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At least 235 records · Page 13

Ladder symmetries and Love numbers of Reissner-Nordström black holes

It is well known that asymptotically flat black holes in general relativity have vanishing tidal Love numbers. In the case of Schwarzschild and Kerr black holes, this property has been shown to be a consequence of a hidden structure of ladder symmetries for the perturbations. In this work, we extend the ladder symmetries to non-rotating charged black holes in general relativity. As opposed to previous works in this context, we adopt a more general definition of Love numbers, including quadratic operators that mix gravitational and electromagnetic perturbations in the point-particle effective field theory. We show that the calculation of a subset of those couplings in full general relativity is affected by an ambiguity in the split between source and response, which we resolve through an analytic continuation. As a result, we derive a novel master equation that unifies scalar, electromagnetic and gravitational perturbations around Reissner-Nordström black holes. The equation is hypergeometric and can be obtained from previous formulations via nontrivial field redefinitions, which allow to systematically remove some of the singularities and make the presence of the ladder symmetries more manifest.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Solving gyrokinetic systems with higher-order time dependence

We discuss theoretical and numerical aspects of gyrokinetics as a Lagrangian field theory when the field perturbation is introduced into the symplectic part. A consequence is that the field equations and particle equations of motion in general depend on the time derivatives of the field. The most well-known example is when the parallel vector potential is introduced as a perturbation, where a time derivative of the field arises only in the equations of motion, so an explicit equation for the fields may still be written. We will consider the conceptually more problematic case where the time-dependent fields appear in both the field equations and equations of motion, but where the additional term in the field equations is formally small. The conceptual issues were described by Burby (J. Plasma Phys., vol. 82 (3), 2016, 905820304): these terms lead to apparent additional degrees of freedom to the problem, so that the electric field now requires an initial condition, which is not required in low-frequency (Darwin) Vlasov–Maxwell equations. Also, the small terms in the Euler–Lagrange equations are a singular perturbation, and these two issues are interlinked. For well-behaved problems the apparent additional degrees of freedom are spurious, and the physically relevant solution may be directly identified. Because we needed to assume that the system is well behaved for small perturbations when deriving gyrokinetic theory, we must continue to assume that when solving it, and the physical solutions are thus the regular ones. The spurious nature of the singular degrees of freedom may also be seen by changing coordinate systems so the varying field appears only in the Hamiltonian. We then describe how methods appropriate for singular perturbation theory may be used to solve these asymptotic equations numerically. We then describe a proof-of-principle implementation of these methods for an electrostatic strong-flow gyrokinetic system; two basic test cases are presented to illustrate code functionality.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Optical and Plasmonic Properties of High-Electron-Density Epitaxial and Oxidative Controlled Titanium Nitride Thin Films

The present paper reports on the fabrication, detailed structural characterizations, and theoretical modeling of titanium nitride (TiN) and its isostructural oxide derivative, titanium oxynitride (TiNO) thin films that have excellent plasmonic properties and that also have the potential to overcome the limitation of noble metal and refractory metals. The TiNO films deposited at 700 °C in high vacuum conditions have the highest reflectance (R = ~ 95%), largest negative dielectric constant (ε 1 = –161), and maximal plasmonic figure of merit (FoM = –ε 1 /ε 2 ) of 1.2, followed by the 600 °C samples deposited in a vacuum (R = ~ 85%, ε 1 = –145, FoM = 0.8) and 700 °C–5 mTorr sample (R = ~ 82%, ε 1 = –8, FoM = 0.3). To corroborate our experimental observations, we calculated the phonon dispersions and Raman active modes of TiNO by using the virtual crystal approximation. From the experimental and theoretical studies, a multilayer optical model has been proposed for the TiN/TiNO epitaxial thin films for obtaining individual complex dielectric functions from which many other optical parameters can be calculated. The advantages of oxide derivatives of TiN are the continuation of similar free electron density as in TiN and the acquisition of additional features such as oxygen-dependent semiconductivity with a tunable bandgap.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Improving small-scale CMB lensing reconstruction

Over the past decade, the gravitational lensing of the Cosmic Microwave Background (CMB) has become a powerful tool for probing the matter distribution in the Universe. The standard technique used to reconstruct the CMB lensing signal employs the quadratic estimator (QE) method, which has recently been shown to be suboptimal for lensing measurements on very small scales in temperature and polarization data. We implement a simple, more optimal method for the small-scale regime, which involves taking the direct inverse of the background gradient. We derive new techniques to make continuous maps of lensing using this "Gradient-Inversion" (GI) method and validate our method with simulated data, finding good agreement with predictions. For idealized simulations of lensing cross- and autospectra that neglect foregrounds, we demonstrate that our method performs significantly better than previous quadratic estimator methods in temperature; at $L=5000-9000$, it reduces errors on the lensing auto-power spectrum by a factor of $\sim 4$ for both idealized CMB-S4 and Simons Observatory-like experiments and by a factor of $\sim 2.6$ for cross-correlations of CMB-S4-like lensing reconstruction and the true lensing field. Finally, we caution that the level of the neglected small-scale foreground power, while low in polarization, is very high in temperature; though we briefly outline foreground mitigation methods, further work on this topic is required. Nevertheless, our results show the future potential for improved small-scale CMB lensing measurements, which could provide stronger constraints on cosmological parameters and astrophysics at high redshifts.

79 ASTRONOMY AND ASTROPHYSICS↗

Interplay Between Time and Energy in Bosonic Noisy Quantum Metrology

Quantum entanglement and coherence often allow for protocols that outperform classical ones in estimating a system’s parameter. When using infinite-dimensional probes (such as a bosonic mode), one could, in principle, obtain infinite precision in a finite time for both classical and quantum protocols, which makes it hard to quantify potential quantum advantage. However, such a situation is unphysical, as it would require infinite resources, so one needs to impose some additional constraint: typically the average energy employed by the probe is finite. Here we treat both energy and time as a resource, showing that, in the presence of noise, there is a nontrivial interplay between the average energy and the time devoted to the estimation. Our results are valid for the most general metrological schemes (e.g., adaptive schemes, which may involve entanglement with external ancillae or any kind of continuous measurement). We apply recently derived precision bounds for all parameters characterizing the paradigmatic case of a bosonic mode, subject to Lindbladian noise. We show how the time employed in the estimation should be partitioned in order to achieve the best possible precision. In most cases, the optimal performance may be obtained without the necessity of adaptivity or entanglement with ancilla. We compare results with classical strategies. Interestingly, for temperature estimation, applying a fast-prepare-and-measure protocol with Fock states provides better scaling with the number of photons than any classical strategy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Error Estimates of Residual Minimization Using Neural Networks for Linear PDES

We propose an abstract framework for analyzing the convergence of least-squares methods based on residual minimization when feasible solutions are neural networks. With the norm relations and compactness arguments, we derive error estimates for both continuous and discrete formulations of residual minimization in strong and weak forms. The formulations cover recently developed physicsinformed neural networks based on strong and variational formulations.

97 MATHEMATICS AND COMPUTING↗

Characterizing the Turbulent Structure of the Convective Boundary Layer Using ARM/ASR Observations and LES Model Output

This project used high-resolution observations and output from large-eddy simulation models to characterize turbulent motions within the planetary boundary layer. As part of this research, we (a) continued development of techniques to derive profiles of temperature and humidity from ground-based instruments, (b) characterized the higher order moments of water vapor at a tropical location, (c) evaluated the time-of-day dependent turbulent mixing within the boundary layer, (d) developed an improved method to derive turbulent quantities at the top of the boundary layer from profiles of temperature, humidity, and wind, (e) organized and conducted a large field campaign to study the interactions between the land surface and atmosphere, and (f) developed improved ways to determine the depth of the boundary layer.

54 ENVIRONMENTAL SCIENCES↗

Comparison of Artificial Compressibility Methods for Coupled Laminar Fluid Flow and Heat Transfer

Artificial compressibility (AC) methods for incompressible flows perturb the mass continuity equation by the time derivative of the pressure field to achieve direct coupling between pressure and velocity without the need for a projection method. Several variations of the original AC method have been proposed (e.g., the entropically damped artificial compressibility [EDAC] method) that can, in some scenarios, improve on the original model. In this paper, we methodically compare the results of the original AC model and the EDAC model for both steady-state and transient problems with coupling between the momentum and energy equations. We demonstrate that the EDAC model and the AC model yield similar numerical results, and the EDAC model is 10%-20% faster than the AC model for a given problem.

Oz, Furkan [ORNL] (ORCID:0000000265831724)↗

Observations of zeta Puppis.

The visual line spectrum of zeta Puppis (O4f) cannot be matched by theoretical line profiles computed by Auer and Mihalas (1971) from their non-LTE models. The discrepancy between observation and prediction suggests that deviations from plane-parallel geometry and hydrostatic equilibrium must be accounted for in order for models to represent the atmospheric regions forming the observed lines. Relaxation of these classical assumptions may affect the value of effective temperature for this star derived from observations of its continuous spectrum.

Heap, S. R.↗

Topologies for neutral functional differential equations.

Bounded topologies are considered for functional differential equations of the neutral type in which present dynamics of the system are influenced by its past behavior. A special bounded topology is generated on a collection of absolutely continuous functions with essentially bounded derivatives, and an application to a class of nonlinear neutral functional differential equations due to Driver (1965) is presented.

Melvin, W. R.↗

Optimum shell design.

Comparison of two methods, namely Nedler and Mead's (1965) simplex method and Davidon's (1959) variable metric method, for achieving optimum design in terms of minimum weight for rotational shells under certain constraints. The superiority of one of the methods over the other is shown to depend, among other things, upon the form of the function to be minimized, and whether or not it is continuous everywhere in values and derivatives.

Salama, A. M.↗

Low thrust space vehicle trajectory optimization using regularized variables

Optimizing the trajectory of a low thrust space vehicle usually means solving a nonlinear two point boundary value problem. In general, accuracy requirements necessitate extensive computation times. In celestial mechanics, regularizing transformations of the equations of motion are used to eliminate computational and analytical problems that occur during close approaches to gravitational force centers. It was shown in previous investigations that regularization in the formulation of the trajectory optimization problem may reduce the computation time. In this study, a set of regularized equations describing the optimal trajectory of a continuously thrusting space vehicle is derived. The computational characteristics of the set are investigated and compared to the classical Newtonian unregularized set of equations. The comparison is made for low thrust, minimum time, escape trajectories and numerical calculations of Keplerian orbits. The comparison indicates that in the cases investigated for bad initial guesses of the known boundary values a remarkable reduction in the computation time was achieved. Furthermore, the investigated set of regularized equations shows high numerical stability even for long duration flights and is less sensitive to errors in the guesses of the unknown boundary values.

Schwenzfeger, K. J.↗

Effects of variables upon pyrotechnically induced shock response spectra, part 2

Throughout the aerospace industry, large variations of 50 percent (6 dB) or more in shock response spectra (SRS) derived from pyrotechnic separation events continue to be reported from actual spaceflight data and from laboratory tests. As a result of these variations, NASA funded a research program for 1984 through 1986. The purpose of the 1984 through 1986 project was to analyze variations in pyrotechnically induced SRS and to determine if and to what degree manufacturing and assembly variables and tolerances, distance from the shock source, data acquisition instrumentation, and shock energy propagation affect the SRS. Sixty-four free-free boundary plate tests were performed. NASA funded an additional study for 1987 through 1988. This paper is a summary of the additional study. The purpose was to evaluate shock dissipation through various spacecraft structural joint types, to evaluate shock variation for various manufacturing and assembly variables on clamped boundary test plates, and to verify data correction techniques. Five clamped boundary plate tests investigated manufacturing and assembly variables and mass loading effects. Six free-free boundary plate tests investigated shock dissipation across spacecraft joint structures.

Smith, James Lee↗

Unsteady solution of incompressible Navier-Stokes equations

The numerical scheme used by the present time-accurate FEM numerical method for incompressible Navier-Stokes equations, using primitive variables as the unknowns, is a Crank-Nicholson implicit treatment of all equation terms with central differencing for space derivatives. The introduction of a continuous auxilliary system in pseudo-time, with artificial compressibility, yields the incompressible solution at the advanced time level; time-accurate solutions are thereby obtained for two-dimensional fluid flows in a square cavity, in the cases of both an impulsively starting lid and an oscillating lid.

Soh, W. Y.↗

A theoretical framework for convergence and continuous dependence of estimates in inverse problems for distributed parameter systems

Numerical techniques for parameter identification in distributed-parameter systems are developed analytically. A general convergence and stability framework (for continuous dependence on observations) is derived for first-order systems on the basis of (1) a weak formulation in terms of sesquilinear forms and (2) the resolvent convergence form of the Trotter-Kato approximation. The extension of this framework to second-order systems is considered.

Banks, H. T.↗

Spanwise measurements of vertical components of atmospheric turbulence

Correlation and spectrum magnitude estimates are computed for vertical gust velocity measurements at the nose and wing tips of a NASA B-57B aircraft for six level flight, low speed and low altitude runs and are compared with those of the von Karman atmospheric turbulence model extended for spanwise relationships. The distance between the wing tips was 62.6 ft. Airspeeds ranged from about 330 to 400 ft/sec, heights above the ground ranged from near ground level to about 5250 ft. and gust velocity standard deviations ranged from 4.10 to 8.86 ft/sec. Integral scale lengths, determined by matching measured autocorrelation estimates with those of the model, ranged from 410 to 2050 ft. Digital signals derived from piezoelectric sensors provided continuous pressure and airspeed measurements. Some directional acceleration sensitivity of the sensors was eliminated by sensor orientation, and their performance was spectrally verified for the higher frequencies with supplemental onboard piezoresistive sensors. The model appeared to satisfactorily predict the trends of the measured cross-correlations and cross-spectrum magnitudes, particularly between the nose and wing tips. However, the measured magnitude estimates of the cross-spectra between the wing tips exceeded the predicted levels at the higher frequencies. Causes for the additional power across the wing tips were investigated. Vertical gust velocity components evaluated along and lateral to the flight path implied that the frozen-turbulence-field assumption is a suitable approximation.

Sleeper, Robert K.↗

Multiple symbol partially coherent detection of MPSK

It is shown that by using the known (or estimated) value of carrier tracking loop signal to noise ratio (SNR) in the decision metric, it is possible to improve the error probability performance of a partially coherent multiple phase-shift-keying (MPSK) system relative to that corresponding to the commonly used ideal coherent decision rule. Using a maximum-likeihood approach, an optimum decision metric is derived and shown to take the form of a weighted sum of the ideal coherent decision metric (i.e., correlation) and the noncoherent decision metric which is optimum for differential detection of MPSK. The performance of a receiver based on this optimum decision rule is derived and shown to provide continued improvement with increasing length of observation interval (data symbol sequence length). Unfortunately, increasing the observation length does not eliminate the error floor associated with the finite loop SNR. Nevertheless, in the limit of infinite observation length, the average error probability performance approaches the algebraic sum of the error floor and the performance of ideal coherent detection, i.e., at any error probability above the error floor, there is no degradation due to the partial coherence. It is shown that this limiting behavior is virtually achievable with practical size observation lengths. Furthermore, the performance is quite insensitive to mismatch between the estimate of loop SNR (e.g., obtained from measurement) fed to the decision metric and its true value. These results may be of use in low-cost Earth-orbiting or deep-space missions employing coded modulations.

Simon, M. K.↗

Micromechanical analysis of thermo-inelastic multiphase short-fiber composites

A micromechanical formulation is presented for the prediction of the overall thermo-inelastic behavior of multiphase composites which consist of short fibers. The analysis is an extension of the generalized method of cells that was previously derived for inelastic composites with continuous fibers, and the reliability of which was critically examined in several situations. The resulting three dimensional formulation is extremely general, wherein the analysis of thermo-inelastic composites with continuous fibers as well as particulate and porous inelastic materials are merely special cases.

Aboudi, Jacob↗