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NASA NTRS1974

Analysis of multiple pulse NMR in solids. II

A systematic method, an extension of the average Hamiltonian formalism, is presented for calculating the effects of pulse errors and imperfections in the multiple pulse nuclear magnetic resonance experiments. Application of this method to account for effects of pulse nonidealities such as phase errors, phase transient effects, pulse size errors, and rf inhomogeneity is found to agree with experimental observation, and the results furnish a basis for understanding the complex couplings between the pulse errors and other interactions such as the dipolar and the chemical shift Hamiltonians.

Rhim, W.-K.↗

NASA NTRS1994

Redshift data and statistical inference

Frequency histograms and the 'power spectrum analysis' (PSA) method, the latter developed by Yu & Peebles (1969), have been widely employed as techniques for establishing the existence of periodicities. We provide a formal analysis of these two classes of methods, including controlled numerical experiments, to better understand their proper use and application. In particular, we note that typical published applications of frequency histograms commonly employ far greater numbers of class intervals or bins than is advisable by statistical theory sometimes giving rise to the appearance of spurious patterns. The PSA method generates a sequence of random numbers from observational data which, it is claimed, is exponentially distributed with unit mean and variance, essentially independent of the distribution of the original data. We show that the derived random processes is nonstationary and produces a small but systematic bias in the usual estimate of the mean and variance. Although the derived variable may be reasonably described by an exponential distribution, the tail of the distribution is far removed from that of an exponential, thereby rendering statistical inference and confidence testing based on the tail of the distribution completely unreliable. Finally, we examine a number of astronomical examples wherein these methods have been used giving rise to widespread acceptance of statistically unconfirmed conclusions.

Newman, William I.↗

NASA NTRSDate not supplied

Design, Formalization, and Verification of Decision Making for Intelligent Systems

The development of autonomous systems requires a rigorous process that can guarantee a system’s reliability in critical applications. At its core, an autonomous system bases its behavior on a well-defined decision making system. In this paper, we present a methodological basis for the design, formalization and formal verification of Decision Making systems for autonomous agents. The approach is generally applicable to operational objectives that can be functionally decomposed and subsequently represented as Hierarchical Finite State Machines. As a case study, we present the application of this method to implement a Decision Making model in Simulink. Furthermore, we present how we use NASA’s FRET tool to write requirements in structured natural language and generate formal specifications that can be automatically digested by NASA’s CoCoSim tool. Finally, we present how, by leveraging CoCoSim, we perform formal verification against the Simulink model and present analysis results.

Model-based development↗

NASA NTRSDate not supplied

Design, Formalization, and Verification of Decision Making for Intelligent Systems

Model-based development↗

DOE OSTI2023

Analysis of the MUSIC 3 He Multiplicity Data

A measurement campaign called the Measurement of Uranium Subcritical and Critical (MUSiC) was performed on a range of configurations of highly-enriched uranium (HEU) from December 2020 through April of 2021. While part of the focus was to measure reactor kinetics parameters on delayed supercritical systems, an additional focus was performing neutron noise measurements on subcritical configurations from deeply subcritical to nearly delayed critical. Multiple detector systems were used to perform these measurements, such as a 3 He multiplicity detector called the Neutron Multiplicity Array Detector (NoMAD) and a liquid scintillator system called the Rossi-α Measurement Rapid Organic Discriminating Detector (RAM-RODD). Also included were a scintillator system from the University of Michigan and a set of small 3He tubes that have previously been used to measure Rossi-α values on near-critical systems. The focus of this paper will be a comparison of prospective analysis methods for the NoMAD measurements. Previous subcritical measurements at the National Criticality Experiments Research Center (NCERC) submitted to the International Criticality Safety Benchmark Evaluation Project (ICSBEP) used the Hage-Cifarelli formalism of the Feynman Variance-to-Mean method. This relies on the time correlations of neutron detections to infer the spontaneous fission rate and neutron multiplication of a system through binning the time tagged detections and analyzing resulting histograms of the numbers of counts. However, there are other neutron noise methods that rely on similar processes, such as the Hansen-Dowdy formalism which uses a slightly different methodology to extract multiplication from the neutron multiplicity counting moments. Comparisons can be made between these experimental results and those obtained through simulations to validate or identify deficiencies in analysis, detection methods, or the underlying nuclear data. Different time gating strategies and their effects on count rate uncertainties are also investigated.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2017

Efficient electronic structure theory via hierarchical scale-adaptive coupled-cluster formalism: I. Theory and computational complexity analysis

In this work, a novel reduced-scaling, general-order coupled-cluster approach is formulated by exploiting hierarchical representations of many-body tensors, combined with the recently suggested formalism of scale-adaptive tensor algebra. Inspired by the hierarchical techniques from the renormalization group approach, H/H 2 -matrix algebra and fast multipole method, the computational scaling reduction in our formalism is achieved via coarsening of quantum many-body interactions at larger interaction scales, thus imposing a hierarchical structure on many-body tensors of coupled-cluster theory. In our approach, the interaction scale can be defined on any appropriate Euclidean domain (spatial domain, momentum-space domain, energy domain, etc.). Additionally, we show that the hierarchically resolved many-body tensors reduce the storage requirements to O(N), where N is the number of simulated quantum particles. Subsequently, we prove that any connected many-body diagram with arbitrary-order tensors, e.g., an arbitrary coupled-cluster diagram, can be evaluated in O(NlogN) floating-point operations. On top of that, we elaborate an additional approximation to further reduce the computational complexity of higher-order coupled-cluster equations, i.e., equations involving higher than double excitations, which otherwise would introduce a large prefactor into formal O(NlogN) scaling.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Energy/dissipation-preserving Birkhoffian multi-symplectic methods for Maxwell's equations with dissipation terms

In this study, we propose two new energy/dissipation-preserving Birkhoffian multi-symplectic methods (Birkhoffian and Birkhoffian box) for Maxwell's equations with dissipation terms. After investigating the non-autonomous and autonomous Birkhoffian formalism for Maxwell's equations with dissipation terms, we first apply a novel generating functional theory to the non-autonomous Birkhoffian formalism to propose our Birkhoffian scheme, and then implement a central box method to the autonomous Birkhoffian formalism to derive the Birkhoffian box scheme. We have obtained four formal local conservation laws and three formal energy global conservation laws. We have also proved that both of our derived schemes preserve the discrete version of the global/local conservation laws. Furthermore, the stability, dissipation and dispersion relations are also investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, dissipation-preserving for Maxwell's equations in a perfectly matched layer (PML) medium and have second order accuracy in both time and space. Numerical experiments for problems with exact theoretical results are given to demonstrate that the Birkhoffian multi-symplectic schemes are much more accurate in preserving energy than both the exponential finite-difference time-domain (FDTD) method and traditional Hamiltonian scheme. Finally, we also solve the electromagnetic pulse (EMP) propagation problem and the numerical results show that the Birkhoffian scheme recovers the magnitude of the current source and reaction history very well even after long time propagation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Time-dependent non-equilibrium dielectric response in QM/continuum approaches

The Polarizable Continuum Models (PCMs) are some of the most inexpensive yet successful methods for including the effects of solvation in quantum-mechanical calculations of molecular systems. However, when applied to the electronic excitation process, these methods are restricted to dichotomously assuming either that the solvent has completely equilibrated with the excited solute charge density (infinite-time limit), or that it retains the configuration that was in equilibrium with the solute prior to excitation (zero-time limit). This renders the traditional PCMs inappropriate for resolving time-dependent solvent effects on non-equilibrium solute electron dynamics like those implicated in the instants following photoexcitation of a solvated molecular species. To extend the existing methods to this non-equilibrium regime, we herein derive and apply a new formalism for a general time-dependent continuum embedding method designed to be propagated alongside the solute’s electronic degrees of freedom in the time domain. Given the frequency-dependent dielectric constant of the solvent, an equation of motion for the dielectric polarization is derived within the PCM framework and numerically integrated simultaneously with the time-dependent Hartree fock/density functional theory equations. Results for small molecular systems show the anticipated dipole quenching and electronic state dephasing/relaxation resulting from out-of-phase charge fluctuations in the dielectric and embedded quantum system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

Opinion: Making the Most of Colour Rendition Research

After decades of debate, new methods for characterizing color rendition have been formalized, providing an improved system of tools to aid technology developers and lighting specifiers. Solid-state lighting, previously burdened by legacy measures based on outdated science, is positioned to take advantage of these new tools to provide tailored, efficient lighting that better meets the needs of specific architectural lighting applications. This transition requires new guidance, however, presenting an opportunity for researchers. There are several key methodological considerations specific to experiments investigating color rendition that will help build a base of guidance that can be widely applied. The importance of these ideas mostly stems from new knowledge gained in the last five years, but their origins date back much further. 1.The spectral power distribution must be adequately varied to stress the measure(s) of color rendition being evaluated. Often, this means varying the gamut shape—the pattern of shift across different hues—to probe weaknesses of hue-averaged characterizations, avoiding misleading conclusions resulting from limited variation in the stimuli. 2.Evaluating the role of chromaticity on color quality evaluations requires careful accommodation of chromatic adaptation to prevent a centering bias. Asking for delayed responses may be insufficient if chromaticity changes are apparent to participants, just as side-by-side viewing of different chromaticities may not produce results that can be reliably applied in the field. It is also critical that color rendition and chromaticity conditions are varied independently. 3.The stimulus being viewed is the interaction of light and objects’ spectral reflectances. This interaction should be quantified in order to assess how derived guidelines will apply measures using standardized color sample sets. Although light source characterizations are typically used to model responses, the objects and their presentation may strongly influence evaluations. 4.Context is important. Many factors—some investigated, others hypothesized—can influence subjective evaluations of color quality, including illuminance level, type of scene, object familiarity, color composition, viewing duration, and viewer traits. Although their influence on research results is unavoidable, the effects of these contextual factors must be carefully considered in developing guidance. Appropriate experimental design can often mitigate negative consequences arising from these considerations. At a minimum, it is crucial to understand how each of these considerations can influence experimental outcomes, as well as the interpretation and application of the results in practice. Consulting other experts prior to conducting an experiment can help ensure appropriate, up-to-date research methods will be used, so that the results will be novel and useful—and not rejected during peer review. There is an interesting feedback loop: technology development provides new research tools, which allow for refined research methods and new results that lead to more technology development. It is time to make a concerted, collective effort to improve color rendition research so that the full potential of solid-state lighting and new characterization methods can be realized, ensuring that high-efficiency, high-utility, high-appeal lighting systems become standard.

Royer, Michael P.↗

DOE OSTI2015

An auxiliary-field quantum Monte Carlo study of the chromium dimer

The chromium dimer (Cr{sub 2}) presents an outstanding challenge for many-body electronic structure methods. Its complicated nature of binding, with a formal sextuple bond and an unusual potential energy curve (PEC), is emblematic of the competing tendencies and delicate balance found in many strongly correlated materials. We present an accurate calculation of the PEC and ground state properties of Cr{sub 2}, using the auxiliary-field quantum Monte Carlo (AFQMC) method. Unconstrained, exact AFQMC calculations are first carried out for a medium-sized but realistic basis set. Elimination of the remaining finite-basis errors and extrapolation to the complete basis set limit are then achieved with a combination of phaseless and exact AFQMC calculations. Final results for the PEC and spectroscopic constants are in excellent agreement with experiment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

Application of quantum mechanics/molecular mechanics methods in the study of enzymatic reaction mechanisms

Quantum mechanics/molecular mechanics ( QM / MM ) methods offer a very appealing option for the computational study of enzymatic reaction mechanisms, by separating the problem into two parts that can be treated with different computational methods. Hence, in a QM / MM formalism, the part of the system in which catalysis actually occurs and that involves the active site, substrates and directly participating amino acid residues is treated at an adequate quantum mechanical level to describe the chemistry taking place. For the remaining of the enzyme, which does not participate directly in the reaction, but that typically involves a much larger number of atoms, molecular mechanics is employed, traditionally through the application of a biomolecular force field. When applied with care, QM / MM methods can be used with great advantage in comparing, at a structural and energetic level, different mechanistic proposals, discarding mechanistic alternatives and proposing new mechanistic pathways that are consistent with the available experimental data. With time, diverse flavors within the QM / MM methods have emerged, differing in a variety of technical and conceptual aspects. Hence present alternatives differ between additive and subtractive QM / MM schemes, the type of boundary schemes, and the way in which the electrostatic interactions between the two regions are accounted for. Also, single‐conformation QM / MM , multi‐ PES approaches, and QM / MM Molecular Dynamics coexist today, each type with its own advantages and limitations. This review focuses on the application of QM / MM methods in the study of enzymatic reaction mechanisms, briefly presenting also the most important technical aspects involved in these calculations. Particular attention is dedicated to the application of the single‐conformation QM / MM , multi‐ PES QM / MM studies, and QM / MM‐FEP methods and to the advantages and disadvantages of the different types of QM / MM . Recent breakthroughs are also introduced. A selection of hand‐picked examples is used to illustrate such features. WIREs Comput Mol Sci 2017, 7:e1281. doi: 10.1002/wcms.1281 This article is categorized under: Structure and Mechanism > Computational Biochemistry and Biophysics Structure and Mechanism > Reaction Mechanisms and Catalysis Electronic Structure Theory > Combined QM/MM Methods

Sousa, Sérgio Filipe↗

DOE OSTI2016

Generalized quantum master equations in and out of equilibrium: When can one win?

Generalized quantum master equations (GQMEs) are an important tool in modeling chemical and physical processes. For a large number of problems, it has been shown that exact and approximate quantum dynamics methods can be made dramatically more efficient, and in the latter case more accurate, by proceeding via the GQME formalism. However, there are many situations where utilizing the GQME approach with an approximate method has been observed to return the same dynamics as using that method directly. Here, for systems both in and out of equilibrium, we provide a more detailed understanding of the conditions under which using an approximate method can yield benefits when combined with the GQME formalism. In particular, we demonstrate the necessary manipulations, which are satisfied by exact quantum dynamics, that are required to recast the memory kernel in a form that can be analytically shown to yield the same result as a direct application of the dynamics regardless of the approximation used. By considering the connections between these forms of the kernel, we derive the conditions that approximate methods must satisfy if they are to offer different results when used in conjunction with the GQME formalism. These analytical results thus provide new insights as to when proceeding via the GQME approach can be used to improve the accuracy of simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Quantum Monte Carlo estimation of complex-time correlations for the study of the ground-state dynamic structure function

We present a method based on the path integral Monte Carlo formalism for the calculation of ground-state time correlation functions in quantum systems. The key point of the method is the consideration of time as a complex variable whose phase δ acts as an adjustable parameter. By using high-order approximations for the quantum propagator, it is possible to obtain Monte Carlo data all the way from purely imaginary time to δ values near the limit of real time. As a consequence, it is possible to infer accurately the spectral functions using simple inversion algorithms. We test this approach in the calculation of the dynamic structure function S(q, ω) of two one-dimensional model systems, harmonic and quartic oscillators, for which S(q, ω) can be exactly calculated. We notice a clear improvement in the calculation of the dynamic response with respect to the common approach based on the inverse Laplace transform of the imaginary-time correlation function.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1994

A method for the probabilistic design assessment of composite structures

A formal procedure for the probabilistic design assessment of a composite structure is described. The uncertainties in all aspects of a composite structure (constituent material properties, fabrication variables, structural geometry, service environments, etc.), which result in the uncertain behavior in the composite structural responses, are included in the assessment. The probabilistic assessment consists of design criteria, modeling of composite structures and uncertainties, simulation methods, and the decision making process. A sample case is presented to illustrate the formal procedure and to demonstrate that composite structural designs can be probabilistically assessed with accuracy and efficiency.

Shiao, Michael C.↗

DOE OSTI2016

Calculation of the static and dynamical correlation energy of pseudo-one-dimensional beryllium systems via a many-body expansion

Due to the importance of both static and dynamical correlation in the bond formation, low-dimensional beryllium systems constitute interesting case studies to test correlation methods. Aiming to describe the whole dissociation curve of extended Be systems we chose to apply the method of increments (MoI) in its multireference (MR) formalism. To gain insight into the main characteristics of the wave function, we started by focusing on the description of small Be chains using standard quantum chemical methods. In a next step we applied the MoI to larger beryllium systems, starting from the Be{sub 6} ring. The complete active space formalism was employed and the results were used as reference for local MR calculations of the whole dissociation curve. Although this is a well-established approach for systems with limited multireference character, its application regarding the description of whole dissociation curves requires further testing. Subsequent to the discussion of the role of the basis set, the method was finally applied to larger rings and extrapolated to an infinite chain.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

On the simulation of indistinguishable fermions in the many-body Wigner formalism

The simulation of quantum systems consisting of interacting, indistinguishable fermions is an incredible mathematical problem which poses formidable numerical challenges. Many sophisticated methods addressing this problem are available which are based on the many-body Schrödinger formalism. Recently a Monte Carlo technique for the resolution of the many-body Wigner equation has been introduced and successfully applied to the simulation of distinguishable, spinless particles. This numerical approach presents several advantages over other methods. Indeed, it is based on an intuitive formalism in which quantum systems are described in terms of a quasi-distribution function, and highly scalable due to its Monte Carlo nature. In this work, we extend the many-body Wigner Monte Carlo method to the simulation of indistinguishable fermions. To this end, we first show how fermions are incorporated into the Wigner formalism. Then we demonstrate that the Pauli exclusion principle is intrinsic to the formalism. As a matter of fact, a numerical simulation of two strongly interacting fermions (electrons) is performed which clearly shows the appearance of a Fermi (or exchange–correlation) hole in the phase-space, a clear signature of the presence of the Pauli principle. To conclude, we simulate 4, 8 and 16 non-interacting fermions, isolated in a closed box, and show that, as the number of fermions increases, we gradually recover the Fermi–Dirac statistics, a clear proof of the reliability of our proposed method for the treatment of indistinguishable particles.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Superspin renormalization and slow relaxation in random spin systems

We develop an excited-state real-space renormalization group (RSRG-X) formalism to describe the dynamics of conserved densities in randomly interacting spin-12 systems. Our formalism is suitable for systems with U(1) and Z2 symmetries, and we apply it to chains of randomly positioned spins with dipolar XX+YY interactions, as arise in Rydberg quantum simulators and other platforms. The formalism generates a sequence of effective Hamiltonians that provide approximate descriptions for dynamics on successively smaller energy scales. These effective Hamiltonians involve “superspins”: two-level collective degrees of freedom constructed from (anti)aligned microscopic spins. Conserved densities can then be understood as relaxing via coherent collective spin flips. For the well-studied simpler case of randomly interacting nearest-neighbor XX+YY chains, the superspins reduce to single spins. Our formalism also leads to a numerical method capable of simulating the dynamics up to an otherwise inaccessible combination of large system size and late time. Focusing on disorder-averaged infinite-temperature autocorrelation functions, in particular the spin survival probability Sp¯(t), we demonstrate quantitative agreement between our algorithm and exact diagonalization (ED) at low but nonzero frequencies. Such agreement holds for chains with nearest-neighbor, next-nearest-neighbor, and long-range dipolar interactions. Our results indicate decay of Sp¯(t) slower than any power law and feature no significant deviation from the ∼1/ln2(t) asymptote expected from the infinite-randomness fixed-point of the nearest-neighbor model. We also apply the RSRG-X formalism to two-dimensional long-range systems of moderate size and find slow late-time decay of Sp¯(t).

Zhao, Yi J↗

DOE OSTI2015

S-TYPE AND P-TYPE HABITABILITY IN STELLAR BINARY SYSTEMS: A COMPREHENSIVE APPROACH. II. ELLIPTICAL ORBITS

In the first paper of this series, a comprehensive approach has been provided for the study of S-type and P-type habitable regions in stellar binary systems, which was, however, restricted to circular orbits of the stellar components. Fortunately, a modest modification of the method also allows for the consideration of elliptical orbits, which of course entails a much broader range of applicability. This augmented method is presented here, and numerous applications are conveyed. In alignment with Paper I, the selected approach considers a variety of aspects, which comprise the consideration of a joint constraint including orbital stability and a habitable region for a possible system planet through the stellar radiative energy fluxes ({sup r}adiative habitable zone{sup ;} RHZ). The devised method is based on a combined formalism for the assessment of both S-type and P-type habitability; in particular, mathematical criteria are deduced for which kinds of systems S-type and P-type habitable zones are realized. If the RHZs are truncated by the additional constraint of orbital stability, the notation of ST-type and PT-type habitability applies. In comparison to the circular case, it is found that in systems of higher eccentricity, the range of the RHZs is significantly reduced. Moreover, for a considerable number of models, the orbital stability constraint also reduces the range of S-type and P-type habitability. Nonetheless, S-, P-, ST-, and PT-type habitability is identified for a considerable set of system parameters. The method as presented is utilized for BinHab, an online code available at The University of Texas at Arlington.

79 ASTRONOMY AND ASTROPHYSICS↗