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At least 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

The (IR-)relevance of the Gribov ambiguity in SU(2)×U(1) gauge theories with fundamental Higgs matter

It is well accepted that dealing with the Gribov ambiguity has a major impact on correlation functions in gauge-fixed Yang–Mills theories, in particular in the low momentum regime where standard perturbation theory based on the Faddeev–Popov approach fails. Recent results, derived from functional tools (Dyson–Schwinger equations or exact RG) or the effective Gribov–Zwanziger action method, pointed towards e.g. gauge boson correlation functions that are not compatible with the properties of observable degrees of freedom. Although such an observation is a welcome feature for gauge theories exhibiting confinement, it would be a discomfort for gauge theories supplemented with Higgs fields, cf. the experimental success of the electroweak model based on a SU(2)×U(1) gauge group. The purpose of this short note is to assure that the effective action resolution to the Gribov ambiguity reduces to the standard Faddeev–Popov method in the perturbative regime of sufficiently small coupling/large Higgs condensate, thereby not compromising the physical particle spectrum of massive gauge bosons and a massless photon for the SU(2)×U(1) gauge–Higgs model. The closer the theory gets to the limit of vanishing Higgs condensate, the more the Gribov problem resurfaces with all its consequences. We give some speculations w.r.t. the Fradkin–Shenker insights about the phase diagram. -- Highlights: •Gribov horizon influences gauge propagators in a strong-coupling regime. •No influence of Gribov horizon in weak-coupling. •Inclusion of U(1) factor leads to very rich behavior of propagators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1991

A parallel vectorized implementation of triple excitations in CCSD(T) - Application to the binding energies of the AlH3, AlH2F, AlHF2 and AlF3 dimers

An efficient method for various noniterative estimates of connected triple excitations in coupled-cluster theory is outlined and related to a similar expression occurring in Moller-Plesset perturbation theory. The method is highly vectorized and capable of utilizing multiple processors on a shared-memory machine, leading to computational rates in excess of one billion floating-point operations per second on four processors of a CRAY Y-MP. Using the new procedure, the binding energies of the D(2h) diborane-type dimers of AlH3, AlH2F, AlHF2, and AlF3 have been determined to be 32, 40, 20, and 47 kcal/mol, respectively. For Al2F6, the correlation procedure includes 232 molecular orbitals and over 1.5 x 10 to the 6th single and double coupled-cluster amplitudes, effectively accounting for over 2 x 10 to the 9th connected triple excitations.

Rendell, Alistair P.↗
DOE OSTI2021

Analytical derivatives of the individual state energies in ensemble density functional theory. II. Implementation on graphical processing units (GPUs)

Conical intersections control excited state reactivity, and thus, elucidating and predicting their geometric and energetic characteristics are crucial for understanding photochemistry. Locating these intersections requires accurate and efficient electronic structure methods. Unfortunately, the most accurate methods (e.g., multireference perturbation theories such as XMS-CASPT2) are computationally challenging for large molecules. The state-interaction state-averaged restricted ensemble referenced Kohn–Sham (SI-SA-REKS) method is a computationally efficient alternative. The application of SI-SA-REKS to photochemistry was previously hampered by a lack of analytical nuclear gradients and nonadiabatic coupling matrix elements. We have recently derived analytical energy derivatives for the SI-SA-REKS method and implemented the method effectively on graphical processing units. We demonstrate that our implementation gives the correct conical intersection topography and energetics for several examples. Furthermore, our implementation of SI-SA-REKS is computationally efficient, with observed sub-quadratic scaling as a function of molecular size. This demonstrates the promise of SI-SA-REKS for excited state dynamics of large molecular systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Extended Møller-Plesset perturbation theory for dynamical and static correlations

We present a novel method that appropriately handles both dynamical and static electron correlations in a balanced manner, using a perturbation theory on a spin-extended Hartree-Fock (EHF) wave function reference. While EHF is a suitable candidate for degenerate systems where static correlation is ubiquitous, it is known that most of dynamical correlation is neglected in EHF. In this work, we derive a perturbative correction to a fully spin-projected self-consistent wave function based on second-order Møller-Plesset perturbation theory (MP2). The proposed method efficiently captures the ability of EHF to describe static correlation in degeneracy, combined with MP2's ability to treat dynamical correlation effects. We demonstrate drastic improvements on molecular ground state and excited state potential energy curves and singlet-triplet splitting energies over both EHF and MP2 with similar computational effort to the latter.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2018

Hybrid Correlation Energy (HyCE): An Approach Based on Separate Evaluations of Internal and External Components

In this work, a novel hybrid correlation energy (HyCE) approach is proposed that determines the total correlation energy via distinct computation of its internal and external components. This approach evolved from two related studies. First, rigorous assessment of the accuracies and size extensivities of a number of electron correlation methods, that include perturbation theory (PT2), coupled-cluster (CC), configuration interaction (CI), and coupled electron pair approximation (CEPA), shows that the CEPA(0) variant of the latter and triples-corrected CC methods consistently perform very similarly. These findings were obtained by comparison to near full CI results for four small molecules and by charting recovered correlation energies for six steadily growing chain systems. Second, by generating valence virtual orbitals (VVOs) and utilizing the CEPA(0) method, we were able to partition total correlation energies into internal (or nondynamic) and external (or dynamic) parts for the aforementioned six chain systems and a benchmark test bed of 36 molecules. When using triple-ζ basis sets it was found that per orbital internal correlation energies were appreciably larger than per orbital external energies and that the former showed far more chemical variation than the latter. Additionally, accumulations of external correlation energies were seen to proceed smoothly, and somewhat linearly, as the virtual space is gradually increased. Combination of these two studies led to development of the HyCE approach, whereby the internal and external correlation energies are determined separately by CEPA(0)/VVO and PT2/external calculations, respectively. When applied to the six chain systems and the 36-molecule benchmark test set it was found that HyCE energies followed closely those of triples-corrected CC and CEPA(0) while easily outperforming MP2 and CCSD. Lastly, the success of the HyCE approach is more notable when considering that its cost is only slightly more than MP2 and significantly cheaper than the CC approaches.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Communication: A reduced scaling J-engine based reformulation of SOS-MP2 using graphics processing units

We present a low-prefactor, cubically scaling scaled-opposite-spin second-order Møller-Plesset perturbation theory (SOS-MP2) method which is highly suitable for massively parallel architectures like graphics processing units (GPU). The scaling is reduced from O(N{sup 5}) to O(N{sup 3}) by a reformulation of the MP2-expression in the atomic orbital basis via Laplace transformation and the resolution-of-the-identity (RI) approximation of the integrals in combination with efficient sparse algebra for the 3-center integral transformation. In contrast to previous works that employ GPUs for post Hartree-Fock calculations, we do not simply employ GPU-based linear algebra libraries to accelerate the conventional algorithm. Instead, our reformulation allows to replace the rate-determining contraction step with a modified J-engine algorithm, that has been proven to be highly efficient on GPUs. Thus, our SOS-MP2 scheme enables us to treat large molecular systems in an accurate and efficient manner on a single GPU-server.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

A per-cent-level determination of the nucleon axial coupling from quantum chromodynamics

The axial coupling of the nucleon, g A , is the strength of its coupling to the weak axial current of the standard model of particle physics, in much the same way as the electric charge is the strength of the coupling to the electromagnetic current. This axial coupling dictates the rate at which neutrons decay to protons, the strength of the attractive long-range force between nucleons and other features of nuclear physics. Precision tests of the standard model in nuclear environments require a quantitative understanding of nuclear physics that is rooted in quantum chromodynamics, a pillar of the standard model. The importance of g A makes it a benchmark quantity to determine theoretically—a difficult task because quantum chromodynamics is non-perturbative, precluding known analytical methods. Lattice quantum chromodynamics provides a rigorous, non-perturbative definition of quantum chromodynamics that can be implemented numerically. It has been estimated that a precision of two per cent would be possible by 2020 if two challenges are overcome: contamination of g A from excited states must be controlled in the calculations and statistical precision must be improved markedly. Here we use an unconventional method inspired by the Feynman–Hellmann theorem that overcomes these challenges. Furthermore, we calculate a g A value of 1.271 ± 0.013, which has a precision of about one per cent.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1979

Asymptotic continuation method for trajectory optimization

A continuation method is applied to a singular perturbation parameter to obtain a new numerical method for computing optimal trajectories. This method allows one to use simply calculated reduced order approximations as starting solutions and continue the perturbation parameter until the optimal full-order solution is obtained. The method does not require the calculation of higher order correction terms nor does it require the perturbation parameter to be small - thus, it has potentially superior convergence properties compared to conventional asymptotic expansions when the perturbation parameter is large. A simple trajectory optimization problem is considered to illustrate the method.

Washburn, R. B., Jr.↗
DOE OSTI2016

Kato expansion in quantum canonical perturbation theory

This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson’s ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. We compare the efficiency of the corresponding computational algorithm with the efficiencies of the Van Vleck and Magnus methods for high perturbative orders.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Energy levels, lifetimes and radiative rates for transitions in the bromine isoelectronic sequence La XXIII-Dy XXXII, W XL

Using the multiconfiguration Dirac–Fock method, calculations for the lowest 62 levels of the ([Ar] 3d{sup 10})4s{sup 2}4p{sup 5}, ([Ar] 3d{sup 10})4s{sup 2}4p{sup 3}4d{sup 2}, ([Ar] 3d{sup 10})4s{sup 2}4p{sup 4}4d, ([Ar] 3d{sup 10})4s4p{sup 6}, and ([Ar] 3d{sup 10})4s4p{sup 5}4d configurations are performed for the bromine isoelectronic sequence La XXIII-Dy XXXII, W XL. Results of energy levels, lifetimes, wavelengths, and electric dipole, magnetic dipole, electric quadrupole, and magnetic quadrupole radiative rates are presented. In order to assess the accuracy of results, independent calculations for W XL have been carried out using the many-body perturbation theory (MBPT) method. Comparisons are made with available theoretical results from other calculations and the observed values of the Atomic Spectra Database of the National Institute of Standards and Technology. Energy levels are estimated to be accurate to better than 1%, and radiative rates (and lifetimes) are accurate to better than 20% for a majority of strong transitions. These results should be useful in many applications of lanthanide ions related to broad area of research such as applied physics, laser physics and fusion science.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1989

An explicit Runge-Kutta method for turbulent reacting flow calculations

The paper presents a numerical method for the solution of the conservation equations governing steady, reacting, turbulent viscous flow in two-dimensional geometries, in both Cartesian and axisymmetric coordinates. These equations are written in Favre-averaged form and closed with a first order model. A two-equation K-epsilon model, where low Reynolds number and compressibility effects are included, and a modified eddy-break up model are used to simulate fluid mechanics turbulence, chemistry and turbulence-combustion interaction. The solution is obtained by using a pseudo-unsteady method with improved perturbation propagation properties. The equations are discretized in space by using a finite volume formulation. An explicit multi-stage dissipative Runge-Kutta algorithm is then used to advance the flow equations in the pseudo-time. The method is applied to the computation of both diffusion and premixed turbulent reacting flows. The computed temperature distributions compare favorably with experimental data.

Boretti, A. A.↗
DOE OSTI2012

A low order flow/acoustics interaction method for the prediction of sound propagation using 3D adaptive hybrid grids

A low-order flow/acoustics interaction method for the prediction of sound propagation and diffraction in unsteady subsonic compressible flow using adaptive 3-D hybrid grids is investigated. The total field is decomposed into the flow field described by the Euler equations, and the acoustics part described by the Nonlinear Perturbation Equations. The method is shown capable of predicting monopole sound propagation, while employment of acoustics-guided adapted grid refinement improves the accuracy of capturing the acoustic field. Interaction of sound with solid boundaries is also examined in terms of reflection, and diffraction. Sound propagation through an unsteady flow field is examined using static and dynamic flow/acoustics coupling demonstrating the importance of the latter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2009

Advances in Land Data Assimilation at the NASA Goddard Space Flight Center

Research in land surface data assimilation has grown rapidly over the last decade. In this presentation we provide a brief overview of key research contributions by the NASA Goddard Space Flight Center (GSFC). The GSFC contributions to land assimilation primarily include the continued development and application of the Land Information System (US) and the ensemble Kalman filter (EnKF). In particular, we have developed a method to generate perturbation fields that are correlated in space, time, and across variables and that permit the flexible modeling of errors in land surface models and observations, along with an adaptive filtering approach that estimates observation and model error input parameters. A percentile-based scaling method that addresses soil moisture biases in model and observational estimates opened the path to the successful application of land data assimilation to satellite retrievals of surface soil moisture. Assimilation of AMSR-E surface soil moisture retrievals into the NASA Catchment model provided superior surface and root zone assimilation products (when validated against in situ measurements and compared to the model estimates or satellite observations alone). The multi-model capabilities of US were used to investigate the role of subsurface physics in the assimilation of surface soil moisture observations. Results indicate that the potential of surface soil moisture assimilation to improve root zone information is higher when the surface to root zone coupling is stronger. Building on this experience, GSFC leads the development of the Level 4 Surface and Root-Zone Soil Moisture (L4_SM) product for the planned NASA Soil-Moisture-Active-Passive (SMAP) mission. A key milestone was the design and execution of an Observing System Simulation Experiment that quantified the contribution of soil moisture retrievals to land data assimilation products as a function of retrieval and land model skill and yielded an estimate of the error budget for the SMAP L4_SM product. Terrestrial water storage observations from GRACE satellite system were also successfully assimilated into the NASA Catchment model and provided improved estimates of groundwater variability when compared to the model estimates alone. Moreover, satellite-based land surface temperature (LST) observations from the ISCCP archive were assimilated using a bias estimation module that was specifically designed for LST assimilation. As with soil moisture, LST assimilation provides modest yet statistically significant improvements when compared to the model or satellite observations alone. To achieve the improvement, however, the LST assimilation algorithm must be adapted to the specific formulation of LST in the land model. An improved method for the assimilation of snow cover observations was also developed. Finally, the coupling of LIS to the mesoscale Weather Research and Forecasting (WRF) model enabled investigations into how the sensitivity of land-atmosphere interactions to the specific choice of planetary boundary layer scheme and land surface model varies across surface moisture regimes, and how it can be quantified and evaluated against observations. The on-going development and integration of land assimilation modules into the Land Information System will enable the use of GSFC software with a variety of land models and make it accessible to the research community.

Reichle, Rolf↗
DOE OSTI2012

Stability and error analysis of nodal expansion method for convection-diffusion equation

The development, and stability and error analyses of nodal expansion method (NEM) for one dimensional steady-state convection diffusion equation is presented. Following the traditional procedure to develop NEM, the discrete formulation of the convection-diffusion equation, which is similar to the standard finite difference scheme, is derived. The method of discrete perturbation analysis is applied to this discrete form to study the stability of the NEM. The scheme based on the NEM is found to be stable for local Peclet number less than 4.644. A maximum principle is proved for the NEM scheme, followed by an error analysis carried out by applying the Maximum principle together with a carefully constructed comparison function. The scheme for the convection diffusion equation is of second-order. Numerical experiments are carried and the results agree with the conclusions of the stability and error analyses. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Destabilizing a Social Network Model via Intrinsic Feedback Vulnerabilities

Social influence plays a significant role in shaping individual sentiments and actions, particularly in a world of ubiquitous digital interconnection. The rapid development of generative artificial intelligence (AI) has given rise to well-founded concerns regarding the potential implementation of radicalization techniques in social media. Motivated by these developments, we present a case study investigating the effects of small but intentional perturbations on a simple social network. We employ Taylor's classic model of social influence and tools from robust control theory (most notably the Dynamical Structure Function (DSF)), to identify perturbations that qualitatively alter the system's behavior while remaining as unobtrusive as possible. We examine two such scenarios: perturbations to an existing link and perturbations that introduce a new link to the network. In each case, we identify destabilizing perturbations of minimal norm and simulate their effects. Remarkably, we find that small but targeted alterations to network structure may lead to the radicalization of all agents, exhibiting the potential for large-scale shifts in collective behavior to be triggered by comparatively minuscule adjustments in social influence. Given that this method of identifying perturbations that are innocuous yet destabilizing applies to any suitable dynamical system, our findings emphasize a need for similar analyses to be carried out on real systems (e.g., real social networks), to identify the places where such dynamics may already exist.

Rogers, Lane [ORNL]↗