Evolution of circular, non-equatorial orbits of Kerr black holes due to gravitational-wave emission: II. Inspiral trajectories and gravitational waveforms

The inspiral of a ``small'' ($\mu \sim 1-100 M_\odot$) compact body into a ``large'' ($M \sim 10^{5-7} M_\odot$) black hole is a key source of gravitational radiation for the space-based gravitational-wave observatory LISA. The waves from such inspirals will probe the extreme strong-field nature of the Kerr metric. In this paper, I investigate the properties of a restricted family of such inspirals (the inspiral of circular, inclined orbits) with an eye toward understanding observable properties of the gravitational waves that they generate. Using results previously presented to calculate the effects of radiation reaction, I assemble the inspiral trajectories (assuming that radiation reacts adiabatically, so that over short timescales the trajectory is approximately geodesic) and calculate the wave generated as the compact body spirals in. I do this analysis for several black hole spins, sampling a range that should be indicative of what spins we will encounter in nature. The spin has a very strong impact on the waveform. In particular, when the hole rotates very rapidly, tidal coupling between the inspiraling body and the event horizon has a very strong influence on the inspiral time scale, which in turn has a big impact on the gravitational wave phasing. The gravitational waves themselves are very usefully described as ``multi-voice chirps'': the wave is a sum of ``voices'', each corresponding to a different harmonic of the fundamental orbital frequencies. Each voice has a rather simple phase evolution. Searching for extreme mass ratio inspirals voice-by-voice may be more effective than searching for the summed waveform all at once.Comment: 15 pages, 11 figures, accepted for publication in PRD. This version incorporates referee's comments, and is much less verbos

The custom-made titanium orbital floor prosthesis in reconstruction for orbital floor fractures

The custom-made titanium orbital floor prosthesis in reconstruction for orbital floor fracture

Changes in mean sea level around Great Britain over the past 200 years

We systematically assimilate a wide range of historical sea level data from around the coast of Great Britain, much of it previously unpublished, into a single comprehensive framework. We show that this greatly increased dataset allows the construction of a robust and extended Mean Sea Level curve for Great Britain covering a period of more than two centuries, and confirms that the 19th century trend was much weaker than that in the 20th century and beyond. As well as attempting to maximise the amount of newly recovered sea level observations, we have also recovered the levelling metadata necessary to connect this 19th and early 20th century data with modern records. We adjust this data for known sources of variability and estimate overall uncertainties over the entire period. Data are processed in 36 regional clusters, before recombining to compute national statistics. We investigate the advantages of extending and adjusting the time series on sea level rise trends and low order variability. Confidence limits are improved by better than 60%. The weighted linear trend since 1900 for the fully adjusted data points from all clusters when averaged annually and adjusted for Glacial Isostatic Adjustment is 2.12 mm/year ± 0.02 mm/year (1-sigma). The much lower trend estimated for the 19th Century alone is 0.24 ± 0.12 mm/yr. There is an acceleration of 0.012 mm/yr2 ± 0.003 mm/yr2 in the rate of rise over the period 1813 to 2018. These trends are quite sensitive to the GIA correction used, but their differences and accelerations are not

Improved and extended tide gauge records for the British Isles leading to more consistent estimates of sea level rise and acceleration since 1958

This paper describes methods of obtaining improved estimates of long-term sea level trends for the British Isles. This is achieved by lengthening the sea level records where possible, then removing known sources of variability, and then further adjusting for datum errors that are revealed by the previous processes after verification using metadata from archived sources. Local sea level variability is accounted for using a tide and surge model. Far field variability is accounted for using a “common mode”. This combination reduces the residual variability seen at tide gauges around the coast of the British Isles to the point that a number of previously unrecognised steps in individual records become apparent, permitting a higher level of quality control to be applied. A comprehensive data archaeology exercise was carried out which showed that these step-like errors are mostly coincident with recorded site-specific changes in instrumentation, and that in many cases the periodic tide gauge calibration records can be used to quantify these steps. A smaller number of steps are confirmed by “buddy-checking” against neighbouring tide gauges. After accounting for the observed steps, using levelling information where possible and an empirical fit otherwise, the records become significantly more consistent. The steps are not found to make a large difference to the trend and acceleration observed in UK sea level overall, but their correction results in much more consistent estimates of first order (Sea Level Rise) and second order (Sea Level Acceleration) trends over this 60-year period. We find a mean rate of sea level rise of 2.39 ± 0.27 mm yr−1, and an acceleration of 0.058 ± 0.030 mm yr−2 between Jan. 1958 and Dec. 2018. The cleaner dataset also permits us to show more clearly that the variability other than that derived from local meteorology is indeed consistent around the UK, and relates to sea level changes along the eastern boundary of the North Atlantic

Block-Transitive Designs in Affine Spaces

This paper deals with block-transitive $t$-$(v,k,\lambda)$ designs in affine spaces for large $t$, with a focus on the important index $\lambda=1$ case. We prove that there are no non-trivial 5-$(v,k,1)$ designs admitting a block-transitive group of automorphisms that is of affine type. Moreover, we show that the corresponding non-existence result holds for 4-$(v,k,1)$ designs, except possibly when the group is one-dimensional affine. Our approach involves a consideration of the finite 2-homogeneous affine permutation groups.Comment: 10 pages; to appear in: "Designs, Codes and Cryptography

Relativistic calculations of isotope shifts in highly charged ions

The isotope shifts of forbidden transitions in Be- and B-like argon ions are calculated. It is shown that only using the relativistic recoil operator can provide a proper evaluation of the mass isotope shift, which strongly dominates over the field isotope shift for the ions under consideration. Comparing the isotope shifts calculated with the current experimental uncertainties indicates very good perspectives for a first test of the relativistic theory of the recoil effect in middle-Z ions

Effect of Weld Schedule on the Residual Stress Distribution of Boron Steel Spot Welds

Press-hardened boron steel has been utilized in anti-intrusion systems in automobiles, providing high strength and weight-saving potential through gage reduction. Boron steel spot welds exhibit a soft heat-affected zone which is surrounded by a hard nugget and outlying base material. This soft zone reduces the strength of the weld and makes it susceptible to failure. Additionally, different welding regimes lead to significantly different hardness distributions, making failure prediction difficult. Boron steel sheets, welded with fixed and adaptive schedules, were characterized. These are the first experimentally determined residual stress distributions for boron steel resistance spot welds which have been reported. Residual strains were measured using neutron diffraction, and the hardness distributions were measured on the same welds. Additionally, similar measurements were performed on spot welded DP600 steel as a reference material. A correspondence between residual stress and hardness profiles was observed for all welds. A significant difference in material properties was observed between the fixed schedule and adaptively welded boron steel samples, which could potentially lead to a difference in failure loads between the two boron steel welds

Anomalous diffusion with absorption: Exact time-dependent solutions

Recently, analytical solutions of a nonlinear Fokker-Planck equation describing anomalous diffusion with an external linear force were found using a non extensive thermostatistical Ansatz. We have extended these solutions to the case when an homogeneous absorption process is also present. Some peculiar aspects of the interrelation between the deterministic force, the nonlinear diffusion and the absorption process are discussed.Comment: RevTex, 16 pgs, 4 figures. Accepted in Physical Review

Relativistic nuclear recoil corrections to the energy levels of hydrogen-like and high ZZ lithium like atoms in all orders in αZ\alpha Z

The relativistic nuclear recoil corrections to the energy levels of low-laying states of hydrogen-like and high $Z$ lithium-like atoms in all orders in $\alpha Z$ are calculated. The calculations are carried out using the B-spline method for the Dirac equation. For low $Z$ the results of the calculation are in good agreement with the $\alpha Z$ -expansion results. It is found that the nuclear recoil contribution, additional to the Salpeter's one, to the Lamb shift ($n=2$) of hydrogen is $-1.32(6)\,kHz$. The total nuclear recoil correction to the energy of the $(1s)^{2}2p_{\frac{1}{2}}-(1s)^{2}2s$ transition in lithium-like uranium constitutes $-0.07\,eV$ and is largely made up of QED contributions.Comment: 19 pages, latex, accepted for publication in Phys. Rev.