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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Universality of the Microcanonical Entropy at Large Spin

We consider rigorous consequences of modular invariance for two-dimensional unitary non-rational CFTs with c > 1. Simple estimates for the torus partition function can lead to remarkably strong results. We show in particular that the spectral density of spin-J operators must grow like exp (π√$\frac{2}{3}$$(c - 1)$J})/√2J in any twist interval at or above (c - 1)/12, with a known twist-dependent prefactor. This proves that the large J spectrum becomes dense even without averaging over spins. For twists below (c - 1)/12 we establish that the growth must be strictly slower. Finally, we estimate how fast the maximal gap between two spin-J operators must go to zero as J becomes large.

Pal, Sridip [California Institute of Technology (C↗
DOE OSTI2015

First-principles energy band calculation of Ruddlesden–Popper compound Sr{sub 3}Sn{sub 2}O{sub 7} using modified Becke–Johnson exchange potential

The electronic structure of Sr{sub 3}Sn{sub 2}O{sub 7} is evaluated by the scalar-relativistic full potential linearized augmented plane wave (FLAPW+lo) method using the modified Becke–Johnson potential (Tran–Blaha potential) combined with the local density approximation correlation (MBJ–LDA). The fundamental gap between the valence band (VB) and conduction band (CB) is estimated to be 3.96 eV, which is close to the experimental value. Sn 5s states and Sr 4d states are predominant in the lower and upper CB, respectively. On the other hand, the lower VB is mainly composed of Sn 5s, 5p, and O 2p states, while the upper VB mainly consists of O 2p states. These features of the DOS are well reflected by the optical transition between the upper VB and lower CB, as seen in the energy dependence of the dielectric function. Furthermore, the absorption coefficient estimated from the MBJ–LDA is similar to the experimental result. - Graphical abstract: Calculated energy band structure along the symmetry lines of the first BZ of Sr{sub 3}Sn{sub 2}O{sub 7} crystal obtained using the MBJ potential. - Highlights: • Electronic structure of Sr{sub 3}Sn{sub 2}O{sub 7} is calculated on the basis of MBJ–LDA method for the first time. • Band gap of Sr{sub 3}Sn{sub 2}O{sub 7} is determined accurately on the basis of MBJ–LDA method. • The experimental absorption spectrum of Sr{sub 3}Sn{sub 2}O{sub 7} produced by MBJ–LDA is more accurate than that obtained by GGA method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Extragalactic sources in Cosmic Microwave Background maps

We discuss the potential of a next generation space-borne CMB experiment for studies of extragalactic sources with reference to COrE+, a project submitted to ESA in response to the call for a Medium-size mission (M4). We consider three possible options for the telescope size: 1 m, 1.5 m and 2 m (although the last option is probably impractical, given the M4 boundary conditions). The proposed instrument will be far more sensitive than Planck and will have a diffraction-limited angular resolution. These properties imply that even the 1 m telescope option will perform substantially better than Planck for studies of extragalactic sources. The source detection limits as a function of frequency have been estimated by means of realistic simulations taking into account all the relevant foregrounds. Predictions for the various classes of extragalactic sources are based on up-to-date models. The most significant improvements over Planck results are presented for each option. COrE+ will provide much larger samples of truly local star-forming galaxies (by about a factor of 8 for the 1 m telescope, of 17 for 1.5 m, of 30 for 2 m), making possible analyses of the properties of galaxies (luminosity functions, dust mass functions, star formation rate functions, dust temperature distributions, etc.) across the Hubble sequence. Even more interestingly, COrE+ will detect, at |b| > 30°, thousands of strongly gravitationally lensed galaxies (about 2,000, 6,000 and 13,000 for the 1 m, 1.5 m and 2 m options, respectively). Such large samples are of extraordinary astrophysical and cosmological value in many fields. Moreover, COrE+ high frequency maps will be optimally suited to pick up proto-clusters of dusty galaxies, i.e. to investigate the evolution of large scale structure at larger redshifts than can be reached by other means. Thanks to its high sensitivity COrE+ will also yield a spectacular advance in the blind detection of extragalactic sources in polarization: we expect that it will detect up to a factor of 40 (1 m option) or of 160 (1.5 m option) more radio sources than can be detected by Planck and, for the first time, from several tens (1 m option) to a few hundreds (1.5 m option) of star forming galaxies. This will open a new window for studies of the global properties of magnetic fields in star forming galaxies and of their relationships with star formation rates.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Kohn-Sham orbitals and potentials from quantum Monte Carlo molecular densities

In this work we show the possibility to extract Kohn-Sham orbitals, orbital energies, and exchange correlation potentials from accurate Quantum Monte Carlo (QMC) densities for atoms (He, Be, Ne) and molecules (H{sub 2}, Be{sub 2}, H{sub 2}O, and C{sub 2}H{sub 4}). The Variational Monte Carlo (VMC) densities based on accurate Jastrow Antisymmetrised Geminal Power wave functions are calculated through different estimators. Using these reference densities, we extract the Kohn-Sham quantities with the method developed by Zhao, Morrison, and Parr (ZMP) [Phys. Rev. A 50, 2138 (1994)]. We compare these extracted quantities with those obtained form CISD densities and with other data reported in the literature, finding a good agreement between VMC and other high-level quantum chemistry methods. Our results demonstrate the applicability of the ZMP procedure to QMC molecular densities, that can be used for the testing and development of improved functionals and for the implementation of embedding schemes based on QMC and Density Functional Theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Corrections to nucleon capture cross sections computed in truncated Hilbert spaces

Nucleon capture cross sections enter various astrophysical processes. Here, the measurement of proton capture on nuclei at astrophysically relevant low energies is a challenge, and theoretical computations in this long-wavelength regime are sensitive to the long-distance asymptotics of the wave functions. A theoretical foundation for estimating and correcting errors introduced in capture cross sections due to Hilbert space truncation has so far been lacking. We derive extrapolation formulas that relate the infrared regularized capture amplitudes to the infinite basis limit and demonstrate their efficacy for proton-proton fusion. Our results are thus relevant to current calculations of few-body capture reactions such as proton-proton fusion or proton capture on the deuteron, and they also open the way for the use of ab initio many-body wave functions represented in finite Hilbert spaces in precision calculations of nucleon capture on heavier nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2002

Adjoint-Based, Three-Dimensional Error Prediction and Grid Adaptation

Engineering computational fluid dynamics (CFD) analysis and design applications focus on output functions (e.g., lift, drag). Errors in these output functions are generally unknown and conservatively accurate solutions may be computed. Computable error estimates can offer the possibility to minimize computational work for a prescribed error tolerance. Such an estimate can be computed by solving the flow equations and the linear adjoint problem for the functional of interest. The computational mesh can be modified to minimize the uncertainty of a computed error estimate. This robust mesh-adaptation procedure automatically terminates when the simulation is within a user specified error tolerance. This procedure for estimating and adapting to error in a functional is demonstrated for three-dimensional Euler problems. An adaptive mesh procedure that links to a Computer Aided Design (CAD) surface representation is demonstrated for wing, wing-body, and extruded high lift airfoil configurations. The error estimation and adaptation procedure yielded corrected functions that are as accurate as functions calculated on uniformly refined grids with ten times as many grid points.

Park, Michael A.↗
DOE OSTI2020

Calibration of energy density functionals with deformed nuclei

Nuclear density functional theory is the prevalent theoretical framework for accurately describing nuclear properties at the scale of the entire chart of nuclides. Given an energy functional and a many-body scheme (e.g., single- or multireference level), the predictive power of the theory depends strongly on how the parameters of the energy functionals have been calibrated with experimental data. Expanded algorithms and computing power have enabled recent optimization protocols to include data in deformed nuclei in order to optimize the coupling constants of the energy functional. The primary motivation of this work is to test the robustness of such protocols with respect to some of the technical and numerical details of the underlying calculations, especially when the calibration explores a large parameter space. To this end, we quantify the effect of these uncertainties on both the optimization and statistical emulation of composite objective functions. We also emphasize that Bayesian calibration can provide better estimates of the theoretical errors used to define objective functions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1998

Modeling, Monitoring and Fault Diagnosis of Spacecraft Air Contaminants

Control of air contaminants is a crucial factor in the safety considerations of crewed space flight. Indoor air quality needs to be closely monitored during long range missions such as a Mars mission, and also on large complex space structures such as the International Space Station. This work mainly pertains to the detection and simulation of air contaminants in the space station, though much of the work is easily extended to buildings, and issues of ventilation systems. Here we propose a method with which to track the presence of contaminants using an accurate physical model, and also develop a robust procedure that would raise alarms when certain tolerance levels are exceeded. A part of this research concerns the modeling of air flow inside a spacecraft, and the consequent dispersal pattern of contaminants. Our objective is to also monitor the contaminants on-line, so we develop a state estimation procedure that makes use of the measurements from a sensor system and determines an optimal estimate of the contamination in the system as a function of time and space. The real-time optimal estimates in turn are used to detect faults in the system and also offer diagnoses as to their sources. This work is concerned with the monitoring of air contaminants aboard future generation spacecraft and seeks to satisfy NASA's requirements as outlined in their Strategic Plan document (Technology Development Requirements, 1996).

Ramirez, W. Fred↗
NASA NTRS2019

A Ground Footprint Eccentricity Model For Asteroid Airbursts

Uncertainties in early observations of potentially hazardous asteroids result in preliminary impact corridors that can stretch across large portions of the Earth’s surface. At this early stage of detection, the corridor width and potential for damage are typically estimated using techniques from nuclear weapons research. These estimates often employ spherical blast assumptions resulting in a constant width impact corridor. In actuality, however, the ground damage footprint of obliquely entering asteroids is generally roughly elliptical or “butterfly” shaped, with the major axis extending in the cross range direction and the minor axis aligned with ground-track of the meteoroid. Since actual ground footprints for oblique entries may have aspect ratios greater than two or three, the assumption of a circular blast may significantly underestimate the area of the impact swath and the at-risk population. This work develops an engineering model that can be used to quickly estimate the eccentricity of the ground footprint as a function of local impact parameters. This yields vastly improved local estimates of the corridor width and can significantly enhance the accuracy of risk analysis.

Aftosmis, Michael J.↗
NASA NTRS2006

Exploring the Connection Between Sampling Problems in Bayesian Inference and Statistical Mechanics

The Bayesian and statistical mechanical communities often share the same objective in their work - estimating and integrating probability distribution functions (pdfs) describing stochastic systems, models or processes. Frequently, these pdfs are complex functions of random variables exhibiting multiple, well separated local minima. Conventional strategies for sampling such pdfs are inefficient, sometimes leading to an apparent non-ergodic behavior. Several recently developed techniques for handling this problem have been successfully applied in statistical mechanics. In the multicanonical and Wang-Landau Monte Carlo (MC) methods, the correct pdfs are recovered from uniform sampling of the parameter space by iteratively establishing proper weighting factors connecting these distributions. Trivial generalizations allow for sampling from any chosen pdf. The closely related transition matrix method relies on estimating transition probabilities between different states. All these methods proved to generate estimates of pdfs with high statistical accuracy. In another MC technique, parallel tempering, several random walks, each corresponding to a different value of a parameter (e.g. "temperature"), are generated and occasionally exchanged using the Metropolis criterion. This method can be considered as a statistically correct version of simulated annealing. An alternative approach is to represent the set of independent variables as a Hamiltonian system. Considerab!e progress has been made in understanding how to ensure that the system obeys the equipartition theorem or, equivalently, that coupling between the variables is correctly described. Then a host of techniques developed for dynamical systems can be used. Among them, probably the most powerful is the Adaptive Biasing Force method, in which thermodynamic integration and biased sampling are combined to yield very efficient estimates of pdfs. The third class of methods deals with transitions between states described by rate constants. These problems are isomorphic with chemical kinetics problems. Recently, several efficient techniques for this purpose have been developed based on the approach originally proposed by Gillespie. Although the utility of the techniques mentioned above for Bayesian problems has not been determined, further research along these lines is warranted

Pohorille, Andrew↗
DOE OSTI2026

Quantum-classical embedding via ghost Gutzwiller approximation for enhanced simulations of correlated electron systems

Simulating correlated materials on present-day quantum hardware remains challenging due to limited quantum resources. Quantum embedding methods offer a promising route by reducing computational complexity through the mapping of bulk systems onto effective impurity models, allowing more feasible simulations on pre- and early-fault-tolerant quantum devices. Here, this work develops a quantum-classical embedding framework based on the ghost Gutzwiller approximation to enable quantum-enhanced simulations of ground-state properties and spectral functions of correlated electron systems. Circuit complexity is analyzed using an adaptive variational quantum algorithm on a statevector simulator, applied to the infinite-dimensional Hubbard model with increasing ghost mode numbers from 3 to 5, resulting in circuit depths growing from 16 to 104. Noise effects are examined using a realistic error model, revealing significant impact on the spectral weight of the Hubbard bands. To mitigate these effects, the Iceberg quantum error detection code is employed, achieving up to 40% error reduction in simulations. Finally, the accuracy of the density matrix estimation and the derived spectral function is benchmarked on IBM and Quantinuum quantum hardware, featuring distinct qubit-connectivity and employing multiple levels of error mitigation techniques.

Chen, I-Chi [Ames Laboratory (AMES), Ames, IA (Uni↗
DOE OSTI2017

Turbulent transport and mixing in transitional Rayleigh-Taylor unstable flow: A priori assessment of gradient-diffusion and similarity modeling

Data from a 1152×760×1280 direct numerical simulation of a Rayleigh-Taylor mixing layer modeled after a small-Atwood-number water-channel experiment is used to investigate the validity of gradient diffusion and similarity closures a priori. The budgets of the mean flow, turbulent kinetic energy, turbulent kinetic energy dissipation rate, heavy-fluid mass fraction variance, and heavy-fluid mass fraction variance dissipation rate transport equations across the mixing layer were previously analyzed at different evolution times to identify the most important transport and mixing mechanisms. Here a methodology is introduced to systematically estimate model coefficients as a function of time in the closures of the dynamically significant terms in the transport equations by minimizing the L2 norm of the difference between the model and correlations constructed using the simulation data. It is shown that gradient-diffusion and similarity closures used for the turbulent kinetic energy K, turbulent kinetic energy dissipation rate ε, heavy-fluid mass fraction variance S, and heavy-fluid mass fraction variance dissipation rate χ equations capture the shape of the exact, unclosed profiles well over the nonlinear and turbulent evolution regimes. Using order-of-magnitude estimates for the terms in the exact transport equations and their closure models, it is shown that several of the standard closures for the turbulent production and dissipation (destruction) must be modified to include Reynolds-number scalings appropriate for Rayleigh-Taylor flow at small to intermediate Reynolds numbers. The late-time, large Reynolds number coefficients are determined to be different from those used in shear flow applications and largely adopted in two-equation Reynolds-averaged Navier-Stokes (RANS) models of Rayleigh-Taylor turbulent mixing. In addition, it is shown that the predictions of the Boussinesq model for the Reynolds stress agree better with the data when additional buoyancy-related terms are included. It is shown that an unsteady RANS paradigm is needed to predict the transitional flow dynamics from early evolution times, analogous to the small Reynolds number modifications in RANS models of wall-bounded flows in which the production-to-dissipation ratio is far from equilibrium. Although the present study is specific to one particular flow and one set of initial conditions, the methodology could be applied to calibrations of other Rayleigh-Taylor flows with different initial conditions (which may give different results during the early-time, transitional flow stages, and perhaps asymptotic stage). Finally, the implications of these findings for developing high-fidelity eddy viscosity-based turbulent transport and mixing models of Rayleigh-Taylor turbulence are discussed.

42 ENGINEERING↗
DOE OSTI2017

The Arrow of Time in the Collapse of Collisionless Self-gravitating Systems: Non-validity of the Vlasov–Poisson Equation during Violent Relaxation

The collapse of a collisionless self-gravitating system, with the fast achievement of a quasi-stationary state, is driven by violent relaxation, with a typical particle interacting with the time-changing collective potential. It is traditionally assumed that this evolution is governed by the Vlasov–Poisson equation, in which case entropy must be conserved. We run N-body simulations of isolated self-gravitating systems, using three simulation codes, NBODY-6 (direct summation without softening), NBODY-2 (direct summation with softening), and GADGET-2 (tree code with softening), for different numbers of particles and initial conditions. At each snapshot, we estimate the Shannon entropy of the distribution function with three different techniques: Kernel, Nearest Neighbor, and EnBiD. For all simulation codes and estimators, the entropy evolution converges to the same limit as N increases. During violent relaxation, the entropy has a fast increase followed by damping oscillations, indicating that violent relaxation must be described by a kinetic equation other than the Vlasov–Poisson equation, even for N as large as that of astronomical structures. This indicates that violent relaxation cannot be described by a time-reversible equation, shedding some light on the so-called “fundamental paradox of stellar dynamics.” The long-term evolution is well-described by the orbit-averaged Fokker–Planck model, with Coulomb logarithm values in the expected range 10--12. By means of NBODY-2, we also study the dependence of the two-body relaxation timescale on the softening length. The approach presented in the current work can potentially provide a general method for testing any kinetic equation intended to describe the macroscopic evolution of N-body systems.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1999

How to Estimate Attitude from Vector Observations

The most robust estimators minimizing Wahba's loss function are Davenport's q method and the Singular Value Decomposition (SVD) method. The q method is faster than the SVD method with three or more measurements. The other algorithms are less robust since they solve the characteristic polynomial equation to find the maximum eigenvalue of Davenport's K matrix. They are only preferable when speed or processor power is an important consideration. Of these, Fast Optimal Attitude Matrix (FOAM) is the most robust and faster than the q method. Robustness is only an issue for measurements with widely differing accuracies, so the fastest algorithms, Quaternion ESTimator (QUEST), EStimator of the Optimal Quaternion (ESOQ), and ESOQ2, are well suited to star sensor applications.

Markley, F. Landis↗
DOE OSTI2014

Sequential Monte Carlo sampling in hidden Markov models of nonlinear dynamical systems

We investigate the issue of which state functionals can have their uncertainty estimated efficiently in dynamical systems with uncertainty. Because of the high dimensionality and complexity of the problem, sequential Monte Carlo (SMC) methods are used. We investigate SMC methods where the proposal distribution is computed by maximum likelihood or by a linearization approach. We prove that the variance of the SMC method is bounded linearly in the number of time steps when the proposal distribution is truncated normal distribution. We also show that for a moderate large number of steps the error produced by approximation of dynamical systems linearly accumulates on the condition that the logarithm of the density function of noise is Lipschitz continuous. This finding is significant because the uncertainty in many dynamical systems, in particular, in chemical engineering systems, can be assumed to have this nature. We demonstrate our findings for a simple test case from chemical engineering. The theoretical findings provide a foundation for the parallel software SISTOS.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1994

Time scales of pattern evolution from cross-spectrum analysis of advanced very high resolution radiometer and coastal zone color scanner imagery

We have selected square subareas (110 km on a side) from coastal zone color scanner (CZCS) and advanced very high resolution radiometer (AVHRR) images for 1981 in the California Current region off northern California for which we could identify sequences of cloud-free data over periods of days to weeks. We applied a two-dimensional fast Fourier transformation to images after median filtering, (x, y) plane removal, and cosine tapering. We formed autospectra and coherence spectra as functions of a scalar wavenumber. Coherence estimates between pairs of images were plotted against time separation between images for several wide wavenumber bands to provide a temporal lagged coherence function. The temporal rate of loss of correlation (decorrelation time scale) in surface patterns provides a measure of the rate of pattern change or evolution as a function of spatial dimension. We found that patterns evolved (or lost correlation) approximately twice as rapidly in upwelling jets as in the 'quieter' regions between jets. The rapid evolution of pigment patterns (lifetime of about 1 week or less for scales of 50-100 km) ought to hinder biomass transfer to zooplankton predators compared with phytoplankton patches that persist for longer times. We found no significant differences between the statistics of CZCS and AVHRR images (spectral shape or rate of decorrelation). In addition, in two of the three areas studied, the peak correlation between AVHRR and CZCS images from the same area occurred at zero lag, indicating that the patterns evolved simutaneously. In the third area, maximum coherence between thermal and pigment patterns occurred when pigment images lagged thermal images by 1-2 days, mirroring the expected lag of high pigment behind low temperatures (and high nutrients) in recently upwelled water. We conclude that in dynamic areas such as coastal upwelling systems, the phytoplankton cells (identified by pigment color patterns) behave largely as passive scalars at the mesoscale and that growth, death, and sinking of phytoplankton collectively play at most a mariginal role in determining the spectral statistics of the pigment patterns.

Denman, Kenneth L.↗
DOE OSTI2018

Field-Induced Desorption of Cesium from Rhenium

Desorption of cesium atoms from a rhenium point emitter in an electric field has been studied by method of field-desorption microscopy (FDM). Dependence of the desorbing field on degree of emitter surface coverage with Cs atoms is established. The heat of Cs-atom adsorption, which is dependent on the surface concentration of adsorbate and work function of the surface, is estimated in the framework of the model of mirror-image forces for field-induced desorption. Saturation of the rhenium emitter with carbon leads to changes in the character of desorption and in the distribution of desorption zones on the emitter surface.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Assessment of the dose reduction potential of a model-based iterative reconstruction algorithm using a task-based performance metrology

Purpose: Different computed tomography (CT) reconstruction techniques offer different image quality attributes of resolution and noise, challenging the ability to compare their dose reduction potential against each other. The purpose of this study was to evaluate and compare the task-based imaging performance of CT systems to enable the assessment of the dose performance of a model-based iterative reconstruction (MBIR) to that of an adaptive statistical iterative reconstruction (ASIR) and a filtered back projection (FBP) technique. Methods: The ACR CT phantom (model 464) was imaged across a wide range of mA setting on a 64-slice CT scanner (GE Discovery CT750 HD, Waukesha, WI). Based on previous work, the resolution was evaluated in terms of a task-based modulation transfer function (MTF) using a circular-edge technique and images from the contrast inserts located in the ACR phantom. Noise performance was assessed in terms of the noise-power spectrum (NPS) measured from the uniform section of the phantom. The task-based MTF and NPS were combined with a task function to yield a task-based estimate of imaging performance, the detectability index (d′). The detectability index was computed as a function of dose for two imaging tasks corresponding to the detection of a relatively small and a relatively large feature (1.5 and 25 mm, respectively). The performance of MBIR in terms of the d′ was compared with that of ASIR and FBP to assess its dose reduction potential. Results: Results indicated that MBIR exhibits a variability spatial resolution with respect to object contrast and noise while significantly reducing image noise. The NPS measurements for MBIR indicated a noise texture with a low-pass quality compared to the typical midpass noise found in FBP-based CT images. At comparable dose, the d′ for MBIR was higher than those of FBP and ASIR by at least 61% and 19% for the small feature and the large feature tasks, respectively. Compared to FBP and ASIR, MBIR indicated a 46%–84% dose reduction potential, depending on task, without compromising the modeled detection performance. Conclusions: The presented methodology based on ACR phantom measurements extends current possibilities for the assessment of CT image quality under the complex resolution and noise characteristics exhibited with statistical and iterative reconstruction algorithms. The findings further suggest that MBIR can potentially make better use of the projections data to reduce CT dose by approximately a factor of 2. Alternatively, if the dose held unchanged, it can improve image quality by different levels for different tasks.

60 APPLIED LIFE SCIENCES↗