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At least 1,297 records · Page 72

Multiple Solutions of Boundary-Value Problems for Hamiltonian Systems

We consider two-point boundary-value problems for a Hamiltonian system of the form x′ = f(k, y), y′ = g(x, 𝜆), where k and 𝜆 are parameters. The numbers of solutions, both positive and oscillatory, for the boundary-value problems are estimated. Our main tool is the analysis of the phase plane combined with the evaluation of time-map functions. The bifurcation diagram and solution curves are constructed for the Hamiltonian system. We also present examples illustrating the bifurcations with respect to the parameters k and 𝜆:.

97 MATHEMATICS AND COMPUTING↗

Neutrinos from type Ia supernovae: The deflagration-to-detonation transition scenario

It has long been recognized that the neutrinos detected from the next core-collapse supernova in the Galaxy have the potential to reveal important information about the dynamics of the explosion and the nucleosynthesis conditions as well as allowing us to probe the properties of the neutrino itself. The neutrinos emitted from thermonuclear—type Ia—supernovae also possess the same potential, although these supernovae are dimmer neutrino sources. For the first time, we calculate the time, energy, line of sight, and neutrino-flavor-dependent features of the neutrino signal expected from a three-dimensional delayed-detonation explosion simulation, where a deflagration-to-detonation transition triggers the complete disruption of a near-Chandrasekhar mass carbon-oxygen white dwarf. We also calculate the neutrino flavor evolution along eight lines of sight through the simulation as a function of time and energy using an exact three-flavor transformation code. We identify a characteristic spectral peak at ˜10 MeV as a signature of electron captures on copper. This peak is a potentially distinguishing feature of explosion models since it reflects the nucleosynthesis conditions early in the explosion. We simulate the event rates in the Super-K, Hyper-K, JUNO, and DUNE neutrino detectors with the SNOwGLoBES event rate calculation software and also compute the IceCube signal. Hyper-K will be able to detect neutrinos from our model out to a distance of ˜10 kpc. Here, at 1 kpc, JUNO, Super-K, and DUNE would register a few events while IceCube and Hyper-K would register several tens of events.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Reinventing the Solar Power Satellite

The selling price of electrical power varies with time. The economic viability of space solar power is maximum if the power can be sold at peak power rates, instead of baseline rate. Price and demand of electricity was examined from spot-market data from four example markets: New England, New York City, suburban New York, and California. The data was averaged to show the average price and demand for power as a function of time of day and time of year. Demand varies roughly by a factor of two between the early-morning minimum demand, and the afternoon maximum; both the amount of peak power, and the location of the peak, depends significantly on the location and the weather. The demand curves were compared to the availability curves for solar energy and for tracking and non-tracking satellite solar power systems in order to compare the market value of terrestrial and solar electrical power. In part 2, new designs for a space solar power (SSP) system were analyzed to provide electrical power to Earth for economically competitive rates. The approach was to look at innovative power architectures to more practical approaches to space solar power. A significant barrier is the initial investment required before the first power is returned. Three new concepts for solar power satellites were invented and analyzed: a solar power satellite in the Earth-Sun L2 point, a geosynchronous no-moving parts solar power satellite, and a nontracking geosynchronous solar power satellite with integral phased array. The integral-array satellite had several advantages, including an initial investment cost approximately eight times lower than the conventional design.

Landis, Geoffrey A.↗

Improvements on the minimax algorithm for the Laplace transformation of orbital energy denominators

We present a robust and non-heuristic algorithm that finds all extremum points of the error distribution function of numerically Laplace-transformed orbital energy denominators. The extremum point search is one of the two key steps for finding the minimax approximation. If pre-tabulation of initial guesses is supposed to be avoided, strategies for a sufficiently robust algorithm have not been discussed so far. We compare our non-heuristic approach with a bracketing and bisection algorithm and demonstrate that 3 times less function evaluations are required altogether when applying it to typical non-relativistic and relativistic quantum chemical systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The Mercury Laser Altimeter Instrument for the MESSENGER Mission

The Mercury Laser Altimeter (MLA) is one of the payload science instruments on the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) mission, which launched on 3 August 2004. The altimeter will measure the round trip time-of-flight of transmitted laser pulses reflected from the surface of the planet that, in combination with the spacecraft orbit position and pointing data, gives a high-precision measurement of surface topography referenced to Mercury's center of mass. The altimeter measurements will be used to determine the planet's forced librations by tracking the motion of large-scale topographic features as a function of time. MLA's laser pulse energy monitor and the echo pulse energy estimate will provide an active measurement of the surface reflectivity at 1064 nm. This paper describes the instrument design, prelaunch testing, calibration, and results of post-launch testing.

Cavanaugh, John F.↗

Semiclassical Green’s functions and an instanton formulation of electron-transfer rates in the nonadiabatic limit

We present semiclassical approximations to Green’s functions of multidimensional systems, extending Gutzwiller’s work to the classically forbidden region. Based on steepest-descent integrals over these functions, we derive an instanton method for computing the rate of nonadiabatic reactions, such as electron transfer, in the weak-coupling limit, where Fermi’s golden-rule can be employed. This generalizes Marcus theory to systems for which the environment free-energy curves are not harmonic and where nuclear tunnelling plays a role. The derivation avoids using the Im F method or short-time approximations to real-time correlation functions. A clear physical interpretation of the nuclear tunnelling processes involved in an electron-transfer reaction is thus provided. In Paper II [J. O. Richardson, J. Chem. Phys. 143, 134116 (2015)], we discuss numerical evaluation of the formulae.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modulation of Galactic Cosmic Rays in the Inner Heliosphere, Comparing with PAMELA Measurements

We develop a numerical model to study the time-dependent modulation of galactic cosmic rays in the inner heliosphere. In the model, a time-delayed modified Parker heliospheric magnetic field (HMF) and a new diffusion coefficient model, NLGCE-F, from Qin and Zhang, are adopted. In addition, the latitudinal dependence of magnetic turbulence magnitude is assumed to be ∼(1+sin{sup 2}θ)/2 from the observations of Ulysses, and the radial dependence is assumed to be ∼r{sup S}, where we choose an expression of S as a function of the heliospheric current sheet tilt angle. We show that the analytical expression used to describe the spatial variation of HMF turbulence magnitude agrees well with the Ulysses, Voyager 1, and Voyager 2 observations. By numerically calculating the modulation code, we get the proton energy spectra as a function of time during the recent solar minimum, it is shown that the modulation results are consistent with the Payload for Antimatter-Matter Exploration and Light-nuclei Astrophysics measurements.

79 ASTRONOMY AND ASTROPHYSICS↗

Vehicle management and mission planning in support of shuttle operations.

An operational approach to shuttle mission planning during high flight frequency years (20 or more flights per year) is described wherein diverse mission planning functions interface via an interactive computer system and common data base. The Vehicle Management and Mission Planning System (VMMPS) is proposed as a means of helping to accomplish the mission planning function. The VMMPS will link together into an interactive system the major mission planning areas such as trajectory, crew, vehicle performance, and launch operations. A common data base will be an integral part of the system and the concept of standard mission types and phases will be used to minimize mission to mission uniqueness. The use of this system will eliminate much redundancy and replanning, shorten interface times between functions, and provide a means to evaluate unplanned events and modify schedules.

Pruett, W. R.↗

Stability of the flow around a cylinder: The spin-up problem

A concern is the flow around an infinite cylinder, which at a certain instant impulsively starts to spin. The growth of vortices in the resulting boundary layer occurring outside the cylinder is investigated. This layer is essentially a Rayleigh layer which grows with time, so the mechanism involved is similar to that studied in Hall (1983). Vortices with wavenumber comparable to the layer thickness are shown to be described by partial differential equations that govern the system numerically. It is assumed that the Rayleigh layer is thin, so particles are confined to move in a path with radius of curvature the same as the cylinder. The Goertler number is a function of time, so the time scale which produces an order, is considered one Goertler number. The right hand branch calculation is considered by letting the time tend to infinity, also inviscid Goertler modes are considered.

Otto, S. R.↗

Derivation of hard deadlines for real-time control systems

The computation-time delay in the feedback controller of a real-time control system may cause failure to update the control input during one or more sampling periods. A dynamic failure is said to occur if this delay exceeds a certain limit called a hard deadline. The authors present a method for calculating the hard deadlines in linear time-invariant control systems. To derive necessary conditions for (asymptotic) system stability, the state difference equation is modified based on an assumed maximum delay and the probability distribution of delays whose magnitudes are less than, or equal to, the assumed maximum delay. Moreover, the allowed state-space-which is derived from given input and state constraints-is used to calculate the hard deadline as a function of time and the system state. The authors consider a one-shot delay model in which a single event causes a dynamic failure.

Shin, Kang G.↗

Lanthanum Bromide Detector System for Mu2e Stopping Target Monitor

The stopping target monitor (STM) in the Mu2e experiment is used to normalize the muon decay branching ratio in the Mu2e experiment, by estimating the number of muons that have been captured on the Mu2e nuclear target. The STM measures the distinctive muonic atomic transition lines and muonic nuclear excitations produced in the Aluminum Stopping Target of Mu2e. These signals must be disentangled in the presence of high rate Bremsstrahlung and other backgrounds produced in the target. An HPGe detector with fine energy resolution, ~0.1% will be employed but has limited count rate capability, ~20kcps. Time-to-Decision, that is the time to make an estimate of the experiments observed luminosity, is inversely proportional to the signal rate squared. For this reason the STM will also use a Lanthanum Bromide(LaBr3) detector, having ~2% energy resolution but capable of ~1 Mcps counting rate. This higher rate will allow not only an orthogonal verification of the HPGe luminosity measurements, but will also yield much finer luminosity measurements as a function of time because of its significantly higher counting rate capabilities. Geant4 simulations are presented comparing the performance of different sized, LaBr3 crystals. The results highly favor the use of the commercially available right circular cylindrical, 3x3-in. detector. Modifications to the STM design are discussed in order to take full advantage of the LaBr3 high rate and fast decision making capabilities. A preliminary design will be presented for a custom read-out system needed to fulfill these requirements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Edge crack growth of thermally aged graphite/polyimide composites

Laminates of Celion 6000/LARC-160 and Celion 6000/PMR-15 graphite/polyimide composite materials were aged in air at temperatures of 202, 232, 260 and 288 C for various times up to 15,000 hours. Three unidirectional specimen types were studied: short beam shear (SBS), flexure, and 153 mm square panels. The interior region of the square panels exhibited little or no property degradation, whereas both laminate materials degraded and cracked preferentially at the specimen edge perpendicular to the fibers. Using a dye penetrant, the specimens were X-rayed and the crack depth measured as a function of time and temperature. A time temperature superposition of the crack data was successfully performed using an Arrhenius form for the shift factor. A direct correlation was found for edge crack depth and SBS strength for the LARC-160 laminates but the correlation for PMR-15 laminates was more complex.

Nelson, J. B.↗

Receiver-Based Auralization of Broadband Aircraft Flyover Noise Using the NASA Auralization Framework

The NASA Auralization Framework (NAF) consists of a set of dynamic link libraries (DLLs) to facilitate auralization of aircraft noise. Advanced capabilities for synthesis, propagation, and external interfaces are provided by the NAF Advanced Plugin Libraries (APL); a separate set of DLLs that are made accessible through the NAF’s plugin architecture. In the typical time domain use case, the sound is first synthesized at the source location based on a source noise definition, and is then propagated in the time domain to a receiver on or near the ground. Alternatively, it may be desirable to synthesize the sound at the receiver, after it has been propagated in the frequency domain, e.g., when the source definition is inaccessible or when alternative propagation methods are needed. Receiver-based auralization requires three new developments in the NAF APL: a component plugin to interpolate the propagated noise spectra as a function of time for input to sound synthesis, and a path finder and path traversal plugin to calculate the effects of the differential propagation path length between the direct and ground reflected rays. This paper describes those developments and demonstrates their use in the auralization of broadband flyover noise.

Aumann, Aric R.↗

Improving the accuracy and efficiency of time-resolved electronic spectra calculations: Cellular dephasing representation with a prefactor

Time-resolved electronic spectra can be obtained as the Fourier transform of a special type of time correlation function known as fidelity amplitude, which, in turn, can be evaluated approximately and efficiently with the dephasing representation. Here we improve both the accuracy of this approximation—with an amplitude correction derived from the phase-space propagator—and its efficiency—with an improved cellular scheme employing inverse Weierstrass transform and optimal scaling of the cell size. We demonstrate the advantages of the new methodology by computing dispersed time-resolved stimulated emission spectra in the harmonic potential, pyrazine, and the NCO molecule. In contrast, we show that in strongly chaotic systems such as the quartic oscillator the original dephasing representation is more appropriate than either the cellular or prefactor-corrected methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Approximating the linear quadratic optimal control law for hereditary systems with delays in the control

The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary systems. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.

Milman, Mark H.↗

Approximating the linear quadratic optimal control law for hereditary systems with delays in the control

The fundamental control synthesis issue of establishing a priori convergence rates of approximation schemes for feedback controllers for a class of distributed parameter systems is addressed within the context of hereditary schemes. Specifically, a factorization approach is presented for deriving approximations to the optimal feedback gains for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the controls, trajectories and feedback kernels. Two algorithms are derived from the basic approximation scheme, including a fast algorithm, in the time-invariant case. A numerical example is also considered.

Milman, Mark H.↗

The wind geometry of the Wolf-Rayet star HD 191765

A time-dependent spectropolarimetric data set of HD 191765 in the wavelength range 3159-7593 A is presented. At all epochs the present observations display a large and strongly wavelength-dependent continuum polarization and reduced levels of polarization across the emission lines. The data imply a significant intrinsic continuum polarization which requires a general deviation of the electron distribution from spherical symmetry. The global shape is quite stable as a function of time; small fluctuations may arise from localized density/temperature changes. The line polarizations are consistent with an axisymmetric wind geometry and ionization stratification. A qualitative model for polarization in a Wolf-Rayet atmosphere is developed. It is argued that the blueward rise of the continuum polarization in HD 191765 can be explained if the density in the wind is high, resulting in a competition of thermal and electron-scattering continuum opacity in the vertical.

Schulte-Ladbeck, R. F.↗

Development of the US3D Code for Advanced Compressible and Reacting Flow Simulations

Aerothermodynamics and hypersonic flows involve complex multi-disciplinary physics, including finite-rate gas-phase kinetics, finite-rate internal energy relaxation, gas-surface interactions with finite-rate oxidation and sublimation, transition to turbulence, large-scale unsteadiness, shock-boundary layer interactions, fluid-structure interactions, and thermal protection system ablation and thermal response. Many of the flows have a large range of length and time scales, requiring large computational grids, implicit time integration, and large solution run times. The University of Minnesota NASA US3D code was designed for the simulation of these complex, highly-coupled flows. It has many of the features of the well-established DPLR code, but uses unstructured grids and has many advanced numerical capabilities and physical models for multi-physics problems. The main capabilities of the code are described, the physical modeling approaches are discussed, the different types of numerical flux functions and time integration approaches are outlined, and the parallelization strategy is overviewed. Comparisons between US3D and the NASA DPLR code are presented, and several advanced simulations are presented to illustrate some of novel features of the code.

CFD↗