Perceived Noise Analysis for Offset Jets Applied to Commercial Supersonic Aircraft

A systems analysis was performed with experimental jet noise data, engine/aircraft performance codes and aircraft noise prediction codes to assess takeoff noise levels and mission range for conceptual supersonic commercial aircraft. A parametric study was done to identify viable engine cycles that meet NASA's N+2 goals for noise and performance. Model scale data from offset jets were used as input to the aircraft noise prediction code to determine the expected sound levels for the lateral certification point where jet noise dominates over all other noise sources. The noise predictions were used to determine the optimal orientation of the offset nozzles to minimize the noise at the lateral microphone location. An alternative takeoff procedure called "programmed lapse rate" was evaluated for noise reduction benefits. Results show there are two types of engines that provide acceptable mission range performance; one is a conventional mixed-flow turbofan and the other is a three-stream variable-cycle engine. Separate flow offset nozzles reduce the noise directed toward the thicker side of the outer flow stream, but have less benefit as the core nozzle pressure ratio is reduced. At the systems level for a three-engine N+2 aircraft with full throttle takeoff, there is a 1.4 EPNdB margin to Chapter 3 noise regulations predicted for the lateral certification point (assuming jet noise dominates). With a 10% reduction in thrust just after clearing the runway, the margin increases to 5.5 EPNdB. Margins to Chapter 4 and Chapter 14 levels will depend on the cumulative split between the three certification points, but it appears that low specific thrust engines with a 10% reduction in thrust (programmed lapse rate) can come close to meeting Chapter 14 noise levels. Further noise reduction is possible with engine oversizing and derated takeoff, but more detailed mission studies are needed to investigate the range impacts as well as the practical limits for safety and takeoff regulations

Merger of binary neutron stars of unequal mass in full general relativity

We present results of three dimensional numerical simulations of the merger of unequal-mass binary neutron stars in full general relativity. A $\Gamma$-law equation of state $P=(\Gamma-1)\rho\epsilon$ is adopted, where $P$, $\rho$, \varep, and $\Gamma$ are the pressure, rest mass density, specific internal energy, and the adiabatic constant, respectively. We take $\Gamma=2$ and the baryon rest-mass ratio $Q_M$ to be in the range 0.85--1. The typical grid size is $(633,633,317)$ for $(x,y,z)$ . We improve several implementations since the latest work. In the present code, the radiation reaction of gravitational waves is taken into account with a good accuracy. This fact enables us to follow the coalescence all the way from the late inspiral phase through the merger phase for which the transition is triggered by the radiation reaction. It is found that if the total rest-mass of the system is more than $\sim 1.7$ times of the maximum allowed rest-mass of spherical neutron stars, a black hole is formed after the merger irrespective of the mass ratios. The gravitational waveforms and outcomes in the merger of unequal-mass binaries are compared with those in equal-mass binaries. It is found that the disk mass around the so formed black holes increases with decreasing rest-mass ratios and decreases with increasing compactness of neutron stars. The merger process and the gravitational waveforms also depend strongly on the rest-mass ratios even for the range $Q_M= 0.85$--1.Comment: 32 pages, PRD68 to be publishe

Three-dimensional general relativistic hydrodynamics II: long-term dynamics of single relativistic stars

This is the second in a series of papers on the construction and validation of a three-dimensional code for the solution of the coupled system of the Einstein equations and of the general relativistic hydrodynamic equations, and on the application of this code to problems in general relativistic astrophysics. In particular, we report on the accuracy of our code in the long-term dynamical evolution of relativistic stars and on some new physics results obtained in the process of code testing. The tests involve single non-rotating stars in stable equilibrium, non-rotating stars undergoing radial and quadrupolar oscillations, non-rotating stars on the unstable branch of the equilibrium configurations migrating to the stable branch, non-rotating stars undergoing gravitational collapse to a black hole, and rapidly rotating stars in stable equilibrium and undergoing quasi-radial oscillations. The numerical evolutions have been carried out in full general relativity using different types of polytropic equations of state using either the rest-mass density only, or the rest-mass density and the internal energy as independent variables. New variants of the spacetime evolution and new high resolution shock capturing (HRSC) treatments based on Riemann solvers and slope limiters have been implemented and the results compared with those obtained from previous methods. Finally, we have obtained the first eigenfrequencies of rotating stars in full general relativity and rapid rotation. A long standing problem, such frequencies have not been obtained by other methods. Overall, and to the best of our knowledge, the results presented in this paper represent the most accurate long-term three-dimensional evolutions of relativistic stars available to date.Comment: 19 pages, 17 figure

C^2/Z_n Fractional branes and Monodromy

We construct geometric representatives for the C^2/Z_n fractional branes in terms of branes wrapping certain exceptional cycles of the resolution. In the process we use large radius and conifold-type monodromies, and also check some of the orbifold quantum symmetries. We find the explicit Seiberg-duality which connects our fractional branes to the ones given by the McKay correspondence. We also comment on the Harvey-Moore BPS algebras.Comment: 34 pages, v1 identical to v2, v3: typos fixed, discussion of Harvey-Moore BPS algebras update

Computing gravitational waves from slightly nonspherical stellar collapse to black hole: Odd-parity perturbation

Nonspherical stellar collapse to a black hole is one of the most promising gravitational wave sources for gravitational wave detectors. We numerically study gravitational waves from a slightly nonspherical stellar collapse to a black hole in linearized Einstein theory. We adopt a spherically collapsing star as the zeroth-order solution and gravitational waves are computed using perturbation theory on the spherical background. In this paper we focus on the perturbation of odd-parity modes. Using the polytropic equations of state with polytropic indices $n_p=1$ and 3, we qualitatively study gravitational waves emitted during the collapse of neutron stars and supermassive stars to black holes from a marginally stable equilibrium configuration. Since the matter perturbation profiles can be chosen arbitrarily, we provide a few types for them. For $n_p=1$, the gravitational waveforms are mainly characterized by a black hole quasinormal mode ringing, irrespective of perturbation profiles given initially. However, for $n_p=3$, the waveforms depend strongly on the initial perturbation profiles. In other words, the gravitational waveforms strongly depend on the stellar configuration and, in turn, on the ad hoc choice of the functional form of the perturbation in the case of supermassive stars.Comment: 31 pages, accepted for publication in Phys. Rev. D, typos and minor errors correcte

Preserved white matter microstructure in young patients with anorexia nervosa?

A massive but reversible reduction of cortical thickness and subcortical gray matter (GM) volumes in Anorexia Nervosa (AN) has been recently reported. However, the literature on alterations in white matter (WM) volume and microstructure changes in both acutely underweight AN (acAN) and after recovery (recAN) is sparse and results are inconclusive. Here, T1-weighted and diffusion-weighted MRI data in a sizable sample of young and medication-free acAN (n = 35), recAN (n = 32), and age-matched female healthy controls (HC, n = 62) were obtained. For analysis, a well-validated global probabilistic tractography reconstruction algorithm including rigorous motion correction implemented in FreeSurfer: TRACULA (TRActs Constrained by UnderLying Anatomy) were used. Additionally, a clustering algorithm and a multivariate pattern classification technique to WM metrics to predict group membership were applied. No group differences in either WM volume or WM microstructure were detected with standard analysis procedures either in acAN or recAN relative to HC after controlling for the number of performed statistical tests. These findings were not affected by age, IQ, or psychiatric symptoms. While cluster analysis was unsuccessful at discriminating between groups, multivariate pattern classification showed some ability to separate acAN from HC (but not recAN from HC). However, these results were not compatible with a straightforward hypothesis of impaired WM microstructure. The current findings suggest that WM integrity is largely preserved in non-chronic AN. This finding stands in contrast to findings in GM, but may help to explain the relatively intact cognitive performance of young patients with AN and provide the basis for the fast recovery of GM structures. Hum Brain Mapp 37:4069–4083, 2016. © 2016 Wiley Periodicals, Inc

Towards a Stable Numerical Evolution of Strongly Gravitating Systems in General Relativity: The Conformal Treatments

We study the stability of three-dimensional numerical evolutions of the Einstein equations, comparing the standard ADM formulation to variations on a family of formulations that separate out the conformal and traceless parts of the system. We develop an implementation of the conformal-traceless (CT) approach that has improved stability properties in evolving weak and strong gravitational fields, and for both vacuum and spacetimes with active coupling to matter sources. Cases studied include weak and strong gravitational wave packets, black holes, boson stars and neutron stars. We show under what conditions the CT approach gives better results in 3D numerical evolutions compared to the ADM formulation. In particular, we show that our implementation of the CT approach gives more long term stable evolutions than ADM in all the cases studied, but is less accurate in the short term for the range of resolutions used in our 3D simulations.Comment: 17 pages, 15 figures. Small changes in the text, and a change in the list of authors. One new reference adde

Relativistic Hydrodynamic Evolutions with Black Hole Excision

We present a numerical code designed to study astrophysical phenomena involving dynamical spacetimes containing black holes in the presence of relativistic hydrodynamic matter. We present evolutions of the collapse of a fluid star from the onset of collapse to the settling of the resulting black hole to a final stationary state. In order to evolve stably after the black hole forms, we excise a region inside the hole before a singularity is encountered. This excision region is introduced after the appearance of an apparent horizon, but while a significant amount of matter remains outside the hole. We test our code by evolving accurately a vacuum Schwarzschild black hole, a relativistic Bondi accretion flow onto a black hole, Oppenheimer-Snyder dust collapse, and the collapse of nonrotating and rotating stars. These systems are tracked reliably for hundreds of M following excision, where M is the mass of the black hole. We perform these tests both in axisymmetry and in full 3+1 dimensions. We then apply our code to study the effect of the stellar spin parameter J/M^2 on the final outcome of gravitational collapse of rapidly rotating n = 1 polytropes. We find that a black hole forms only if J/M^2<1, in agreement with previous simulations. When J/M^2>1, the collapsing star forms a torus which fragments into nonaxisymmetric clumps, capable of generating appreciable ``splash'' gravitational radiation.Comment: 17 pages, 14 figures, submitted to PR

Hypercyclic algebras for convolution and composition operators

[EN] We provide an alternative proof to those by Shkarin and by Bayart and Matheron that the operator D of complex differentiation supports a hypercyclic algebra on the space of entire functions. In particular we obtain hypercyclic algebras for many convolution operators not induced by polynomials, such as , , or , where . In contrast, weighted composition operators on function algebras of analytic functions on a plane domain fail to support supercyclic algebras.This work is supported in part by MEC, Project MTM 2016-7963-P. We also thank Angeles Prieto for comments and suggestions.Bès, J.; Conejero, JA.; Papathanasiou, D. (2018). Hypercyclic algebras for convolution and composition operators. Journal of Functional Analysis. 274(10):2884-2905. https://doi.org/10.1016/j.jfa.2018.02.003S288429052741

Linear Sigma Models for Open Strings

We formulate and study a class of massive N=2 supersymmetric gauge field theories coupled to boundary degrees of freedom on the strip. For some values of the parameters, the infrared limits of these theories can be interpreted as open string sigma models describing D-branes in large-radius Calabi-Yau compactifications. For other values of the parameters, these theories flow to CFTs describing branes in more exotic, non-geometric phases of the Calabi-Yau moduli space such as the Landau-Ginzburg orbifold phase. Some simple properties of the branes (like large radius monodromies and spectra of worldvolume excitations) can be computed in our model. We also provide simple worldsheet models of the transitions which occur at loci of marginal stability, and of Higgs-Coulomb transitions.Comment: 51 pages, 2 figures; very minor corrections, refs adde