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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
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 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

The Role of Instability Waves in Predicting Jet Noise

Debate over whether linear instability waves play a role in the prediction of jet noise has been going on for many years. Parallel mean flow models, such as the one proposed by Lilley, usually neglect these waves because they cause the solution to become infinite. The present paper solves the true non-parallel acoustic equations for a two-dimensional shear layer by using a vector Greens function and assuming small mean flow spread rate. The results show that linear instability waves must be accounted for in order to construct a proper causal solution to the problem.

Goldstein, Marvin E.↗
NASA NTRS2005

Constraining Oceanic Sources and Sinks of CO2 by Inverse Modeling: A First Step Toward Assimilation of In Situ and Remote Data

The primary goal of this collaborative project, lead by Nicholas Gruber at UCLA, is to better quantify the air-sea fluxes of pre-industrial and anthropogenic carbon dioxide CO2 for the global ocean with a newly developed inverse method. The method involves using ocean general circulation models (OGCMs) to characterize the subsurface distribution of tracers injected for different regions of the ocean surface. By linearly combining a series of these basis (or Greens) functions, one should be able to recreate any arbitrary ocean tracer field. In our case, we are using the global database of ocean dissolved inorganic carbon (DIC) from the WOCE/JGOFS global CO2 survey from the 1990s. The observed DIC field has been partitioned into pre-industrial and anthropogenic components using the empirical C* technique. We then solve for an optimal combination of the regional basis functions that best match the two sets observations in a least-squares sense with singular value decomposition. This in turn provides solutions for the regional air-sea CO2 fluxes (pre-industrial and anthropogenic) that are independent of more traditional estimates derived from surface water disequilibria in the partial pressure of CO2 and wind speed gas exchange parameterizations. We are apply the method to a suite of nine different OGCMs to test the robustness of the derived surface fluxes fields to differences in ocean circulation. Together with a collegue Keith Lindsay at NCAR, S. Doney's role in this project was to create the appropriate steady-state and temporally evolving basis functions from the NCAR CSM-1 ocean circulation model. Because of a slow start across the project in defining a common set of experimental protocols, we requested and were given a one year, no cost extension. Both the steady-state and temporally evolving basis functions were delivered to the UCLA group for further analysis. Additional information is included in the original extended abstract.

Doney, Scott↗
NASA NTRS1997

Global Analysis of Empirical Relationships Between Annual Climate and Seasonality of NDVI

This study describes the use of satellite data to calibrate a new climate-vegetation greenness function for global change studies. We examined statistical relationships between annual climate indexes (temperature, precipitation, and surface radiation) and seasonal attributes of the AVHRR Normalized Difference Vegetation Index (NDVI) time series for the mid-1980s in order to refine our empirical understanding of intraannual patterns and global abiotic controls on natural vegetation dynamics. Multiple linear regression results using global l(sup o) gridded data sets suggest that three climate indexes: growing degree days, annual precipitation total, and an annual moisture index together can account to 70-80 percent of the variation in the NDVI seasonal extremes (maximum and minimum values) for the calibration year 1984. Inclusion of the same climate index values from the previous year explained no significant additional portion of the global scale variation in NDVI seasonal extremes. The monthly timing of NDVI extremes was closely associated with seasonal patterns in maximum and minimum temperature and rainfall, with lag times of 1 to 2 months. We separated well-drained areas from l(sup o) grid cells mapped as greater than 25 percent inundated coverage for estimation of both the magnitude and timing of seasonal NDVI maximum values. Predicted monthly NDVI, derived from our climate-based regression equations and Fourier smoothing algorithms, shows good agreement with observed NDVI at a series of ecosystem test locations from around the globe. Regions in which NDVI seasonal extremes were not accurately predicted are mainly high latitude ecosystems and other remote locations where climate station data are sparse.

Potter, C. S.↗
NASA NTRS2010

Proton Lateral Broadening Distribution Comparisons Between GRNTRN, MCNPX, and Laboratory Beam Measurements

Recent developments in NASA s deterministic High charge (Z) and Energy TRaNsport (HZETRN) code have included lateral broadening of primary ion beams due to small-angle multiple Coulomb scattering, and coupling of the ion-nuclear scattering interactions with energy loss and straggling. This new version of HZETRN is based on Green function methods, called GRNTRN, and is suitable for modeling transport with both space environment and laboratory boundary conditions. Multiple scattering processes are a necessary extension to GRNTRN in order to accurately model ion beam experiments, to simulate the physical and biological-effective radiation dose, and to develop new methods and strategies for light ion radiation therapy. In this paper we compare GRNTRN simulations of proton lateral broadening distributions with beam measurements taken at Loma Linda University Proton Therapy Facility. The simulated and measured lateral broadening distributions are compared for a 250 MeV proton beam on aluminum, polyethylene, polystyrene, bone substitute, iron, and lead target materials. The GRNTRN results are also compared to simulations from the Monte Carlo MCNPX code for the same projectile-target combinations described above.

Mertens, Christopher J.↗
NASA NTRS2015

Analytic Thermoelectric Couple Modeling: Variable Material Properties and Transient Operation

To gain a deeper understanding of the operation of a thermoelectric couple a set of analytic solutions have been derived for a variable material property couple and a transient couple. Using an analytic approach, as opposed to commonly used numerical techniques, results in a set of useful design guidelines. These guidelines can serve as useful starting conditions for further numerical studies, or can serve as design rules for lab built couples. The analytic modeling considers two cases and accounts for 1) material properties which vary with temperature and 2) transient operation of a couple. The variable material property case was handled by means of an asymptotic expansion, which allows for insight into the influence of temperature dependence on different material properties. The variable property work demonstrated the important fact that materials with identical average Figure of Merits can lead to different conversion efficiencies due to temperature dependence of the properties. The transient couple was investigated through a Greens function approach; several transient boundary conditions were investigated. The transient work introduces several new design considerations which are not captured by the classic steady state analysis. The work helps to assist in designing couples for optimal performance, and also helps assist in material selection.

Seebeck Effect↗
NASA NTRS2015

Jet Surface Interaction Scrubbing Noise from High Aspect-Ratio Rectangular Jets

Concepts envisioned for the future of civil air transport consist of unconventional propulsion systems in the close proximity of the airframe. Distributed propulsion system with exhaust configurations that resemble a high aspect ratio rectangular jet are among geometries of interest. Nearby solid surfaces could provide noise shielding for the purpose of reduced community noise. Interaction of high-speed jet exhaust with structure could also generate new sources of sound as a result of flow scrubbing past the structure, and or scattered noise from sharp edges. The present study provides a theoretical framework to predict the scrubbing noise component from a high aspect ratio rectangular exhaust in proximity of a solid surface. The analysis uses the Greens function (GF) to the variable density Pridmore-Brown equation in a transversely sheared mean flow. Sources of sound are defined as the auto-covariance function of second-rank velocity fluctuations in the jet plume, and are modeled using a RANS-based acoustic analogy approach. Acoustic predictions are presented in an 8:1 aspect ratio rectangular exhaust at three subsonic Mach numbers. The effect of nearby surface on the scrubbing noise component is shown on both reflected and shielded sides of the plate.

Propulsion Noise↗
DOE OSTI2021

Variational Monte Carlo Calculations of A ≤ 4 Nuclei with an Artificial Neural-Network Correlator Ansatz

Here, the complexity of many-body quantum wave functions is a central aspect of several fields of physics and chemistry where nonperturbative interactions are prominent. Artificial neural networks (ANNs) have proven to be a flexible tool to approximate quantum many-body states in condensed matter and chemistry problems. In this work we introduce a neural-network quantum state ansatz to model the ground-state wave function of light nuclei, and approximately solve the nuclear many-body Schrodinger equation. Using efficient stochastic sampling and optimization schemes, our approach extends pioneering applications of ANNs in the field, which present exponentially scaling algorithmic complexity. We compute the binding energies and point-nucleon densities of A ≤ 4 nuclei as emerging from a leading-order pionless effective field theory Hamiltonian. We successfully benchmark the ANN wave function against more conventional parametrizations based on two- and three-body Jastrow functions, and virtually exact Green's function Monte Carlo results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1989

A closed form solution to HZE propagation

An analytic solution for high energy heavy ion transport assuming straightahead and velocity conserving interactions with constant nuclear cross reactions is given in terms of a Green's function. The series solution for the Green's function is rapidly convergent for most practical applications. The Green's function technique can be applied with equal success to laboratory beams as well as to galactic cosmic rays allowing laboratory validation of the resultant space shielding code.

Wilson, John W.↗
NASA NTRS1990

A closed-form solution to HZE propagation

An analytic solution for high energy heavy ion transport assuming straightahead and velocity conserving interactions with constant nuclear cross reactions is given in terms of a Green's function. The series solution for the Green's function is rapidly convergent for most practical applications. The green's function technique can be applied with equal success to laboratory beams as well as to galactic cosmic rays allowing laboratory validation of the resultant space shielding code.

Wilson, John W.↗
DOE OSTI2021

Nonparametric, data-based kernel interpolation for particle-tracking simulations and kernel density estimation

Traditional interpolation techniques for particle tracking include binning and convolutional formulas that use pre-determined (i.e., closed-form, parameteric) kernels. In many instances, the particles are introduced as point sources in time and space, so the cloud of particles (either in space or time) is a discrete representation of the Green’s function of an underlying PDE. As such, each particle is a sample from the Green’s function; therefore, each particle should be distributed according to the Green’s function. In short, the kernel of a convolutional interpolation of the particle sample “cloud” should be a replica of the cloud itself. This idea gives rise to an iterative method by which the form of the kernel may be discerned in the process of interpolating the Green’s function. When the Green’s function is a density, this method is broadly applicable to interpolating a kernel density estimate based on random data drawn from a single distribution. We formulate and construct the algorithm and demonstrate its ability to perform kernel density estimation of skewed and/or heavy-tailed data including breakthrough curves.

42 ENGINEERING↗
NASA NTRS2005

Verification and Validation: High Charge and Energy (HZE) Transport Codes and Future Development

In the present paper, we give the formalism for further developing a fully three-dimensional HZETRN code using marching procedures but also development of a new Green's function code is discussed. The final Green's function code is capable of not only validation in the space environment but also in ground based laboratories with directed beams of ions of specific energy and characterized with detailed diagnostic particle spectrometer devices. Special emphasis is given to verification of the computational procedures and validation of the resultant computational model using laboratory and spaceflight measurements. Due to historical requirements, two parallel development paths for computational model implementation using marching procedures and Green s function techniques are followed. A new version of the HZETRN code capable of simulating HZE ions with either laboratory or space boundary conditions is under development. Validation of computational models at this time is particularly important for President Bush s Initiative to develop infrastructure for human exploration with first target demonstration of the Crew Exploration Vehicle (CEV) in low Earth orbit in 2008.

Wilson, John W.↗
DOE OSTI2023

Quantifying the effect of 3D models on moment tensor results using synthetic data

Moment tensors provide vital information on seismic source properties for seismic events. Moment tensors require seismic wavespeed models to compute Green’s functions, which measure the impulse response between a given source and receiver. Traditionally, researchers have used one-dimensional velocity models to calculate Green’s functions since 1D Green’s functions are computationally cheap to compute. Local 1D velocity models can also accurately model waveforms at short distances (< 500 km). However, 1D velocity models do not account for lateral heterogeneity, which can cause significant misfit in tectonically complex regions such as the Middle East (Covellone and Savage, 2012). Green’s functions calculated using 3D seismic wavespeed models have been shown to perform better in tectonically complex regions (Covellone and Savage, 2012; Kintner and Modrak, 2022), so we are interested in quantifying the effect of considering 3D structure on moment tensor inversion results. The Middle East is an ideal study area for a synthetic moment tensor test for two reasons. Firstly, the Middle East is a tectonically complex region that has been heavily studied. Secondly, the Middle East has significant seismic activity throughout the region, but imperfect station coverage due to limited open data through large swaths of the domain. The tectonic complexity and uneven station coverage will test real-world performance even in a synthetic experiment.

58 GEOSCIENCES↗
DOE OSTI2023

Lepton–Nucleus Interactions within Microscopic Approaches

This review paper emphasizes the significance of microscopic calculations with quantified theoretical error estimates in studying lepton–nucleus interactions and their implications for electron scattering and accelerator neutrino oscillation measurements. We investigate two approaches: Green’s Function Monte Carlo and the extended factorization scheme, utilizing realistic nuclear target spectral functions. In our study, we include relativistic effects in Green’s Function Monte Carlo and validate the inclusive electron scattering cross section on carbon using available data. We compare the flux-folded cross sections for neutrino-carbon scattering with T2K and MINER$v$ A experiments, noting the substantial impact of relativistic effects in reducing the theoretical curve strength when compared to MINER$v$ A data. Additionally, we demonstrate that quantum Monte Carlo-based spectral functions accurately reproduce the quasi-elastic region in electron scattering data and T2K flux-folded cross sections. By comparing results from Green’s Function Monte Carlo and the spectral function approach, which share a similar initial target state description, we quantify errors associated with approximations in the factorization scheme and the relativistic treatment of kinematics in Green’s Function Monte Carlo.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1995

Efficient modeling of interconnects and capacitive discontinuities in high-speed digital circuits

Modeling of interconnects and associated discontinuities with the recent advances high-speed digital circuits has gained a considerable interest over the last decade although the theoretical bases for analyzing these structures were well-established as early as the 1960s. Ongoing research at the present time is focused on devising methods which can be applied to more general geometries than the ones considered in earlier days and, at the same time, improving the computational efficiency and accuracy of these methods. In this thesis, numerically efficient methods to compute the transmission line parameters of a multiconductor system and the equivalent capacitances of various strip discontinuities are presented based on the quasi-static approximation. The presented techniques are applicable to conductors embedded in an arbitrary number of dielectric layers with two possible locations of ground planes at the top and bottom of the dielectric layers. The cross-sections of conductors can be arbitrary as long as they can be described with polygons. An integral equation approach in conjunction with the collocation method is used in the presented methods. A closed-form Green's function is derived based on weighted real images thus avoiding nested infinite summations in the exact Green's function; therefore, this closed-form Green's function is numerically more efficient than the exact Green's function. All elements associated with the moment matrix are computed using the closed-form formulas. Various numerical examples are considered to verify the presented methods, and a comparison of the computed results with other published results showed good agreement.

Oh, K. S.↗
NASA NTRS1994

Nonperturbative methods in HZE propagation

An analytical solution to the perturbative multiple collision series of a fragmenting HZE ion beam has limited usefulness since the first collision term has several hundred contributions, the second collision term has tens of thousands of contributions, and each successive collision term progresses to unwieldy computational proportions. Our previous work has revealed the multiple collision terms in the straight-ahead approximation to be simple products of a spatially dependent factor times a linear energy-dependent factor of limited domain and unit normalization. The properties of these forms allow the development of the nonperturbative summation of the series to all orders assuming energy-independent nuclear cross sections as matrix products of a scaled Green's function described herein. This nonperturbative Green's function with multiple scattering correction factors compares well with experiments using 670 MeV/u neon-20 ion beams in thick water targets.

Non-NASA Center↗
NASA NTRS2011

The Prediction of Broadband Shock-Associated Noise Including Propagation Effects

An acoustic analogy is developed based on the Euler equations for broadband shock- associated noise (BBSAN) that directly incorporates the vector Green's function of the linearized Euler equations and a steady Reynolds-Averaged Navier-Stokes solution (SRANS) as the mean flow. The vector Green's function allows the BBSAN propagation through the jet shear layer to be determined. The large-scale coherent turbulence is modeled by two-point second order velocity cross-correlations. Turbulent length and time scales are related to the turbulent kinetic energy and dissipation. An adjoint vector Green's function solver is implemented to determine the vector Green's function based on a locally parallel mean flow at streamwise locations of the SRANS solution. However, the developed acoustic analogy could easily be based on any adjoint vector Green's function solver, such as one that makes no assumptions about the mean flow. The newly developed acoustic analogy can be simplified to one that uses the Green's function associated with the Helmholtz equation, which is consistent with the formulation of Morris and Miller (AIAAJ 2010). A large number of predictions are generated using three different nozzles over a wide range of fully expanded Mach numbers and jet stagnation temperatures. These predictions are compared with experimental data from multiple jet noise labs. In addition, two models for the so-called 'fine-scale' mixing noise are included in the comparisons. Improved BBSAN predictions are obtained relative to other models that do not include the propagation effects, especially in the upstream direction of the jet.

Miller, Steven↗