Rotating black hole orbit functionals in the frequency domain

In many astrophysical problems, it is important to understand the behavior of functions that come from rotating (Kerr) black hole orbits. It can be particularly useful to work with the frequency domain representation of those functions, in order to bring out their harmonic dependence upon the fundamental orbital frequencies of Kerr black holes. Although, as has recently been shown by W. Schmidt, such a frequency domain representation must exist, the coupled nature of a black hole orbit's $r$ and $\theta$ motions makes it difficult to construct such a representation in practice. Combining Schmidt's description with a clever choice of timelike coordinate suggested by Y. Mino, we have developed a simple procedure that sidesteps this difficulty. One first Fourier expands all quantities using Mino's time coordinate $\lambda$. In particular, the observer's time $t$ is decomposed with $\lambda$. The frequency domain description is then built from the $\lambda$-Fourier expansion and the expansion of $t$. We have found this procedure to be quite simple to implement, and to be applicable to a wide class of functionals. We test the procedure using a simple test function, and then apply it in a particularly interesting case, the Weyl curvature scalar $\psi_4$ used in black hole perturbation theory.Comment: 16 pages, 2 figures. Submitted to Phys Rev D. New version gives a vastly improved algorithm due to Drasco for computing the Fourier transforms. Drasco has been added as an author. Also fixed some references and exterminated a small herd of typos; final published versio

Approximating the inspiral of test bodies into Kerr black holes

We present a new approximate method for constructing gravitational radiation driven inspirals of test-bodies orbiting Kerr black holes. Such orbits can be fully described by a semi-latus rectum $p$, an eccentricity $e$, and an inclination angle $\iota$; or, by an energy $E$, an angular momentum component $L_z$, and a third constant $Q$. Our scheme uses expressions that are exact (within an adiabatic approximation) for the rates of change ($\dot{p}$, $\dot{e}$, $\dot{\iota}$) as linear combinations of the fluxes ($\dot{E}$, $\dot{L_z}$, $\dot{Q}$), but uses quadrupole-order formulae for these fluxes. This scheme thus encodes the exact orbital dynamics, augmenting it with approximate radiation reaction. Comparing inspiral trajectories, we find that this approximation agrees well with numerical results for the special cases of eccentric equatorial and circular inclined orbits, far more accurate than corresponding weak-field formulae for ($\dot{p}$, $\dot{e}$, $\dot{\iota}$). We use this technique to study the inspiral of a test-body in inclined, eccentric Kerr orbits. Our results should be useful tools for constructing approximate waveforms that can be used to study data analysis problems for the future LISA gravitational-wave observatory, in lieu of waveforms from more rigorous techniques that are currently under development.Comment: 15 pages, 5 figures, submitted to PR

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

Excitation of knotted vortex lines in matter waves

We study the creation of knotted ultracold matter waves in Bose–Einstein condensates via coherent two-photon Raman transitions with a Λ level configuration. The Raman transition allows an indirect transfer of atoms from the internal state $| a\rangle$ to the target state $| b\rangle$ via an excited state $| e\rangle$, that would be otherwise dipole-forbidden. This setup enables us to imprint three-dimensional knotted vortex lines embedded in the probe field to the density in the target state. We elaborate on experimental feasibility as well as on subsequent dynamics of the matter wave

Consideration of the listener in the assessment and treatment of dysarthria

Traditionally, speech production deficits have been the focus of clinical practice and research in dysarthria. However, recent research has begun to examine the role of the listener in communication interaction. This article provides an overview of perceptual processing theory relevant to dysarthria. In addition, it discusses the relationship of current theoretical models of speech perception to the assessment and treatment of dysarthria. Finally, it provides insight into how this information may inform current clinical practices and future research in the field

Abdominal Aortic Aneurysm Genetic Associations: Mostly False? A Systematic Review and Meta-analysis

Objective/BackgroundMany associations between abdominal aortic aneurysm (AAA) and genetic polymorphisms have been reported. It is unclear which are genuine and which may be caused by type 1 errors, biases, and flexible study design. The objectives of the study were to identify associations supported by current evidence and to investigate the effect of study design on reporting associations.MethodsData sources were MEDLINE, Embase, and Web of Science. Reports were dual-reviewed for relevance and inclusion against predefined criteria (studies of genetic polymorphisms and AAA risk). Study characteristics and data were extracted using an agreed tool and reports assessed for quality. Heterogeneity was assessed using I2 and fixed- and random-effects meta-analyses were conducted for variants that were reported at least twice, if any had reported an association. Strength of evidence was assessed using a standard guideline.ResultsSearches identified 467 unique articles, of which 97 were included. Of 97 studies, 63 reported at least one association. Of 92 studies that conducted multiple tests, only 27% corrected their analyses. In total, 263 genes were investigated, and associations were reported in polymorphisms in 87 genes. Associations in CDKN2BAS, SORT1, LRP1, IL6R, MMP3, AGTR1, ACE, and APOA1 were supported by meta-analyses.ConclusionUncorrected multiple testing and flexible study design (particularly testing many inheritance models and subgroups, and failure to check for Hardy–Weinberg equilibrium) contributed to apparently false associations being reported. Heterogeneity, possibly due to the case mix, geographical, temporal, and environmental variation between different studies, was evident. Polymorphisms in nine genes had strong or moderate support on the basis of the literature at this time. Suggestions are made for improving AAA genetics study design and conduct

Finite element model to simulate impact on a soft tissue simulant

A finite element model of an impact test on a soft tissue simulant, used as part of a shoulder surrogate, was developed in Ansys© LS-DYNA®. The surrogate consisted of a metal hemicylindrical core, with a diameter of 75 mm, covered with a 15 mm thick relaxed muscle simulant. The muscle simulant consisted of a 14 mm thick layer of silicone covered with 1 mm thick chamois leather to represent skin. The material properties of the silicone were obtained via quasi-static compression testing (curve fit with hyperelastic models) and compressive stress relaxation testing (curve fit with a Prony series). Outputs of the finite element models were compared against experimental data from impact tests on the shoulder surrogate at energies of 4.9, 9.8 and 14.7 J. The accuracy of the finite element models was assessed using four parameters: peak impact force, maximum deformation, impact duration and impulse. A 5-parameter Mooney-Rivlin material model combined with a 2-term Prony series was found to be suitable for modelling the soft tissue simulant of the shoulder surrogate. This model had under 10% overall mean deviation from the experimental values for the four assessment parameters across the three impact energies. Overall, the model provided a repeatable test method that can be adapted to help predict injuries to skin tissue and the performance/efficacy of personal protective equipment

A review on windcatcher for passive cooling and natural ventilation in buildings, Part 1: Indoor air quality and thermal comfort assessment

The most prominent challenge in 21th century is global warming which seriously threats the mankind. Building sector with 40% of global energy consumption and GHG emission play a key role in this threat. In this regard, the impact of cooling systems cannot be ignored where along with ventilation and heating systems totally account for 60% of energy consumed in buildings. Passive cooling systems can be a promising alternative to reduce energy consumption. One of the oldest passive cooling system that is still being used today is windcatcher. By manipulating pressure differences and the buoyancy effect, an adequate level of ventilation in buildings can be provided by windcatchers. Since most of the previous windcatcher studies assessed the design characteristics, the current investigation focused on the indoor air quality (IAQ) and thermal comfort aspects. The review details and compares the different theoretical and experimental methods employed by researchers in different case studies to assess the IAQ and thermal comfort. It was found that most IAQ studies were conducted in the UK using CFD and experimental techniques. Previous studies assessed IAQ based on several parameters such as air flow rate, air change rate, CO2 concentration, air change effectiveness and mean age of air. The findings of the studies revealed that satisfactory IAQ were generally achieved using the windcatcher. On the other hand, thermal comfort studies of windcatchers were mainly conducted in hot climates such as in the Middle East. In addition to night ventilation, the review also looked into the different types of cooling methods incorporated with windcatchers such as evaporative cooling, earth to air heat exchangers (EAHE) and heat transfer devices (HTD). Night ventilation was found to be effective in temperate and cold conditions while additional cooling using evaporative cooling, EAHE and HTD were found to be necessary in hot climates