Alternatives to standard puncture initial data for binary black hole evolution

Standard puncture initial data have been widely used for numerical binary black hole evolutions despite their shortcomings, most notably the inherent lack of gravitational radiation at the initial time that is later followed by a burst of spurious radiation. We study the evolution of three alternative initial data schemes. Two of the three alternatives are based on post-Newtonian expansions that contain realistic gravitational waves. The first scheme is based on a second-order post-Newtonian expansion in Arnowitt, Deser, and Misner transverse-traceless (ADMTT) gauge that has been resummed to approach standard puncture data at the black holes. The second scheme is based on asymptotic matching of the 4-metrics of two tidally perturbed Schwarzschild solutions to a first-order post-Newtonian expansion in ADMTT gauge away from the black holes. The final alternative is obtained through asymptotic matching of the 4-metrics of two tidally perturbed Schwarzschild solutions to a second-order post-Newtonian expansion in harmonic gauge away from the black holes. When evolved, the second scheme fails to produce quasicircular orbits (and instead leads to a nearly head-on collision). This failure can be traced back to inaccuracies in the extrinsic curvature due to low order matching. More encouraging is that the latter two alternatives lead to quasicircular orbits and show gravitational radiation from the onset of the evolution, as well as a reduction of spurious radiation. Current deficiencies compared to standard punctures data include more eccentric trajectories during the inspiral and larger constraint violations, since the alternative data sets are only approximate solutions of Einstein's equations. The eccentricity problem can be ameliorated by adjusting the initial momentum parameters.Comment: 11 pages, 11 figures, 1 appendix, typos corrected, removed duplicate reference, matches published versio

Improved initial data for black hole binaries by asymptotic matching of post-Newtonian and perturbed black hole solutions

We construct approximate initial data for non-spinning black hole binary systems by asymptotically matching the 4-metrics of two tidally perturbed Schwarzschild solutions in isotropic coordinates to a resummed post-Newtonian 4-metric in ADMTT coordinates. The specific matching procedure used here closely follows the calculation in gr-qc/0503011, and is performed in the so called buffer zone where both the post-Newtonian and the perturbed Schwarzschild approximations hold. The result is that both metrics agree in the buffer zone, up to the errors in the approximations. However, since isotropic coordinates are very similar to ADMTT coordinates, matching yields better results than in the previous calculation, where harmonic coordinates were used for the post-Newtonian 4-metric. In particular, not only does matching improve in the buffer zone, but due to the similarity between ADMTT and isotropic coordinates the two metrics are also close to each other near the black hole horizons. With the help of a transition function we also obtain a global smooth 4-metric which has errors on the order of the error introduced by the more accurate of the two approximations we match. This global smoothed out 4-metric is obtained in ADMTT coordinates which are not horizon penetrating. In addition, we construct a further coordinate transformation that takes the 4-metric from global ADMTT coordinates to new coordinates which are similar to Kerr-Schild coordinates near each black hole, but which remain ADMTT further away from the black holes. These new coordinates are horizon penetrating and lead, for example, to a lapse which is everywhere positive on the t=0 slice. Such coordinates may be more useful in numerical simulations.Comment: 25 pages, 21 figures. Replaced with accepted versio

20th Workshop on Automotive Software Engineering (ASE’23)

Software-based systems play an increasingly important role and enable most innovations in modern cars. This workshop will address various topics related to automotive software development. The participants will discuss appropriate methods, techniques, and tools needed to address the most current challenges for researchers and practitioners

Binary black hole initial data from matched asymptotic expansions

We present an approximate metric for a binary black hole spacetime to construct initial data for numerical relativity. This metric is obtained by asymptotically matching a post-Newtonian metric for a binary system to a perturbed Schwarzschild metric for each hole. In the inner zone near each hole, the metric is given by the Schwarzschild solution plus a quadrupolar perturbation corresponding to an external tidal gravitational field. In the near zone, well outside each black hole but less than a reduced wavelength from the center of mass of the binary, the metric is given by a post-Newtonian expansion including the lowest-order deviations from flat spacetime. When the near zone overlaps each inner zone in a buffer zone, the post-Newtonian and perturbed Schwarzschild metrics can be asymptotically matched to each other. By demanding matching (over a 4-volume in the buffer zone) rather than patching (choosing a particular 2-surface in the buffer zone), we guarantee that the errors are small in all zones. The resulting piecewise metric is made formally $C^\infty$ with smooth transition functions so as to obtain the finite extrinsic curvature of a 3-slice. In addition to the metric and extrinsic curvature, we present explicit results for the lapse and the shift, which can be used as initial data for numerical simulations. This initial data is not accurate all the way to the asymptotically flat ends inside each hole, and therefore must be used with evolution codes which employ black hole excision rather than puncture methods. This paper lays the foundations of a method that can be sraightforwardly iterated to obtain initial data to higher perturbative order.Comment: 24 pages, 15 figures. Replaced with published version. Major editing of text, no major change to the physic

Quasi-equilibrium binary black hole sequences for puncture data derived from helical Killing vector conditions

We construct a sequence of binary black hole puncture data derived under the assumptions (i) that the ADM mass of each puncture as measured in the asymptotically flat space at the puncture stays constant along the sequence, and (ii) that the orbits along the sequence are quasi-circular in the sense that several necessary conditions for the existence of a helical Killing vector are satisfied. These conditions are equality of ADM and Komar mass at infinity and equality of the ADM and a rescaled Komar mass at each puncture. In this paper we explicitly give results for the case of an equal mass black hole binary without spin, but our approach can also be applied in the general case. We find that up to numerical accuracy the apparent horizon mass also remains constant along the sequence and that the prediction for the innermost stable circular orbit is similar to what has been found with the effective potential method.Comment: 6 pages, 3 figures, 1 tabl

Hands-On Russian Culture Lessons

The global diverse society necessitates that teachers develop cultural competency and use authentic resources for teaching. This article presents classroom-tested materials for teaching elementary students about aspects of Russian culture, developed by a native Russian and two education professors. Multiage, multi-racial American Midwestern students from a homeschooling cooperative learned vocabulary and concepts with statistically significant increases from pretest to posttest and a large effect size. The lessons began with recognition of human commonalities between Russian people and Americans, in accordance with omniculturalism theory. Lessons then highlighted and celebrated cultural differences through an exploration of Russian literature and culture. Culminating creative craft-making activities included simulating a Gzhel porcelain statue in white air-dry clay with blue markings, making a pop-up version of a matryoshka nesting doll set, constructing a papier-maché building with onion-domed towers and a Maslenitsa holiday scene, and decorating a paper-covered plastic egg with gems to make a Faberge-style jewelry box. The lessons, greeted with enthusiasm from students, included classification tasks, observation activities, and a Bingo-type game. Students evidenced deeper learning by continuing to connect their lives to Russian cultural content after the lesson unit had concluded

Developing a Predictive Metric to Assess School Viability

This article examines a wide range of parish school indicators that can be used to predict long-term viability

Biochemical markers and assessment of cardiotoxicity during preparative regimen and hematopoietic cell transplantation in acute leukemia

Introduction: Cardiotoxicity is a relatively frequent and potentially serious complication of antitumor treatment. Anthracyclines and other high-dose chemotherapy represent the greatest risk. The aim of the study was to assess cardiotoxicity during preparative regimen (PR) and hematopoietic cell transplantation (HCT) in acute leukemia (AL) with biochemical markers — “N-terminal pro brain natriuretic peptide” (NT-proBNP), cardiac troponin T (cTnT) and creatine kinase MB (CK-MB mass). Methods: Nineteen adult AL patients previously treated with anthracyclines — idarubicine, daunorubicine, mitoxantrone with standard doses for a cycle as 3 х 12 mg/m2, 3 х 50 mg/m2, 3 х 10 mg/m2 accordingly were studied. PR consisted of high-dose cyclophosphamide (HD-C) in combination with busulphan or total body irradiation (TBI). Plasma NT-proBNP, cTnT and CK-MB mass concentrations were measured the day before PR, the day after PR, the day after HCT and 14 days after HCT. Results: Before PR, mean plasma NT-proBNP value was 106.3 ± 55.7 ng/l. After PR, it increased to 426.1 ± 391.5 ng/l. After HCT, a further increase to 847.6 ± 780.6 ng/l was observed. Fourteen days after HCT, the mean NT-proBNP was 330.8±236.8 ng/l. The differences were statistically significant in comparison with the baseline values (p < 0.01). The NT-proBNP elevations were more pronounced in patients with cumulative doses (CD) of anthracyclines above 450 mg/m2 (p < 0.05), in patients with PR containing HD-C and TBI (p < 0.05). In all patients, plasma cTnT and CK-MB mass concentrations remained unchangable during PR and HCT. Conclusion: Our results suggest that administration of PR and HCT is in most AL patients associated with acute neurohumoral activation (significant rise in NT-proBNP). Persistent NT-proBNP elevations, in our study in 12 (63.2 %) patients, indicate subclinical cardiotoxicity (risk for development of heart failure) and require further follow-up. More pronounced NT-proBNP elevations in patients with higher CD of anthracyclines and in patients with PR containing combination of HD-C and TBI confirm that these therapeutic procedures seem to be more cardiotoxic and not very appropriate for patients with cumulation of risk factors for cardiotoxicity. Negative plasma cTnT and CK-MB mass concentrations show no detectable damage of cardiomyocyte structure during PR and HCT.Введение: кардиотоксические осложнения — это относительно частые и потенциально опасные последствия противоопухолевой терапии. Наибольшую кардиотоксичность отмечают при применении высоких доз химиопрепаратов, в частности антибиотиков антрациклинового ряда. Целью данного исследования была оценка кардиотоксичности при лекарственной подготовке пациентов с острым лейкозом (ОЛ) и проведении им трансплантации гематопоэтических стволовых клеток (ГСК), а также определение следующих биохимических маркеров – N-терминального промозгового натрийуретического пептида (NT-proBNP), сердечного тропонина T (cTnT) и креатинкиназы MB (CK-MB). Методы: обследованы 19 взрослых пациентов с ОЛ, прошедших предварительное лечение (ПЛ) с применением антрациклиновых антибиотиков (АА) – идарубицина, даунорубицина, митотриксантрона в дозах 3 х 12 мг/м2 , 3 х 50 мг/м2 , 3 х 10 мг/м2 соответственно. Кроме применения АА, ПЛ включало высокие дозы циклофосфамида (ВД-Ц) в сочетании с бусульфаном или радиолучевой терапией (РЛТ). Концентрацию NT-proBNP, cTnT и CK-MB определяли в плазме крови за день до и через день после проведения ПЛ, а также за день до и через 14 дней после трансплантации ГСК. Результаты: уровень NT-proBNP перед проведением ПЛ составил 106,3 ± 55,7 нг/л, а после повышался до 426,1 ± 391,5 нг/л. После трансплантации ГСК отмечали дальнейшее возрастание исследуемого показателя до 847,6 ± 780,6 нг/л. Через 14 дней после трансплантации ГСК концентрация NT-proBNP достигла 330,8 ± 236,8 нг/л, при этом разница была статистически достоверна по сравнению с исходными значениями (p < 0,01). Повышение уровня NT-proBNP в плазме крови более выражено у пациентов, получавших АА в суммарной дозе (СД) выше 450 мг/м2 (p < 0,05), а также у больных, получавших ВД-Ц и РЛТ (p < 0,05). Концентрация cTnT и CK-MB при проведении ПЛ и трансплантации ГСК не изменялась по отношению к исходному уровню. Выводы: показано, что применение ПЛ и трансплантация ГСК у большинства пациентов с ОЛ сопровождается острой нейрогуморальной активацией, что проявлялось в существенном повышении уровня NT-proBNP. Постоянно высокий уровень NTproBNP, отмеченный у 12 (63,2%) пациентов, свидетельствует о бессимптомной кардиотоксичности (риске развития сердечной недостаточности) и требует последующего врачебного наблюдения больных. Более выраженное повышение уровня NT-proBNP у пациентов с более высокой СД АА и у больных, получавших ВД-Ц и РЛТ, свидетельствует о том, что такое лечение является более кардиотоксичным и не рекомендовано для применения в случае наличия факторов риска проявления кардиотоксичности