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

Estimation of the Pitzer Parameters for 1–1, 2–1, 3–1, 4–1, and 2–2 Single Electrolytes at 25 °C

The Pitzer model is one of the most important thermodynamic models to predict the behavior of aqueous electrolyte solutions, especially at high ionic strengths. However, most of the parameters in the Pitzer equations have to be obtained experimentally and this represents an important drawback to this model. Therefore, in order to make the Pitzer equations less dependent on experimental data and more dependent on the properties of the solution, new equations that correlate the Pitzer equations with the properties of the solution have been successfully developed for 1-1, 2-1, 3-1, 4-1 and 2-2 electrolytes. In particular, these equations were developed for two cases: (i) considers the original Pitzer equations and (ii) considers some simplifications to the Pitzer equation (assuming CMX , BMX (2) and 2 = 0). In particular, for case (ii), the second virial coefficients BMX (0) and BMX (1) of the Pitzer equations were re-estimated using published experimental data of the osmotic coefficient obtained from the literature. As a conclusion, both the simplified and the original Pitzer equations presented a very good match with this published experimental data for the osmotic coefficients. Additionally, the second virial coefficients BMX (0) and BMX (1) for both cases were successfully correlated with the ionic radius and the ionic charge, and this is confirmed by the very high coefficients of determination achieved (R2>0.96). However, these new equations are valid only to cases in which no significant ion association occurs, which is also the basic premise of the original Pitzer model

Towards a formalism for mapping the spacetimes of massive compact objects: Bumpy black holes and their orbits

Observations have established that extremely compact, massive objects are common in the universe. It is generally accepted that these objects are black holes. As observations improve, it becomes possible to test this hypothesis in ever greater detail. In particular, it is or will be possible to measure the properties of orbits deep in the strong field of a black hole candidate (using x-ray timing or with gravitational-waves) and to test whether they have the characteristics of black hole orbits in general relativity. Such measurements can be used to map the spacetime of a massive compact object, testing whether the object's multipoles satisfy the strict constraints of the black hole hypothesis. Such a test requires that we compare against objects with the ``wrong'' multipole structure. In this paper, we present tools for constructing bumpy black holes: objects that are almost black holes, but that have some multipoles with the wrong value. The spacetimes which we present are good deep into the strong field of the object -- we do not use a large r expansion, except to make contact with weak field intuition. Also, our spacetimes reduce to the black hole spacetimes of general relativity when the ``bumpiness'' is set to zero. We propose bumpy black holes as the foundation for a null experiment: if black hole candidates are the black holes of general relativity, their bumpiness should be zero. By comparing orbits in a bumpy spacetime with those of an astrophysical source, observations should be able to test this hypothesis, stringently testing whether they are the black holes of general relativity. (Abridged)Comment: 16 pages + 2 appendices + 3 figures. Submitted to PR

Temperature Dependence of the Parameters in the Pitzer Equations

The effects of temperature on the virial coefficients in the Pitzer equations are not known in general, and this is because the vast majority of experiments performed to investigate the properties of the aqueous electrolytes were conducted only at a temperature of 25 °C. Consequently, most of the parameters in the Pitzer equations that are available in the literature were estimated at this temperature. Therefore, finding a way to estimate the virial coefficients at different temperatures is highly important. To achieve this, new equations that correlate the virial coefficients with the temperature and the properties of the ions, i.e., ionic radius and ionic charge, are derived. As a result, these new derived equations were able to accurately predict the apparent relative molal enthalpies at 25 °C, as well as the activity and osmotic coefficients at temperatures up to 150 °C for electrolytes that are unlikely to form ion pairs. Moreover, comparison plots are presented to demonstrate the good agreement between the predictions of the correlating equations and the experimental data obtained from the literature

Estimation of the Thermochemical Radii and Ionic Volumes of Complex Ions

The estimation of the thermochemical radius is very important because most of the properties of the electrolyte solutions are, to some extent, linked to this property. Also, these thermochemical radii can be used to estimate lattice energies, which can be a very important parameter to be evaluated when assessing the possibility of synthesizing new inorganic materials. This study presents a formulation for estimating the thermochemical radii of complex ions. More specifically, these thermochemical radii are estimated using a weighted sum based on the radii of the contributing cations and anions. Also, the influence of the ionic charge on these thermochemical radii is assessed and discussed. Finally, the parameters obtained from the estimation of the thermochemical radii of complex cations are used to estimate cation volumes, and this estimation is then validated through comparison with literature values. As a result, the equations developed for thermochemical radii of complex ions produce predictions that are accurate to within 15% in general, whereas the equation developed to estimate cation volumes produces predictions that are accurate to within 20% considering cation volumes greater than 70 Å(3)

Predicting Speciation of Ammonia, Monoethanolamine, and Diethanolamine Using only Ionic Radius and Ionic Charge

This study investigates the speciation of CO 2 involving the most common solvents used to capture carbon from flue gas, i.e. ammonia, monoethanolamine (MEA), and diethanolamine (DEA). This requires the knowledge of both the activity coefficients of the species involved and the equilibrium constants of the relevant reactions. In contrast to the equilibrium constants, which can be obtained from the literature, the activity coefficients of the aqueous species are required to be estimated. Normally, semiempirical models are used to estimate these activity coefficients, i.e. equations that contain unknown parameters that are obtained through regression against experimental data. In contrast, in this study the activity coefficients are predicted using equations that require only the knowledge of the ionic radii and charges of the species involved in the equilibrium. As a conclusion, the model developed shows very good agreement with the experimental data obtained, either from spectroscopy or from vapor-liquid equilibrium (VLE), up to a solvent mass fraction of 20%

Sources of elevated heavy metal concentrations in sediments and benthic marine invertebrates of the western Antarctic Peninsula

Antarctica is one of the least anthropogenically-impacted areas of the world. Metal sources to the marine environment include localised activities of research stations and glacial meltwater containing metals of lithogenic origin. In this study, concentrations of nine metals (Cd, Co, Cr, Cu, Fe, Mn, Ni, Pb, Zn) were examined in three species of benthic invertebrates collected from four locations near Rothera Research Station on the western Antarctic Peninsula: Laternula elliptica (mudclam, filter feeder), Nacella concinna (limpet, grazer) and Odontaster validus (seastar, predator and scavenger). In addition, metals were evaluated in sediments at the same locations. Metal concentrations in different body tissues of invertebrates were equivalent to values recorded in industrialized non-polar sites and were attributed to natural sources including sediment input resulting from glacial erosion of local granodioritic rocks. Anthropogenic activities at Rothera Research Station appeared to have some impact on metal concentrations in the sampled invertebrates, with concentrations of several metals higher in L. elliptica near the runway and aircraft activities, but this was not a trend that was detected in the other species. Sediment analysis from two sites near the station showed lower metal concentrations than the control site 5 km distant and was attributed to differences in bedrock metal content. Differences in metal concentrations between organisms were attributed to feeding mechanisms and habitat, as well as depuration routes. L. elliptica kidneys showed significantly higher concentrations of eight metals, with some an order of magnitude greater than other organs, and the internal structure of O. validus had significantly higher Ni. This study supports previous assessments of N. concinna and L. elliptica as good biomonitors of metal concentrations and suggests O. validus as an additional biomonitor for use in future Antarctic metal monitoring programs

Haloperidol and Ziprasidone for Treatment of Delirium in Critical Illness

BACKGROUND: There are conflicting data on the effects of antipsychotic medications on delirium in patients in the intensive care unit (ICU). METHODS: In a randomized, double-blind, placebo-controlled trial, we assigned patients with acute respiratory failure or shock and hypoactive or hyperactive delirium to receive intravenous boluses of haloperidol (maximum dose, 20 mg daily), ziprasidone (maximum dose, 40 mg daily), or placebo. The volume and dose of a trial drug or placebo was halved or doubled at 12-hour intervals on the basis of the presence or absence of delirium, as detected with the use of the Confusion Assessment Method for the ICU, and of side effects of the intervention. The primary end point was the number of days alive without delirium or coma during the 14-day intervention period. Secondary end points included 30-day and 90-day survival, time to freedom from mechanical ventilation, and time to ICU and hospital discharge. Safety end points included extrapyramidal symptoms and excessive sedation. RESULTS: Written informed consent was obtained from 1183 patients or their authorized representatives. Delirium developed in 566 patients (48%), of whom 89% had hypoactive delirium and 11% had hyperactive delirium. Of the 566 patients, 184 were randomly assigned to receive placebo, 192 to receive haloperidol, and 190 to receive ziprasidone. The median duration of exposure to a trial drug or placebo was 4 days (interquartile range, 3 to 7). The median number of days alive without delirium or coma was 8.5 (95% confidence interval [CI], 5.6 to 9.9) in the placebo group, 7.9 (95% CI, 4.4 to 9.6) in the haloperidol group, and 8.7 (95% CI, 5.9 to 10.0) in the ziprasidone group (P=0.26 for overall effect across trial groups). The use of haloperidol or ziprasidone, as compared with placebo, had no significant effect on the primary end point (odds ratios, 0.88 [95% CI, 0.64 to 1.21] and 1.04 [95% CI, 0.73 to 1.48], respectively). There were no significant between-group differences with respect to the secondary end points or the frequency of extrapyramidal symptoms. CONCLUSIONS: The use of haloperidol or ziprasidone, as compared with placebo, in patients with acute respiratory failure or shock and hypoactive or hyperactive delirium in the ICU did not significantly alter the duration of delirium. (Funded by the National Institutes of Health and the VA Geriatric Research Education and Clinical Center; MIND-USA ClinicalTrials.gov number, NCT01211522 .)

Magnetic Field Stimulated Transitions of Excited States in Fast Muonic Helium Ions

It is shown that one can stimulate, by using the present-day laboratory magnetic fields, transitions between the $lm$ sub-levels of fast $\mu He^+$ ions formating in muon catalyzed fusion. Strong fields also cause the self-ionization from highly excited states of such muonic ions. Both effects are the consequence of the interaction of the bound muon with the oscillating field of the Stark term coupling the center-of-mass and muon motions of the $\mu He^+$ ion due to the non-separability of the collective and internal variables in this system. The performed calculations show a possibility to drive the population of the $lm$ sub-levels by applying a field of a few $Tesla$, which affects the reactivation rate and is especially important to the $K\alpha$ $x$-ray production in muon catalyzed fusion. It is also shown that the $2s-2p$ splitting in $\mu He^+$ due to the vacuum polarization slightly decreases the stimulated transition rates.Comment: 5 figure