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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Finite-volume formalism for physical processes with an electroweak loop integral

This study investigates finite-volume effects in physical processes that involve the combination of long-range hadronic matrix elements with electroweak loop integrals. We adopt the approach of implementing the electroweak part as the infinite-volume version, which is denoted as the EW ∞ method in this work. A general approach is established for correcting finite-volume effects in cases where the hadronic intermediate states are dominated by either a single particle or two particles. For the single-particle case, this work derives the infinite volume reconstruction method from a new perspective. For the two-particle case, we provide the correction formulas for power-law finite-volume effects and unphysical terms with exponentially divergent time dependence. The finite-volume formalism developed in this study has broad applications, including the QED corrections in various processes and the two-photon exchange contribution in 𝐾 𝐿 → 𝜇 + ⁢𝜇 − or 𝜂 → 𝜇 + ⁢𝜇 − decays.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Magneto-structural transformations via a solid-state nudged elastic band method: Application to iron under pressure

We extend the solid-state nudged elastic band method to handle a non-conserved order parameter, in particular, magnetization, that couples to volume and leads to many observed effects in magnetic systems. We apply this formalism to the well-studied magneto-volume collapse during the pressure-induced transformation in iron—from ferromagnetic body-centered cubic (bcc) austenite to hexagonal close-packed (hcp) martensite. We find a bcc-hcp equilibrium coexistence pressure of 8.4 GPa, with the transition-state enthalpy of 156 meV/Fe at this pressure. A discontinuity in magnetization and coherent stress occurs at the transition state, which has a form of a cusp on the potential-energy surface (yet all the atomic and cell degrees of freedom are continuous); the calculated pressure jump of 25 GPa is related to the observed 25 GPa spread in measured coexistence pressures arising from martensitic and coherency stresses in samples. Our results agree with experiments, but necessarily differ from those arising from drag and restricted parametrization methods having improperly constrained or uncontrolled degrees of freedom.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Efficient real space formalism for hybrid density functionals

We present an efficient real space formalism for hybrid exchange-correlation functionals in generalized Kohn–Sham density functional theory (DFT). In particular, we develop an efficient representation for any function of the real space finite-difference Laplacian matrix by leveraging its Kronecker product structure, thereby enabling the time to solution of associated linear systems to be highly competitive with the fast Fourier transform scheme while not imposing any restrictions on the boundary conditions. We implement this formalism for both the unscreened and range-separated variants of hybrid functionals. We verify its accuracy and efficiency through comparisons with established planewave codes for isolated as well as bulk systems. In particular, we demonstrate up to an order-of-magnitude speedup in time to solution for the real space method. We also apply the framework to study the structure of liquid water using ab initio molecular dynamics, where we find good agreement with the literature. Overall, the current formalism provides an avenue for efficient real-space DFT calculations with hybrid density functionals.

Chemistry↗
DOE OSTI2017

Two-scale Analysis of Solar Magnetic Helicity

We develop a two-scale formalism to determine global magnetic helicity spectra in systems where the local magnetic helicity has opposite signs on both sides of the equator, giving rise to cancellation with conventional methods. We verify this approach using first a synthetic one-dimensional magnetic field and then two-dimensional slices from a three-dimensional α effect-type dynamo-generated magnetic field, with forced turbulence of opposite helicity above and below the midplane of the domain. We then apply this formalism to global solar synoptic vector magnetograms. To improve the statistics, data from three consecutive Carrington rotations (2161–2163) are combined into a single map. We find that the spectral magnetic helicity representative of the northern hemisphere is negative at all wavenumbers and peaks at ≈0.06 Mm{sup −1} (scales around 100 Mm). There is no evidence of bihelical magnetic fields that are found in three-dimensional turbulence simulations of helicity-driven α effect-type dynamos.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Nonideal stability analysis of differentially rotating plasmas with global curvature effects

The linear stability of global nonaxisymmetric modes in differentially rotating, magnetized, nonideal plasma is critical to classifying turbulence and transport phenomena. We investigate the competition between the local magneto-rotational instability (MRI) and the magneto-curvature instability (MCI)—a distinct nonaxisymmetric low-frequency curvature-driven global branch that appears alongside MRI. Here, to accomplish this, we developed a nonideal global spectral method, which is validated against NIMROD code simulations. This spectral approach allows for the direct derivation of an extended effective potential formalism and a resistive Alfvénic resonance condition, providing a framework for direct analysis of energy contributions and confinement mechanisms. Our study reveals that the global, low-frequency MCI persists at low magnetic Reynolds numbers (Rm), whereas the localized, high-frequency MRI is stabilized by diffusive broadening of its structure around its Alfvénic resonances. Consequently, we identify the global MCI branch as the primary onset mechanism for nonaxisymmetric magnetohydrodynamic instability in systems with finite curvature, e.g., astrophysical rotators. We establish distinct parameter regimes for mode dominance: MCI prevails in geometrically moderate-thickness disks with intermediate curvature and radial gaps, while MRI dominates in thin, low-curvature disks with large radial gaps. Mode competition is also highly sensitive to the flow profile, particularly vorticity and its gradient, with nonuniform shear profiles exhibiting more robust instability due to flow curvature (i.e., the second derivative of the flow profile) and shear contributions. A key outcome is the development of spectral diagrams derived from the global spectral method. These diagrams comprehensively map dominant instabilities and their characteristics, offering a predictive tool for critical onset parameters (i.e., flow curvature, magnetic field, and Rm) and facilitating the interpretation of experimental and simulation results. Notably, these diagrams demonstrate that the global MCI is generally the sole unstable mode at the initial onset of nonaxisymmetric instability.

Haywood, Alexander [Princeton Univ., NJ (United St↗
DOE OSTI2022

Energetically consistent model reduction for metriplectic systems

The metriplectic formalism is useful for describing complete dynamical systems which conserve energy and produce entropy. This creates challenges for model reduction, as the elimination of high-frequency information will generally not preserve the metriplectic structure which governs long-term stability of the system. Based on proper orthogonal decomposition, a provably convergent metriplectic reduced-order model is formulated which is guaranteed to maintain the algebraic structure necessary for energy conservation and entropy formation. Further, numerical results on benchmark problems show that the proposed method is remarkably stable, leading to improved accuracy over long time scales at a moderate increase in cost over naive methods.

42 ENGINEERING↗
DOE OSTI2016

SU-F-T-06: Development of a Formalism for Practical Dose Measurements in Brachytherapy in the German Standard DIN 6803

Purpose: In the steep dose gradients in the vicinity of a radiation source and due to the properties of the changing photon spectra, dose measurements in Brachytherapy usually have large uncertainties. Working group DIN 6803-3 is presently discussing recommendations for practical brachytherapy dosimetry incorporating recent theoretical developments in the description of brachytherapy radiation fields as well as new detectors and phantom materials. The goal is to prepare methods and instruments to verify dose calculation algorithms and for clinical dose verification with reduced uncertainties. Methods: After analysis of the distance dependent spectral changes of the radiation field surrounding brachytherapy sources, the energy dependent response of typical brachytherapy detectors was examined with Monte Carlo simulations. A dosimetric formalism was developed allowing the correction of their energy dependence as function of source distance for a Co-60 calibrated detector. Water equivalent phantom materials were examined with Monte Carlo calculations for their influence on brachytherapy photon spectra and for their water equivalence in terms of generating equivalent distributions of photon spectra and absorbed dose to water. Results: The energy dependence of a detector in the vicinity of a brachytherapy source can be described by defining an energy correction factor kQ for brachytherapy in the same manner as in existing dosimetry protocols which incorporates volume averaging and radiation field distortion by the detector. Solid phantom materials were identified which allow precise positioning of a detector together with small correctable deviations from absorbed dose to water. Recommendations for the selection of detectors and phantom materials are being developed for different measurements in brachytherapy. Conclusion: The introduction of kQ for brachytherapy sources may allow more systematic and comparable dose measurements. In principle, the corrections can be verified or even determined by measurement in a water phantom and comparison with dose distributions calculated using the TG43 dosimetry formalism. Project is supported by DIN Deutsches Institut fuer Normung.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Core polarization effects: Oscillator strengths, transition probabilities and radiative lifetimes of levels in Bi IV

In this work a systematic analysis of Bi IV atomic properties is presented. Ab initio relativistic Hartree–Fock calculations in an intermediate coupling (IC) formalism and taking into account Core Polarization Effects (CPE) are used. We use for the IC calculations the standard method of least square fitting of experimental energy levels by means of computer codes from Cowan which was modified in order to include CPE. Our calculations have been made from 17 configurations of Bi IV: 5d{sup 10}6s{sup 2}, 5d{sup 10}6p{sup 2}, 5d{sup 10}6sns (n= 7–10) and 5d{sup 10}6snd (n= 6–9) for even parity and 5d{sup 10}6snp (n=6,7), 5d{sup 10}6snf (n=5,6), 5d{sup 9}6s{sup 2}6p and 5d{sup 9}6s{sup 2}nf (n=5,6) for odd parity. Transition probabilities and oscillator strengths for 100 lines and some radiative lifetimes of Bi IV have been calculated. Besides a comparison of our results with the scarce experimental values available in the bibliography are presented. The presence of spectral lines of bismuth in stellar atmospheres has been reported in different stars. This is the motivation by this work can be very interest in astrophysical area. Recently the Bi IV is taking importance because it is considered as the main dopant in the prospective used for the design and synthesis of new scintillators.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2016

Health impact assessment – A survey on quantifying tools

Integrating human health into prospective impact assessments is known to be challenging. This is true for both approaches: dedicated health impact assessments (HIA) as well as inclusion of health into more general impact assessments. Acknowledging the full range of participatory, qualitative, and quantitative approaches, this study focuses on the latter, especially on computational tools for quantitative health modelling. We conducted a survey among tool developers concerning the status quo of development and availability of such tools; experiences made with model usage in real-life situations; and priorities for further development. Responding toolmaker groups described 17 such tools, most of them being maintained and reported as ready for use and covering a wide range of topics, including risk & protective factors, exposures, policies, and health outcomes. In recent years, existing models have been improved and were applied in new ways, and completely new models emerged. There was high agreement among respondents on the need to further develop methods for assessment of inequalities and uncertainty. The contribution of quantitative modeling to health foresight would benefit from building joint strategies of further tool development, improving the visibility of quantitative tools and methods, and engaging continuously with actual and potential users. - Highlights: • A survey investigated computational tools for health impact quantification. • Formal evaluation of such tools has been rare. • Handling inequalities and uncertainties are priority areas for further development. • Health foresight would benefit from tool developers and users forming a community. • Joint development strategies across computational tools are needed.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

Numerical solution of the time dependent Ginzburg-Landau equations for mixed (d + s)-wave superconductors

The time-dependent Ginzburg-Landau formalism for (d + s)-wave superconductors and their representation using auxiliary fields is investigated. By using the link variable method, we then develop suitable discretization of these equations. Numerical simulations are carried out for a mesoscopic superconductor in a homogeneous perpendicular magnetic field which revealed peculiar vortex states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

ANALYTICAL MODELS OF EXOPLANETARY ATMOSPHERES. II. RADIATIVE TRANSFER VIA THE TWO-STREAM APPROXIMATION

We present a comprehensive analytical study of radiative transfer using the method of moments and include the effects of non-isotropic scattering in the coherent limit. Within this unified formalism, we derive the governing equations and solutions describing two-stream radiative transfer (which approximates the passage of radiation as a pair of outgoing and incoming fluxes), flux-limited diffusion (which describes radiative transfer in the deep interior), and solutions for the temperature-pressure profiles. Generally, the problem is mathematically underdetermined unless a set of closures (Eddington coefficients) is specified. We demonstrate that the hemispheric (or hemi-isotropic) closure naturally derives from the radiative transfer equation if energy conservation is obeyed, while the Eddington closure produces spurious enhancements of both reflected light and thermal emission. We concoct recipes for implementing two-stream radiative transfer in stand-alone numerical calculations and general circulation models. We use our two-stream solutions to construct toy models of the runaway greenhouse effect. We present a new solution for temperature-pressure profiles with a non-constant optical opacity and elucidate the effects of non-isotropic scattering in the optical and infrared. We derive generalized expressions for the spherical and Bond albedos and the photon deposition depth. We demonstrate that the value of the optical depth corresponding to the photosphere is not always 2/3 (Milne's solution) and depends on a combination of stellar irradiation, internal heat, and the properties of scattering in both the optical and infrared. Finally, we derive generalized expressions for the total, net, outgoing, and incoming fluxes in the convective regime.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Diffusion quantum Monte Carlo approach to the polaritonic ground state

Making and using polaritonic states (i.e., hybrid electron-photon states) for chemical applications has recently become one of the most prominent and active fields that connects the communities of chemistry and quantum optics. Modeling of such polaritonic phenomena using ab initio approaches calls for new methodologies, leading to the reinvention of many commonly used electronic structure methods, such as Hartree-Fock, density functional, and coupled cluster theories. Here in this work, we explore the formally exact diffusion quantum Monte Carlo approach to obtain numerical solutions to the polaritonic ground state during the dissociation of the H 2 molecular system. Here, we examine various electron-nuclear-photon properties throughout the dissociation, such as changes to the minimum of the cavity Born-Oppenheimer surface, the localization of the electronic wave function, and the average mode occupation. Finally, we directly compare our results to that obtained with state-of-the-art, yet approximate, polaritonic coupled cluster approaches.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1992

Validating a large geophysical data set: Experiences with satellite-derived cloud parameters

We are validating the global cloud parameters derived from the satellite-borne HIRS2 and MSU atmospheric sounding instrument measurements, and are using the analysis of these data as one prototype for studying large geophysical data sets in general. The HIRS2/MSU data set contains a total of 40 physical parameters, filling 25 MB/day; raw HIRS2/MSU data are available for a period exceeding 10 years. Validation involves developing a quantitative sense for the physical meaning of the derived parameters over the range of environmental conditions sampled. This is accomplished by comparing the spatial and temporal distributions of the derived quantities with similar measurements made using other techniques, and with model results. The data handling needed for this work is possible only with the help of a suite of interactive graphical and numerical analysis tools. Level 3 (gridded) data is the common form in which large data sets of this type are distributed for scientific analysis. We find that Level 3 data is inadequate for the data comparisons required for validation. Level 2 data (individual measurements in geophysical units) is needed. A sampling problem arises when individual measurements, which are not uniformly distributed in space or time, are used for the comparisons. Standard 'interpolation' methods involve fitting the measurements for each data set to surfaces, which are then compared. We are experimenting with formal criteria for selecting geographical regions, based upon the spatial frequency and variability of measurements, that allow us to quantify the uncertainty due to sampling. As part of this project, we are also dealing with ways to keep track of constraints placed on the output by assumptions made in the computer code. The need to work with Level 2 data introduces a number of other data handling issues, such as accessing data files across machine types, meeting large data storage requirements, accessing other validated data sets, processing speed and throughput for interactive graphical work, and problems relating to graphical interfaces.

Kahn, Ralph↗
NASA NTRSDate not supplied

Minimum-Violation Traffic Management for Urban Air Mobility

Urban air mobility (UAM) refers to air transportation services in and over an urban area and has the potential to revolutionize mobility solutions. However, due to the projected scale of operations, current air traffic management (ATM) techniques are not viable. Increasingly autonomous systems are a pathway to accelerate the realization of UAM operations but must be fielded safely and efficiently. The heavily regulated, safety critical nature of aviation may lead to multiple, competing safety constraints that can be traded off based on the operational context. In this paper, we design a framework which allows for the scalable planning of a UAM ATM system. We formalize safety oriented constraints derived from FAA regulations by encoding them as temporal logic formulae. We then propose a method for UAM ATM that is both scalable and minimally violates the temporal logic constraints. Numerical results show that the runtime for our proposed algorithm is suitable for very large problems and is backed by theoretical guarantees of correctness with respect to given temporal logic constraints.

Urban Air Mobility↗
DOE OSTI2016

Component separation of a isotropic Gravitational Wave Background

A Gravitational Wave Background (GWB) is expected in the universe from the superposition of a large number of unresolved astrophysical sources and phenomena in the early universe. Each component of the background (e.g., from primordial metric perturbations, binary neutron stars, milli-second pulsars etc.) has its own spectral shape. Many ongoing experiments aim to probe GWB at a variety of frequency bands. In the last two decades, using data from ground-based laser interferometric gravitational wave (GW) observatories, upper limits on GWB were placed in the frequency range of 0∼ 50−100 Hz, considering one spectral shape at a time. However, one strong component can significantly enhance the estimated strength of another component. Hence, estimation of the amplitudes of the components with different spectral shapes should be done jointly. Here we propose a method for 'component separation' of a statistically isotropic background, that can, for the first time, jointly estimate the amplitudes of many components and place upper limits. The method is rather straightforward and needs negligible amount of computation. It utilises the linear relationship between the measurements and the amplitudes of the actual components, alleviating the need for a sampling based method, e.g., Markov Chain Monte Carlo (MCMC) or matched filtering, which are computationally intensive and cumbersome in a multi-dimensional parameter space. Using this formalism we could also study how many independent components can be separated using a given dataset from a network of current and upcoming ground based interferometric detectors.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Three-particle formalism for multiple channels: the ηππ + $ K\overline{K}\pi $ system in isosymmetric QCD

We generalize previous three-particle finite-volume formalisms to allow for multiple three-particle channels. For definiteness, we focus on the two-channel ηππ and $ K\overline{K}\pi $ system in isosymmetric QCD, considering the positive G parity sector of the latter channel, and neglecting the coupling to modes with four or more particles. The formalism we obtain is thus appropriate to study the b 1 (1235) and η(1295) resonances. The derivation is made in the generic relativistic field theory approach using the time-ordered perturbation theory method. We study how the resulting quantization condition reduces to that for a single three-particle channel when one drops below the upper ($ K\overline{K}\pi $) threshold. We also present parametrizations of the three-particle K matrices that enter into the formalism.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

SU-E-T-477: An Efficient Dose Correction Algorithm Accounting for Tissue Heterogeneities in LDR Brachytherapy

Purpose: Seed brachytherapy is currently used for adjuvant radiotherapy of early stage prostate and breast cancer patients. The current standard for calculation of dose surrounding the brachytherapy seeds is based on American Association of Physicist in Medicine Task Group No. 43 (TG-43 formalism) which generates the dose in homogeneous water medium. Recently, AAPM Task Group No. 186 emphasized the importance of accounting for tissue heterogeneities. This can be done using Monte Carlo (MC) methods, but it requires knowing the source structure and tissue atomic composition accurately. In this work we describe an efficient analytical dose inhomogeneity correction algorithm implemented using MIM Symphony treatment planning platform to calculate dose distributions in heterogeneous media. Methods: An Inhomogeneity Correction Factor (ICF) is introduced as the ratio of absorbed dose in tissue to that in water medium. ICF is a function of tissue properties and independent of source structure. The ICF is extracted using CT images and the absorbed dose in tissue can then be calculated by multiplying the dose as calculated by the TG-43 formalism times ICF. To evaluate the methodology, we compared our results with Monte Carlo simulations as well as experiments in phantoms with known density and atomic compositions. Results: The dose distributions obtained through applying ICF to TG-43 protocol agreed very well with those of Monte Carlo simulations as well as experiments in all phantoms. In all cases, the mean relative error was reduced by at least 50% when ICF correction factor was applied to the TG-43 protocol. Conclusion: We have developed a new analytical dose calculation method which enables personalized dose calculations in heterogeneous media. The advantages over stochastic methods are computational efficiency and the ease of integration into clinical setting as detailed source structure and tissue segmentation are not needed. University of Toronto, Natural Sciences and Engineering Research Council of Canada.

60 APPLIED LIFE SCIENCES↗