Radiocarbon releases from the 2011 Fukushima nuclear accident

Radiocarbon activities were measured in annual tree rings for the years 2009 to 2015 from Japanese cedar trees (Cryptomeria japonica) collected at six sites ranging from 2.5–38 km northwest and north of the Fukushima Dai-ichi nuclear power plant. The 14C specific activity varied from 280.4 Bq kg−1 C in 2010 to 226.0 Bq kg−1 C in 2015. The elevated 14C activities in the 2009 and 2010 rings confirmed 14C discharges during routine reactor operations, whereas those activities that were indistinguishable from background in 2012–2015 coincided with the permanent shutdown of the reactors after the accident in 2011. High-resolution 14C analysis of the 2011 ring indicated 14C releases during the Fukushima accident. The resulted 14C activity decreased with increasing distance from the plant. The maximum 14C activity released during the period of the accident was measured 42.4 Bq kg−1 C above the natural ambient 14C background. Our findings indicate that, unlike other Fukushima-derived radionuclides, the 14C released during the accident is indistinguishable from ambient background beyond the local environment (~30 km from the plant). Furthermore, the resulting dose to the local population from the excess 14C activities is negligible compared to the dose from natural/nuclear weapons sources

Black Hole Interaction Energy

The interaction energy between two black holes at large separation distance is calculated. The first term in the expansion corresponds to the Newtonian interaction between the masses. The second term corresponds to the spin-spin interaction. The calculation is based on the interaction energy defined on the two black holes initial data. No test particle approximation is used. The relation between this formula and cosmic censorship is discussed.Comment: 18 pages, 2 figures, LaTeX2

Comparing initial-data sets for binary black holes

We compare the results of constructing binary black hole initial data with three different decompositions of the constraint equations of general relativity. For each decomposition we compute the initial data using a superposition of two Kerr-Schild black holes to fix the freely specifiable data. We find that these initial-data sets differ significantly, with the ADM energy varying by as much as 5% of the total mass. We find that all initial-data sets currently used for evolutions might contain unphysical gravitational radiation of the order of several percent of the total mass. This is comparable to the amount of gravitational-wave energy observed during the evolved collision. More astrophysically realistic initial data will require more careful choices of the freely specifiable data and boundary conditions for both the metric and extrinsic curvature. However, we find that the choice of extrinsic curvature affects the resulting data sets more strongly than the choice of conformal metric.Comment: 18 pages, 12 figures, accepted for publication in Phys. Rev.

An integrated approach to modelling the fluid-structure interaction of a collapsible tube

The well known collapsible tube experiment was conducted to obtain flow, pressure and materials property data for steady state conditions. These were then used as the boundary conditions for a fully coupled fluid-structure interaction (FSI) model using a propriety computer code, LS-DYNA. The shape profiles for the tube were also recorded. In order to obtain similar collapse modes to the experiment, it was necessary to model the tube flat, and then inflate it into a circular profile, leaving residual stresses in the walls. The profile shape then agreed well with the experimental ones. Two departures from the physical properties were required to reduce computer time to an acceptable level. One of these was the lowering of the speed of sound by two orders of magnitude which, due to the low velocities involved, still left the mach number below 0.2. The other was to increase the thickness of the tube to prevent the numerical collapse of elements. A compensation for this was made by lowering the Young's modulus for the tube material. Overall the results are qualitatively good. They give an indication of the power of the current FSI algorithms and the need to combine experiment and computer models in order to maximise the information that can be extracted both in terms of quantity and quality

Gravitational waves from inspiralling compact binaries: Parameter estimation using second-post-Newtonian waveforms

The parameters of inspiralling compact binaries can be estimated using matched filtering of gravitational-waveform templates against the output of laser-interferometric gravitational-wave detectors. Using a recently calculated formula, accurate to second post-Newtonian (2PN) order [order $(v/c)^4$, where $v$ is the orbital velocity], for the frequency sweep ($dF/dt$) induced by gravitational radiation damping, we study the statistical errors in the determination of such source parameters as the ``chirp mass'' $\cal M$, reduced mass $\mu$, and spin parameters $\beta$ and $\sigma$ (related to spin-orbit and spin-spin effects, respectively). We find that previous results using template phasing accurate to 1.5PN order actually underestimated the errors in $\cal M$, $\mu$, and $\beta$. For two inspiralling neutron stars, the measurement errors increase by less than 16 percent.Comment: 14 pages, ReVTe

Numerically generated quasi-equilibrium orbits of black holes: Circular or eccentric?

We make a comparison between results from numerically generated, quasi-equilibrium configurations of compact binary systems of black holes in close orbits, and results from the post-Newtonian approximation. The post-Newtonian results are accurate through third PN order (O(v/c)^6 beyond Newtonian gravity), and include rotational and spin-orbit effects, but are generalized to permit orbits of non-zero eccentricity. Both treatments ignore gravitational radiation reaction. The energy E and angular momentum J of a given configuration are compared between the two methods as a function of the orbital angular frequency \Omega. For small \Omega, corresponding to orbital separations a factor of two larger than that of the innermost stable orbit, we find that, if the orbit is permitted to be slightly eccentric, with e ranging from \approx 0.03 to \approx 0.05, and with the two objects initially located at the orbital apocenter (maximum separation), our PN formulae give much better fits to the numerically generated data than do any circular-orbit PN methods, including various ``effective one-body'' resummation techniques. We speculate that the approximations made in solving the initial value equations of general relativity numerically may introduce a spurious eccentricity into the orbits.Comment: 6 pages, 4 figures, to be submitted to Phys. Rev.

On the Circular Orbit Approximation for Binary Compact Objects In General Relativity

One often-used approximation in the study of binary compact objects (i.e., black holes and neutron stars) in general relativity is the instantaneously circular orbit assumption. This approximation has been used extensively, from the calculation of innermost circular orbits to the construction of initial data for numerical relativity calculations. While this assumption is inconsistent with generic general relativistic astrophysical inspiral phenomena where the dissipative effects of gravitational radiation cause the separation of the compact objects to decrease in time, it is usually argued that the timescale of this dissipation is much longer than the orbital timescale so that the approximation of circular orbits is valid. Here, we quantitatively analyze this approximation using a post-Newtonian approach that includes terms up to order ({Gm/(rc^2)})^{9/2} for non-spinning particles. By calculating the evolution of equal mass black hole / black hole binary systems starting with circular orbit configurations and comparing them to the more astrophysically relevant quasicircular solutions, we show that a minimum initial separation corresponding to at least 6 (3.5) orbits before plunge is required in order to bound the detection event loss rate in gravitational wave detectors to < 5% (20%). In addition, we show that the detection event loss rate is > 95% for a range of initial separations that include all modern calculations of the innermost circular orbit (ICO).Comment: 10 pages, 12 figures, revtex

Circular orbits of corotating binary black holes: comparison between analytical and numerical results

We compare recent numerical results, obtained within a ``helical Killing vector'' (HKV) approach, on circular orbits of corotating binary black holes to the analytical predictions made by the effective one body (EOB) method (which has been recently extended to the case of spinning bodies). On the scale of the differences between the results obtained by different numerical methods, we find good agreement between numerical data and analytical predictions for several invariant functions describing the dynamical properties of circular orbits. This agreement is robust against the post-Newtonian accuracy used for the analytical estimates, as well as under choices of resummation method for the EOB ``effective potential'', and gets better as one uses a higher post-Newtonian accuracy. These findings open the way to a significant ``merging'' of analytical and numerical methods, i.e. to matching an EOB-based analytical description of the (early and late) inspiral, up to the beginning of the plunge, to a numerical description of the plunge and merger. We illustrate also the ``flexibility'' of the EOB approach, i.e. the possibility of determining some ``best fit'' values for the analytical parameters by comparison with numerical data.Comment: Minor revisions, accepted for publication in Phys. Rev. D, 19 pages, 6 figure

Interpretation of quantum jump and diffusion-processes illustrated on the Bloch sphere

It is shown that the evolution of an open quantum system whose density operator obeys a Markovian master equation can in some cases be meaningfully described in terms of stochastic Schrödinger equations (SSE’s) for its state vector. A necessary condition for this is that the information carried away from the system by the bath (source of the irreversibility) be recoverable. The primary field of application is quantum optics, where the bath consists of the continuum of electromagnetic modes. The information lost from the system can be recovered using a perfect photodetector. The state of the system conditioned on the photodetections undergoes stochastic quantum jumps. Alternative measurement schemes on the outgoing light (homodyne and heterodyne detection) are shown to give rise to SSE’s with diffusive terms. These three detection schemes are illustrated on a simple quantum system, the two-level atom, giving new perspectives on the interpretation of measurement results. The reality of these and other stochastic processes for state vectors is discussed

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