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NASA NTRS2002

Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning

We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum exitation gap, gmin = O(n2(sup -n/2)), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.

Smelyanskiy, Vadius↗

NASA NTRS2012

Lattice Thermal Conductivity from Atomistic Simulations: ZrB2 and HfB2

Ultra high temperature ceramics (UHTC) including ZrB2 and HfB2 have a number of properties that make them attractive for applications in extreme environments. One such property is their high thermal conductivity. Computational modeling of these materials will facilitate understanding of fundamental mechanisms, elucidate structure-property relationships, and ultimately accelerate the materials design cycle. Progress in computational modeling of UHTCs however has been limited in part due to the absence of suitable interatomic potentials. Recently, we developed Tersoff style parameterizations of such potentials for both ZrB2 and HfB2 appropriate for atomistic simulations. As an application, Green-Kubo molecular dynamics simulations were performed to evaluate the lattice thermal conductivity for single crystals of ZrB2 and HfB2. The atomic mass difference in these binary compounds leads to oscillations in the time correlation function of the heat current, in contrast to the more typical monotonic decay seen in monoatomic materials such as Silicon, for example. Results at room temperature and at elevated temperatures will be reported.

Lawson, John W.↗

NASA NTRS2012

Lattice Thermal Conductivity of Ultra High Temperature Ceramics (UHTC) ZrB2 and HfB2 from Atomistic Simulations

Lawson, John W.↗

NASA NTRS2012

An Empirical Temperature Variance Source Model in Heated Jets

An acoustic analogy approach is implemented that models the sources of jet noise in heated jets. The equivalent sources of turbulent mixing noise are recognized as the differences between the fluctuating and Favre-averaged Reynolds stresses and enthalpy fluxes. While in a conventional acoustic analogy only Reynolds stress components are scrutinized for their noise generation properties, it is now accepted that a comprehensive source model should include the additional entropy source term. Following Goldstein s generalized acoustic analogy, the set of Euler equations are divided into two sets of equations that govern a non-radiating base flow plus its residual components. When the base flow is considered as a locally parallel mean flow, the residual equations may be rearranged to form an inhomogeneous third-order wave equation. A general solution is written subsequently using a Green s function method while all non-linear terms are treated as the equivalent sources of aerodynamic sound and are modeled accordingly. In a previous study, a specialized Reynolds-averaged Navier-Stokes (RANS) solver was implemented to compute the variance of thermal fluctuations that determine the enthalpy flux source strength. The main objective here is to present an empirical model capable of providing a reasonable estimate of the stagnation temperature variance in a jet. Such a model is parameterized as a function of the mean stagnation temperature gradient in the jet, and is evaluated using commonly available RANS solvers. The ensuing thermal source distribution is compared with measurements as well as computational result from a dedicated RANS solver that employs an enthalpy variance and dissipation rate model. Turbulent mixing noise predictions are presented for a wide range of jet temperature ratios from 1.0 to 3.20.

Khavaran, Abbas↗

NASA NTRS1976

Rotational excitation of CO by collisions with He, H, and H2 under conditions in interstellar clouds

Cross sections for rotational excitation of small molecules by low-energy collisions with helium and hydrogen can currently be obtained via accurate numerical solution of the quantum equations that describe both intermolecular forces and collision dynamics. The relevant methods are discussed in some detail and applied to compute excitation rates for carbon monoxide. These calculations also predict collision-induced spectral pressure-broadening constants which are in excellent agreement with available experimental data.

Green, S.↗

NASA NTRS1990

Assured Crew Return Vehicle flowfield and aerodynamic characteristics

A lifting body has been proposed as a candidate for the Assured Crew Return Vehicle which will serve as crew rescue vehicle for the Space Station. The focus of this work is on body surface definition, surface and volume grid definition, and the computation of inviscid flowfields about the vehicle at wind-tunnel conditions. Very good agreement is shown between the computed aerodynamic characteristics of the vehicle at a freestream Mach number of 10 and those measured in wind-tunnel tests.

Weilmuenster, K. James↗

NASA NTRS1999

Determination of Stability and Control Derivatives using Computational Fluid Dynamics and Automatic Differentiation

With the recent interest in novel control effectors there is a need to determine the stability and control derivatives of new aircraft configurations early in the design process. These derivatives are central to most control law design methods and would allow the determination of closed-loop control performance of the vehicle. Early determination of the static and dynamic behavior of an aircraft may permit significant improvement in configuration weight, cost, stealth, and performance through multidisciplinary design. The classical method of determining static stability and control derivatives - constructing and testing wind tunnel models - is expensive and requires a long lead time for the resultant data. Wind tunnel tests are also limited to the preselected control effectors of the model. To overcome these shortcomings, computational fluid dynamics (CFD) solvers are augmented via automatic differentiation, to directly calculate the stability and control derivatives. The CFD forces and moments are differentiated with respect to angle of attack, angle of sideslip, and aircraft shape parameters to form these derivatives. A subset of static stability and control derivatives of a tailless aircraft concept have been computed by two differentiated inviscid CFD codes and verified for accuracy with central finite-difference approximations and favorable comparisons to a simulation database.

Park, Michael A.↗

NASA NTRS1983

Selecting band combinations with thematic mapper data

A problem arises in making color composite images because there are 210 different possible color presentations of TM three-band images. A method is given for reducing that 210 to a single choice, decided by the statistics of a scene or subscene, and taking into full account any correlations that exist between different bands. Instead of using total variance as the measure for information content of the band triplets, the ellipsoid of maximum volume is selected which discourages selection of bands with high correlation. The band triplet is obtained by computing and ranking in order the determinants of each 3 x 3 principal submatrix of the original matrix M. After selection of the best triplet, the assignment of colors is made by using the actual variances (the diagonal elements of M): green (maximum variance), red (second largest variance), blue (smallest variance).

Sheffield, C. A.↗

NASA NTRS1989

The dissociation energy of He2(+)

Ab initio potential energy curves for He2(+) are computed using full CI wavefunctions in conjuction with large Gaussian and Slater basis sets. The computed curves yield rotational-vibrational transitions with errors of less than 1/cm. They also yield quasi-bound levels with energies and lifetimes in reasonable agreement with translational spectroscopy measurements. The best D(e) is estimated to be 2.470 eV. Green's function Monte Carlo calculations yield a very similar value, 2.466 + or - 0.005.

Bauschlicher, Charles W., Jr.↗

NASA NTRS1978

Global crustal response model

A computer program was developed for calculating the radial displacement due to the body tide as a function of spatial position and time. The positions of the moon and sun were evaluated by means of the Hill-Brown and Newcomb theories, respectively. Green's functions were utilized to simulate the elastic Earth responses due to point loads, a convolution program has been developed to evaluate the elastic Earth responses due to ocean loading by a given ocean tide constituent. These responses include radial and horizontal displacement, tilt and gravity acceleration, and strain tensor components.

Source record↗

NASA NTRS1980

A semianalytical satellite theory for weak time-dependent perturbations

The modifications of the semianalytical satellite theory required to include these 'weak' time dependent perturbations are described. The new formulation results in additional terms in the short periodic variations but does not change the averaged equations of motion. Thus the m monthly terms are still included in the averaged equations of motion. This contrasts with the usual approach for the strongly time dependent perturbations in which the m monthly (or m daily, if tesseral harmonics are being considered) terms would be eliminated from the averaged equations of motion and included in the short periodics computation. Numerical test results for the GPS case obtained with a numerical averaging implementation of the new theory demonstrate the accuracy improvement.

Cefola, P.↗

NASA NTRS1989

Computational Aspects of Sensitivity Calculations in Linear Transient Structural Analysis

A study has been performed focusing on the calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, transient response problems. One significant goal was to develop and evaluate sensitivity calculation techniques suitable for large-order finite element analyses. Accordingly, approximation vectors such as vibration mode shapes are used to reduce the dimensionality of the finite element model. Much of the research focused on the accuracy of both response quantities and sensitivities as a function of number of vectors used. Two types of sensitivity calculation techniques were developed and evaluated. The first type of technique is an overall finite difference method where the analysis is repeated for perturbed designs. The second type of technique is termed semianalytical because it involves direct, analytical differentiation of the equations of motion with finite difference approximation of the coefficient matrices. To be computationally practical in large-order problems, the overall finite difference methods must use the approximation vectors from the original design in the analyses of the perturbed models.

Greene, William H.↗

NASA NTRS1991

An upwind-biased space marching algorithm for supersonic viscous flow

The modifications are documented which were made to the Langley Aerothermodynamic Upwind Relaxation Algorithm which allow it to compute solutions in a space marching manner. The space marching flux is formulated to be either first- or second-order accurate, using Roe's upwind differencing or Symmetric Total Variation Diminishing differencing, respectively. The algorithm solves the thin layer Navier-Stokes equations, and is subject to the same flow restrictions as a parabolized Navier-Stokes solver. Each cross flow plane is locally iterated in time until converged, then marched in space to the next station. The algorithm is tested on a sphere-cone geometry and a geometry which models the windward side of the Space Shuttle Orbiter. Computational results for surface heating are compared to ground based experimental data. In addition, space marching predictions for surface pressure are compared against values from the original algorithm.

Greene, Francis A.↗

NASA NTRS2002

Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning

We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum excitation gap. g min, = O(n 2(exp -n/2), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to 'the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.

Smelyanskiy, V. N.↗

NASA NTRS2003

Development of a Real-Time Environmental Monitoring System, Life Cycle Assessment Systems, and Pollution Prevention Programs

Pollution prevention (P2) opportunities and Greening the Government (GtG) activities, including the development of the Real-Time Environmental Monitoring System (RTEMS), are currently under development at the NASA Glenn Research Center. The RTEMS project entails the ongoing development of a monitoring system which includes sensors, instruments, computer hardware and software, plus a data telemetry system.Professor Kocher has been directing the RTEMS project for more than 3 years, and the implementation of the prototype system at GRC will be a major portion of his summer effort. This prototype will provide mulitmedia environmental monitoring and control capabilities, although water quality and air emissions will be the immediate issues addressed this summer. Applications beyond those currently identified for environmental purposes will also be explored.

Kocher, Walter M.↗

NASA NTRS1973

Application of ERTS-1 data to analysis of agricultural crops and forests in Michigan

The results reported are based on analysis of ERTS Frame 1033-15580 collected over southwestern Lower Michigan on August 25, 1972. Major agricultural crops such as corn and soybeans were approaching maturity at this data and forest canopies were dense. Extensive ground truth information was gathered by detailed field study of test strips. This detailed information was supplemented over larger areas by interpretation of RB-57 and C-47 photography and MSS imagery. Recognition processing of ERTS-1 MSS data was carried out on a digital computer. Fields and forest stands were selected as training sets and test areas. Aerial imagery was essential for locating the positions of these selected areas on ERTS digital tapes. The recognition process was successful for each type of vegetation which had a dense green canopy such as forests, corn, and soybeans. Bare soil was also recognizable as a category.

Safir, G. R.↗

NASA NTRS1991

Numerical analysis and simulation of an assured crew return vehicle flow field

A lifting body was proposed as a candidate for the Assured Crew Return Vehicle (ACRV) which will serve as a crew rescue vehicle for the Space Station Freedom. The focus is on body surface definition, both surface and volume grid definition, and the computation of inviscid flow fields about the vehicle at wind tunnel conditions. Very good agreement is shown between the computed aerodynamic characteristics of the vehicle at M(sub infinity) = 10 and those measured in wind tunnel tests at high Reynolds numbers.

Weilmuenster, K. James↗

NASA NTRS1994

Navier-Stokes simulations of Orbiter aerodynamic characteristics including pitch trim and bodyflap

An analysis of the longitudinal aerodynamics of the shuttle orbiter in the hypersonic flight regime is made through the use of computational fluid dynamics. Particular attention is given to establishing the cause of the 'pitching moment anomaly,' which occurred on the orbiter's first flight, and to computing the aerodynamics of a complete orbiter configuration at flight conditions. Data from ground-based facilities as well as orbiter flight data are used to validate the computed results. Analysis shows that the pitching moment anomaly is a real-gas chemistry effect that was not simulated in ground-based facilities, which used air as a test gas. Computed flight aerodynamics for the orbiter are within 5% of the measured flight values and trim bodyflap deflections are predicted to within 10%.

Weilmuenster, K. James↗