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At least 1,333 records · Page 74
All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

Calculation of Scattering Amplitude Without Partial Analysis: Inclusion of Exchange - II

There was a method for calculating the whole scattering amplitude, f(Omega(sub k)), directly. The idea was to calculate the complete wave function Psi numerically, and use it in an integral expression for f, which can be reduced to a 2 dimensional quadrature. The original application was for e-H scattering without exchange. There the Schrodinger reduces a 2-d partial differential equation (pde), which was solved using the finite element method (FEM). Here we extend the method to the exchange approximation. The S.E. can be reduced to a pair of coupled pde's, which are again solved by the FEM. The formal expression for f(Omega(sub k)) consists two integrals, f+/- = f(sub d) +/- f(sub e); f(sub d) is formally the same integral as the no-exchange f. We have also succeeded in reducing f(sub e) to a 2-d integral. Results will be presented at the meeting.

Temkin, Aaron↗
NASA NTRS2003

Electron-H Elastic Scattering

Precision calculations for e^{-}-H and e^{-}-He^{+} for S-wave scattering in the elastic region have been carried out using the optical potential approach. This formalism is now extended to e^{-}-H P-wave scattering in the elastic region. The scattering equations are solved by the non-iterative method. Phase shifts are calculated using Hylleraas-type correlation functions up to 84 terms. Results are rigorous lower bounds to the exact phase shifts and they are compared to those obtained in previous calculations.

Bhatia, A. K.↗
NASA NTRS2003

Principles for Integrating Mars Analog Science, Operations, and Technology Research

During the Apollo program, the scientific community and NASA used terrestrial analog sites for understanding planetary features and for training astronauts to be scientists. Human factors studies (Harrison, Clearwater, & McKay 1991; Stuster 1996) have focused on the effects of isolation in extreme environments. More recently, with the advent of wireless computing, we have prototyped advanced EVA technologies for navigation, scheduling, and science data logging (Clancey 2002b; Clancey et al., in press). Combining these interests in a single expedition enables tremendous synergy and authenticity, as pioneered by Pascal Lee's Haughton-Mars Project (Lee 2001; Clancey 2000a) and the Mars Society s research stations on a crater rim on Devon Island in the High Canadian Arctic (Clancey 2000b; 2001b) and the Morrison Formation of southeast Utah (Clancey 2002a). Based on this experience, the following principles are proposed for conducting an integrated science, operations, and technology research program at analog sites: 1) Authentic work; 2) PI-based projects; 3) Unencumbered baseline studies; 4) Closed simulations; and 5) Observation and documentation. Following these principles, we have been integrating field science, operations research, and technology development at analog sites on Devon Island and in Utah over the past five years. Analytic methods include work practice simulation (Clancey 2002c; Sierhuis et a]., 2000a;b), by which the interaction of human behavior, facilities, geography, tools, and procedures are formalized in computer models. These models are then converted into the runtime EVA system we call mobile agents (Clancey 2002b; Clancey et al., in press). Furthermore, we have found that the Apollo Lunar Surface Journal (Jones, 1999) provides a vast repository or understanding astronaut and CapCom interactions, serving as a baseline for Mars operations and quickly highlighting opportunities for computer automation (Clancey, in press).

Clancey, William J.↗
NASA NTRS2007

Scattering of Low Energy Electrons and Positrons from Hydrogenic Systems and Applications

While the electron scatters from the target, the target no longer stays in its original form. One of the first methods to take into account the distortion of the target at low incident energies is the method of polarized orbitals. In this method the wave function for the process is written using the first-order perturbation theory and the equation for the scattering function is derived from the Schradinger equation. This method has been very successful in calculating the phase shifts and therefore the cross sections at various energies. The total wave function can be used to calculate photoionization cross sections. The disadvantage of this approach is that the method is not variational and therefore does not provide bounds on the phase shifts. These difficulties can be overcome by using the Feshbach projection operator formalism. This approach has been employed for the scattering of electrons and positrons from targets. Results of various calculations will be discussed.

Bhatia, Anand K.↗
NASA NTRS2012

Sensitivity Analysis for Atmospheric Infrared Sounder (AIRS) CO2 Retrieval

The Atmospheric Infrared Sounder (AIRS) is a thermal infrared sensor able to retrieve the daily atmospheric state globally for clear as well as partially cloudy field-of-views. The AIRS spectrometer has 2378 channels sensing from 15.4 micrometers to 3.7 micrometers, of which a small subset in the 15 micrometers region has been selected, to date, for CO2 retrieval. To improve upon the current retrieval method, we extended the retrieval calculations to include a prior estimate component and developed a channel ranking system to optimize the channels and number of channels used. The channel ranking system uses a mathematical formalism to rapidly process and assess the retrieval potential of large numbers of channels. Implementing this system, we identifed a larger optimized subset of AIRS channels that can decrease retrieval errors and minimize the overall sensitivity to other iridescent contributors, such as water vapor, ozone, and atmospheric temperature. This methodology selects channels globally by accounting for the latitudinal, longitudinal, and seasonal dependencies of the subset. The new methodology increases accuracy in AIRS CO2 as well as other retrievals and enables the extension of retrieved CO2 vertical profiles to altitudes ranging from the lower troposphere to upper stratosphere. The extended retrieval method for CO2 vertical profile estimation using a maximum-likelihood estimation method. We use model data to demonstrate the beneficial impact of the extended retrieval method using the new channel ranking system on CO2 retrieval.

sensitivity analysis↗
DOE OSTI2019

High-order gradients with the shifted boundary method: An embedded enriched mixed formulation for elliptic PDEs

Here, we propose an extension of the embedded boundary method known as “shifted boundary method” to elliptic diffusion equations in mixed form (e.g., Darcy flow, heat diffusion problems with rough coefficients, etc.). Our aim is to obtain an improved formulation that, for linear finite elements, is at least second-order accurate for both flux and primary variable, when either Dirichlet or Neumann boundary conditions are applied. Following previous work of Nishikawa and Mazaheri in the context of residual distribution methods, we consider the mixed form of the diffusion equation (i.e., with Darcy-type operators), and introduce an enrichment of the primary variable. This enrichment is obtained exploiting the relation between the primary variable and the flux variable, which is explicitly available at nodes in the mixed formulation. The proposed enrichment mimics a formally quadratic pressure approximation, although only nodal unknowns are stored, similar to a linear finite element approximation. We consider both continuous and discontinuous finite element approximations and present two approaches: a non-symmetric enrichment, which, as in the original references, only improves the consistency of the overall method; and a symmetric enrichment, which enables a full error analysis in the classical finite element context. Combined with the shifted boundary method, these two approaches are extended to high-order embedded computations, and enable the approximation of both primary and flux (gradient) variables with second-order accuracy, independently on the type of boundary conditions applied. We also show that the primary variable is third-order accurate, when pure Dirichlet boundary conditions are embedded.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Self-consistency in GWΓ formalism leading to quasiparticle-quasiparticle couplings

Within many-body perturbation theory, Hedin's formalism offers a systematic way to iteratively compute the self-energy Σ of any dynamically correlated interacting system, provided one can evaluate the interaction vertex Γ exactly. This is, however, impossible, in general, for it involves the functional derivative of Σ with respect to the Green's function. Here, we analyze the structure of this derivative, splitting it into four contributions and outlining the type of quasiparticle interactions that each of them generate. Moreover, we show how, in the implementation of self-consistency, the action of these contributions can be classified into two: A quantitative renormalization of previously included interaction terms and the inclusion of qualitatively distinct interaction terms through successive functional derivatives of Γ itself. Implementing this latter type of self-consistency can extend the validity of perturbative approximations based on Hedin's equations toward the high interaction limit, as we show in the example of the Hubbard dimer. Furthermore, our analysis also provides a unifying perspective on the perturbation theory landscape, showing how the T-matrix approach is completely contained in Hedin's formalism.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Radiative classical gravitational observables at $ \mathcal{O} $(G 3 ) from scattering amplitudes

We compute classical gravitational observables for the scattering of two spinless black holes in general relativity and N =8 supergravity in the formalism of Kosower, Maybee, and O’Connell (KMOC). We focus on the gravitational impulse with radiation reaction and the radiated momentum in black hole scattering at $ \mathcal{O} $(G 3 ) to all orders in the velocity. These classical observables require the construction and evaluation of certain loop-level quantities which are greatly simplified by harnessing recent advances from scattering amplitudes and collider physics. In particular, we make use of generalized unitarity to construct the relevant loop integrands, employ reverse unitarity, the method of regions, integration-by-parts (IBP), and (canonical) differential equations to simplify and evaluate all loop and phase-space integrals to obtain the classical gravitational observables of interest to two-loop order. The KMOC formalism naturally incorporates radiation effects which enables us to explore these classical quantities beyond the conservative two-body dynamics. From the impulse and the radiated momentum, we extract the scattering angle and the radiated energy. Finally, we discuss universality of the impulse in the high-energy limit and the relation to the eikonal phase.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Learning local, quenched disorder in plasticity and other crackling noise phenomena

Abstract When far from equilibrium, many-body systems display behavior that strongly depends on the initial conditions. A characteristic such example is the phenomenon of plasticity of crystalline and amorphous materials that strongly depends on the material history. In plasticity modeling, the history is captured by a quenched, local and disordered flow stress distribution. While it is this disorder that causes avalanches that are commonly observed during nanoscale plastic deformation, the functional form and scaling properties have remained elusive. In this paper, a generic formalism is developed for deriving local disorder distributions from field-response (e.g., stress/strain) timeseries in models of crackling noise. We demonstrate the efficiency of the method in the hysteretic random-field Ising model and also, models of elastic interface depinning that have been used to model crystalline and amorphous plasticity. We show that the capacity to resolve the quenched disorder distribution improves with the temporal resolution and number of samples.

36 MATERIALS SCIENCE↗
DOE OSTI2015

ON THE USE OF SHOT NOISE FOR PHOTON COUNTING

Lieu et al. have recently claimed that it is possible to substantially improve the sensitivity of radio-astronomical observations. In essence, their proposal is to make use of the intensity of the photon shot noise as a measure of the photon arrival rate. Lieu et al. provide a detailed quantum-mechanical calculation of a proposed measurement scheme that uses two detectors and conclude that this scheme avoids the sensitivity degradation that is associated with photon bunching. If correct, this result could have a profound impact on radio astronomy. Here I present a detailed analysis of the sensitivity attainable using shot-noise measurement schemes that use either one or two detectors, and demonstrate that neither scheme can avoid the photon bunching penalty. I perform both semiclassical and fully quantum calculations of the sensitivity, obtaining consistent results, and provide a formal proof of the equivalence of these two approaches. These direct calculations are furthermore shown to be consistent with an indirect argument based on a correlation method that establishes an independent limit to the sensitivity of shot-noise measurement schemes. Furthermore, these calculations are directly applicable to the regime of interest identified by Lieu et al. Collectively, these results conclusively demonstrate that the photon-bunching sensitivity penalty applies to shot-noise measurement schemes just as it does to ordinary photon counting, in contradiction to the fundamental claim made by Lieu et al. The source of this contradiction is traced to a logical fallacy in their argument.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Three-body Faddeev equations in two-particle Alt-Grassberger-Sandhas form with Distorted-Wave-Born-approximation amplitudes as effective potentials

A(d, p)B reactions on heavier nuclei are peripheral at sub-Coulomb energies and can be peripheral even at energies above the Coulomb barrier due to the presence of the distorted waves in the initial and final channels. Usually, to analyze such reactions the distorted-wave-Born-approximation (DWBA) is used. The DWBA amplitude for peripheral reactions is parametrized in terms of the asymptotic normalization coefficient (ANC) of the bound state B = (n A). However, in the DWBA, the coupling of the different channels is not taken into account explicitly. The three-body Faddeev equations written as the two-particle Alt-Grassberger-Sandhas (AGS) equations are very suitable for the analysis of the A(d, p)B reactions because they take into account explicitly the coupling of the different channels. It is well known that the overall normalization of the DWBA amplitude or even of the more advanced continuum-discretized coupled channels (CDCC) amplitude for peripheral reactions (both sub-Coulomb and above the Coulomb barrier) is determined by the ANC. However, it is not apparent that it is the case for the AGS solution due to the coupling of the (d, p) channel to other channels. In this paper, it is proved that the sub-Coulomb A(d, p)B reaction amplitude, which is a solution of the two-body AGS equations, is peripheral and is parametrized in terms of the ANC of the bound state B = (nA) if the corresponding DWBA amplitude is peripheral. Both nonlocal separable and local nuclear interaction potentials between the constituent particles are considered. To prove the peripheral character of the AGS amplitude for the sub-Coulomb A(d, p)B reactions the effective potentials are expressed in terms of the corresponding sub-Coulomb DWBA amplitudes of the different channels. The analysis of the A(d, p)B reactions above the Coulomb barrier requires the inclusion of the optical potentials. Hence, to analyze such reactions, the AGS equations are generalized by including the optical nuclear potentials in the same manner as it is done in the DWBA. The obtained AGS equations contain the DWBA effective potentials with distorted waves generated by the sum of the nuclear optical and the channel Coulomb potentials. It is shown that if the DWBA amplitude is peripheral than it is also the case for the AGS amplitude, which is also parametrized in terms of the ANC of the bound state B = (nA). Furthermore, the inclusion of the coupling of the different channels in the AGS formalism allows one to improve the treatment of the peripheral sub-Coulomb and above the Coulomb (d, p) reactions compared to the DWBA and CDCC method.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

A Game-Theoretic Quantum Algorithm for Solving Magic Squares

Variational quantum algorithms (VQAs) offer a promising near-term approach to finding optimal quantum strategies for playing non-local games. These games test quantum correlations beyond classical limits and enable entanglement verification. In this work, we present a variational framework for the Magic Square Game (MSG), a two-player non-local game with perfect quantum advantage. We construct a value Hamiltonian that encodes the game’s parity and consistency constraints, then optimize parameterize quantum circuits to minimize this cost. Our approach build on the stabilizer formalism, leverages commutation structure for circuit design, and is hardware-efficient. Compared to existing work, our contribution emphasizes algebraic structure an interpretability. We validate our method through numerical experiments and outline generalizations to larger games.

Chehade, Sarah [ORNL]↗
DOE OSTI2020

Symmetry reduction of tensor networks in many-body theory: I. Automated symbolic evaluation of SU(2) algebra

Abstract The ongoing progress in (nuclear) many-body theory is accompanied by an ever-rising increase in complexity of the underlying formalisms used to solve the stationary Schrödinger equation. The associated working equations at play in state-of-the-art ab initio nuclear many-body methods can be analytically reduced with respect to angular-momentum, i.e. SU (2), quantum numbers whenever they are effectively employed in a symmetry-restricted context. The corresponding procedure constitutes a tedious and error-prone but yet an integral part of the implementation of those many-body frameworks. Indeed, this symmetry reduction is a key step to advance modern simulations to higher accuracy since the use of symmetry-adapted tensors can decrease the computational complexity by orders of magnitude. While attempts have been made in the past to automate the (anti-) commutation rules linked to Fermionic and Bosonic algebras at play in the derivation of the working equations, there is no systematic account to achieve the same goal for their symmetry reduction. In this work, the first version of an automated tool performing graph-theory-based angular-momentum reduction is presented. Taking the symmetry-unrestricted expressions of a generic tensor network as an input, the code provides their angular-momentum-reduced form in an error-safe way in a matter of seconds. Several state-of-the-art many-body methods serve as examples to demonstrate the generality of the approach and to highlight the potential impact on the many-body community.

Tichai, A.↗
NASA NTRS1972

A second quantized model of anharmonicity.

A heuristic description is given for a simple harmonic oscillator as a basis for a model of anharmonicity. A formalism is applied in the process, which applies to complex excitation fields involving particle clusters and also facilitates a description of nonequilibrium multibody configurations by classical methods. The heuristic description is based on Streit's results (1965) and is free of linearization requirements in most physically interesting situations.

Rasetti, M.↗
NASA NTRS1973

Energy partitioning of gaseous ions in an electric field.

The partitioning of ion energy among thermal energy, drift energy, and random-field energy is studied by solution of the Boltzmann equation. An expansion in powers of the square of the electric field strength is obtained by Kihara's method. Numerical calculations for several ion-neutral force laws show that Wannier's constant mean-free-time model gives a reasonable first approximation. The formal extension to multicomponent mixtures is also given. The matrix elements obtained are tabulated, and can be used to study the field dependence of other moments of the ion-distribution function.

Hahn, H.-S.↗
NASA NTRS1975

Use of the Wigner representation in scattering problems

The basic equations of quantum scattering were translated into the Wigner representation, putting quantum mechanics in the form of a stochastic process in phase space, with real valued probability distributions and source functions. The interpretative picture associated with this representation is developed and stressed and results used in applications published elsewhere are derived. The form of the integral equation for scattering as well as its multiple scattering expansion in this representation are derived. Quantum corrections to classical propagators are briefly discussed. The basic approximation used in the Monte-Carlo method is derived in a fashion which allows for future refinement and which includes bound state production. Finally, as a simple illustration of some of the formalism, scattering is treated by a bound two body problem. Simple expressions for single and double scattering contributions to total and differential cross-sections as well as for all necessary shadow corrections are obtained.

Bemler, E. A.↗
NASA NTRS1984

Structural optimization of large ocean-going structures

Ocean-going vehicles and platforms are among the largest structures in the world and are subjected to relatively harsh conditions of motions and loads. Some of them, such as semi-submersible platforms, are a relatively new type of structure and hence there is no formal, well evolved and established structural design code as there is for more traditional structures. More recently, efforts have also been made to develop a design method of this type for ships and other ocean structures. One of the many advantages of a rationally based design method is versatility; it can be used for structures that have widely differing purposes, measures of merit, shapes and sizes. The purpose is to describe a rationally based design method that has been developed within the field of ocean structures, in order that persons dealing with other types of structure can judge whether and to what extent its various features may be useful for those other types. Also, even though some features may not be applicable they might stimulate some useful ideas.

Hughes, O. F.↗
NASA NTRS1989

Linestrengths of the nu(2) and nu(4) bands of (C-12)H4 and (C-13)H4

Absorption spectra recorded on the high-resolution Fourier transform spectrometer at Kitt Peak National Observatory/National Solar Observatory were used to measure individual line strengths of the nu(2) and nu(4) bands of (C-12)H4 and (C-13)H4. The measurements were used to obtain expressions that could be used to correctly predict individual line strengths through five orders of magnitude of absorption strength and high values of J-prime. Transition strengths were modeled using the dyad formalism of two interacting bands and a seven-term second-order dipole-moment expansion. The successful fitting of these data indicates that the method can be used to model measurements of 2- to 5-percent precision even at high values of J. For remote sensing applications, the present prediction of the dyad spectrum represents a substantial improvement.

Brown, L. R.↗