we show how to infer the gravitational radiation waveform of a core collapse event from noisy observations in a network of two or more LIGO-like gravitational wave detectors and, from the recovered signal, constrain these source properties. Using these techniques, predictions from recent core collapse modeling efforts, and the LIGO performance during its S4 science run, we also show that gravitational wave observations by LIGO might have been sufficient to provide reasonable estimates of the progenitor mass, angular momentum and differential angular momentum, and depth of the core at bounce, for a rotating core collapse event at a distance of a few kpc.Comment: 44 pages, 12 figures; accepted version scheduled to appear in Ap J 1 April 200

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

Observational Artifacts of NuSTAR: Ghost Rays and Stray Light

The Nuclear Spectroscopic Telescope Array (NuSTAR), launched in June 2012, flies two conical approximation Wolter-I mirrors at the end of a 10.15m mast. The optics are coated with multilayers of Pt/C and W/Si that operate from 3--80 keV. Since the optical path is not shrouded, aperture stops are used to limit the field of view from background and sources outside the field of view. However, there is still a sliver of sky (~1.0--4.0 degrees) where photons may bypass the optics altogether and fall directly on the detector array. We term these photons Stray-light. Additionally, there are also photons that do not undergo the focused double reflections in the optics and we term these Ghost Rays. We present detailed analysis and characterization of these two components and discuss how they impact observations. Finally, we discuss how they could have been prevented and should be in future observatories.Comment: Published in Journal of Astronomical Telescopes, Instruments, and Systems. Open Access. http://dx.doi.org/10.1117/1.JATIS.3.4.04400

Black Hole Spectroscopy: Testing General Relativity through Gravitational Wave Observations

Assuming that general relativity is the correct theory of gravity in the strong field limit, can gravitational wave observations distinguish between black hole and other compact object sources? Alternatively, can gravitational wave observations provide a test of one of the fundamental predictions of general relativity? Here we describe a definitive test of the hypothesis that observations of damped, sinusoidal gravitational waves originated from a black hole or, alternatively, that nature respects the general relativistic no-hair theorem. For astrophysical black holes, which have a negligible charge-to-mass ratio, the black hole quasi-normal mode spectrum is characterized entirely by the black hole mass and angular momentum and is unique to black holes. In a different theory of gravity, or if the observed radiation arises from a different source (e.g., a neutron star, strange matter or boson star), the spectrum will be inconsistent with that predicted for general relativistic black holes. We give a statistical characterization of the consistency between the noisy observation and the theoretical predictions of general relativity, together with a numerical example.Comment: 19 pages, 7 figure