Results for “Set theory” — Page 24

DOE OSTI2026

Testing real WIMPs with CTAO

We forecast the reach of the upcoming Cherenkov Telescope Array Observatory (CTAO) to the full set of real representations within the paradigm of minimal dark matter. We employ effective field theory techniques to compute the annihilation cross section and photon spectrum that results when fermionic dark matter is the neutral component of an arbitrary odd and real representation of SU(2), including the Sommerfeld enhancement, next-to-leading log resummation of the relevant electroweak effects, and the contribution from bound states. We also compute the corresponding signals for scalar dark matter, with the exception of the bound state contribution. Results are presented for all real representations from the ~ 3 TeV triplet (or wino), a 3 of SU(2), to the ~ 300 TeV tredecuplet, a 13 of SU(2) that is at the threshold of the unitarity bound. Using these results, we forecast that with 500 hrs of Galactic Center observations and assuming background systematics are controlled at the level of $\mathcal{(O)}$(1%), then should no signal emerge, CTAO could exclude all representations up to the 11 of SU(2) in even the most conservative models for the dark-matter density in the inner galaxy, in both the fermionic and scalar dark matter cases. Assuming the default CTAO configuration, the tredecuplet will marginally escape exclusion, although we outline steps that CTAO could take to test even this scenario. In summary, CTAO appears poised to make a definitive statement on whether real WIMPs constitute the dark matter of our universe.

Models for Dark Matter↗

DOE OSTI2023

Beyond AdS 2 /dCFT 1 : insertions in two Wilson loops

We consider two-point correlators of local operator insertions in a system of two Wilson-Maldacena loops in $\mathcal{N}$ = 4 supersymmetric Yang-Mills theory on both sides of the AdS/CFT correspondence. On the holographic side the correlator of two Wilson-Maldacena loops is given by a classical string world-sheet which in one phase connects two asymptotically AdS 2 regions and in the other phase is given by two disconnected AdS 2 caps; this configuration breaks supersymmetry as well as conformal invariance. We present a complete systematic account of the string world-sheet fluctuations, including the fermionic sector, and study the behavior of the holographic two-point correlators. On the field theory side we compute certain two-point correlators of local operator insertions by resumming sets of ladder diagrams. Our results demonstrate the efficacy of previously developed methods in tackling this non-conformal, non-susy regime.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Thermodynamic and Kinetic Barriers Limiting Solid-State Reactions Resolved through In Situ Synchrotron Studies of Lithium Halide Salts

Although halide salts such as LiCl and LiBr are routinely used as a source of Li ions during ion exchange reactions, a detailed understanding of the processes controlling the rates of these reactions is presently lacking. Recently, it has been discovered that the rate limiting barriers for ion exchange are commonly associated with these salts rather than the ceramic target of ion exchange, making it important to quantitatively understand of salt processes. Here it is demonstrated that in situ synchrotron studies of ion exchange reactions can be used to precisely quantify the thermodynamic activation energies associated with these solid state reactions in a manner that can be directly compared with predictions from density functional theory (DFT). While the temperature dependence of the LiCl reaction rate is found to be set by a barrier associated with ion hopping, it was discovered that for LiBr it is also affected by the defect formation energy – an energy found to be substantially lower than predicted by DFT. Furthermore, it is shown that when reaction rates for different relative amounts of reactants are varied, it is possible to identify the rate-limiting reagent and to elucidate an overall scaling relationship that controls the concentration-dependence of the reaction rate. Also, it is demonstrated that global fits across doped and undoped salts can be used to probe both intrinsic and extrinsic vacancy concentrations. This improved understanding of ion exchange mechanisms can be used to accelerate ion exchange reaction rates by orders of magnitude. In conclusion, the techniques demonstrated here can be broadly applied to probe the kinetics and thermodynamics of solid state reactions.

36 MATERIALS SCIENCE↗

DOE OSTI2025

The Remarkable I 2 O 3 Molecule: A New View from Theory

Atmospheric iodine chemistry has garnered increasing attention as a result of increased iodine emissions. A key subset of this chemistry involves iodine oxides (I 2 O 2–5 ), which serve as precursors to particle formation. Among these, I 2 O 3 is the simplest iodine oxide involved in particle formation, but it has remained undetected in the atmosphere. Previous theoretical studies have characterized this peculiar molecule, primarily using energies to refine geometries obtained at low levels of theory. Due to the reemerging interest in I 2 O 3 , this study presents geometries optimized at the CCSD(T)/aug-cc-pwCVTZ-PP level of theory─marking the first instance, to the best of our knowledge, where this system has been studied exclusively with CCSD(T). Harmonic vibrational frequencies were computed at the same level of theory. Final energetics were obtained using the very high level CCSDT(Q) method with basis sets up to quintuple-zeta cardinality (aug-cc-pwCV5Z-PP) and extrapolated to the CBS limit to yield CCSDT(Q)/CBS//CCSD(T)/aug-cc-pwCVTZ-PP energies. These energies include harmonic zero-point vibrational energy corrections and scalar relativistic energy corrections. Additionally, this study discovers new isomers along the I 2 O 3 potential energy surface, a novel contribution to the field. The performance of different computational methods and DFT functionals commonly used in atmospheric chemistry is also assessed relative to high-level theoretical methods.

basis sets↗

DOE OSTI2022

Solution-Phase Synthesis of PdH 0.706 Nanocubes with Enhanced Stability and Activity toward Formic Acid Oxidation

We report palladium is one of the few metals capable of forming hydrides, with the catalytic properties being dependent on the elemental composition and spatial distribution of H atoms in the lattice. Herein, we report a facile method for the complete transformation of Pd nanocubes into a stable phase made of PdH 0.706 by treating them with aqueous hydrazine at a concentration as low as 9.2 mM. Using formic acid oxidation (FAO) as a model reaction, we systematically investigated the structure–catalytic property relationship of the resultant nanocubes with different degrees of hydride formation. The current density at 0.4 V was enhanced by four times when the nanocubes were completely converted from Pd to PdH 0.706 . On the basis of a set of slab models with PdH(100) overlayers on Pd(100), we conducted density functional theory calculations to demonstrate that the degree of hybrid formation could influence both the activity and selectivity toward FAO by modulating the relative stability of formate (HCOO) and carboxyl (COOH) intermediates. Furthermore, this work provides a viable strategy for augmenting the performance of Pd-based catalysts toward various reactions without altering the loading of this scarce metal.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Prospects for detecting UF6 hydrolysis intermediates by mass spectrometry, resonance Raman, and NQR spectroscopy

Simulations are performed to consider several spectrometric and spectroscopic candidates for elucidating the mechanism of the hydrolysis of uranium hexafluoride (UF6). This study is among the first to benchmark the def-mTZVP basis sets for actinide-containing molecules, and it is shown to be a suitable basis set for surveying geometrical structures and vibrational spectra when used in conjunction with density functional theory. An experiment is proposed coupling mass spectrometric ion selection with vibrational spectroscopy, and supporting infrared and Raman spectral simulations demonstrate that ionization blue-shifts bands and can change their qualitative features. Ultraviolet resonance Raman is shown to have good prospects for discriminating U–O–U bridged intermediates, evidence for which was observed recently [L. E. McNamara et al., J. Phys. Chem. A 130, 775–786 (2026)]. As a more speculative approach, we also consider the prospect of addressing 233U or 235U nuclei by quadrupole resonance (NQR) spectroscopy for assigning early stage intermediate complexes. In doing so, we provide a first order-of-magnitude estimate for the collision-induced NQR signal for the UF6 dimer, which is of interest for the interpretation of a fast decoherence time observed in liquid-phase nuclear magnetic resonance. Having provided critical insights into the formation and stability of UF6 hydrolysis intermediates in previous studies, this computational spectroscopy survey is expected to help guide and expedite future laboratory campaigns.

Lutz, Jesse J. [Center for Computing Research, San↗

DOE OSTI2020

Magnetism and its coexistence with superconductivity in CaK(Fe 0.949 Ni 0.051 ) 4 As 4 : Muon spin rotation/relaxation studies

Here, the magnetic response of Ca K ( Fe 0.949 Ni 0.051 ) 4 As 4 was investigated by means of the muon spin rotation/relaxation. The long-range commensurate magnetic order sets in below the Néel temperature T N = 50.0 ( 5 ) K. The density-functional theory calculations have identified three possible muon stopping sites. The experimental data were found to be consistent with only one type of magnetic structure, namely, the long-range magnetic spin-vortex-crystal order with the hedgehog motif within the a b plane and the antiferromagnetic stacking along the c direction. The value of the ordered magnetic moment at T ≈ 3 K was estimated to be m Fe = 0.38 ( 11 ) μ B ( μ B is the Bohr magneton). A microscopic coexistence of magnetic and superconducting phases accompanied by a reduction of the magnetic order parameter below the superconducting transition temperature T c ≃ 9 K is observed. Comparison with 11, 122, and 1144 families of Fe-based pnictides points to existence of correlation between the reduction of the magnetic order parameter at T → 0 and the ratio of the transition temperatures T c / T N . Such correlations were found to be described by Machida's model for coexistence of itinerant spin-density-wave magnetism and superconductivity [K. Machida, J. Phys. Soc. Jpn. 50 , 2195 (1981) ; S. L. Bud'ko et al. , Phys. Rev. B 98 , 144520 (2018) ].

36 MATERIALS SCIENCE↗

DOE OSTI2020

A General Framework for Bounding Approximate Dynamic Programming Schemes

For years, there has been interest in approximation methods for solving dynamic programming problems, because of the inherent complexity in computing optimal solutions characterized by Bellman’s principle of optimality. A wide range of approximate dynamic programming (ADP) methods now exists. It is of great interest to guarantee that the performance of an ADP scheme be at least some known fraction, say ß , of optimal. This letter introduces a general approach to bounding the performance of ADP methods, in this sense, in the stochastic setting. The approach is based on new results for bounding greedy solutions in string optimization problems, where one has to choose a string (ordered set) of actions to maximize an objective function. This bounding technique is inspired by submodularity theory, but submodularity is not required for establishing bounds. Instead, the bounding is based on quantifying certain notions of curvature of string functions; the smaller the curvatures the better the bound. The key insight is that any ADP scheme is a greedy scheme for some surrogate string objective function that coincides in its optimal solution and value with those of the original optimal control problem. The ADP scheme then yields to the bounding technique mentioned above, and the curvatures of the surrogate objective determine the value ß of the bound. The surrogate objective and its curvatures depend on the specific ADP.

discrete event systems↗

DOE OSTI2022

[Retracted] Research on Application Experience Design of Ice and Snow Sports Equipment Based on Bee Colony Model

Sports equipment is the key to the smooth development of ice and snow sports. With the rapid development of social economy and the improvement of people’s living standards, the demand for ice and snow sports equipment is increasing day by day. This article presents an improved method based on the chaos theory and the bee colony algorithm to quantify the application experience design of ice and snow sports equipment and reduce the influence of uncertain factors on the design results. First, the chaos theory can establish the dataset of application experience design and analyze the discreteness of the set. According to the bee colony algorithm, the dataset is divided into several groups, and each group obtains the best application experience design by using the design optimization strategy. Finally, the results are mixed to obtain the final experience design results. Through MATLAB simulation analysis and verification, the improved bee colony model can improve the accuracy of application experience design of ice and snow sports equipment in an uncertain environment, shorten the overall design time, and meet the requirements of application experience design of different ice and snow sports equipment. Therefore, the model proposed in this paper is suitable for the application experience design of ice and snow sports equipment.

Li, Yuanjing (ORCID:000000018276647X)↗

DOE OSTI2020

Dakota A Multilevel Parallel Object-Oriented Framework for Design Optimization Parameter Estimation Uncertainty Quantification and Sensitivity Analysis: Version 6.12 Theory Manual

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Dakota A Multilevel Parallel Object-Oriented Framework for Design Optimization Parameter Estimation Uncertainty Quantification and Sensitivity Analysis (V.6.14) (Theory Manual)

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.13 Theory Manual

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Theory Manual (V.6.15)

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.16 Theory Manual

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota’s iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Monte Carlo Analyses of the FOEHN Experiment

The FOEHN critical experiment, which has been carried out at Cadarache (France) in the reactor EOLE in the early 70s, was designed to verify RHF design analyses. This study focuses on the impact of the FOEHN experiment uncertainties on the calculation of the energy deposition. The latter has been obtained by the Monte Carlo codes Serpent and MCNP. In the calculation of the energy deposition, the first code relies on KERMA factors whereas the latter code relies on Q-values. The two Monte Carlo codes share the same geometry and material specifications. In addition to the design and experiment parameters uncertainties, nuclear data also impacts the calculation of the energy deposition. In this study, the MCNP simulations use three different nuclear data library sets: ENDF/B versions VII.0, VII.1, and VIII.0. Finally, the ksens card of MCNP, using perturbation theory, has been used to identify the cross sections and isotopes with largest impact on the effective multiplication factor. By showing that the use of different software and computational methodologies and design parameters uncertainties do not significantly impact the core power distribution, this work demonstrate the appropriateness of the tools and methods employed for the conversion of involute-plate reactors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Topological Link Models of Multipartite Entanglement

We introduce a novel model of multipartite entanglement based on topological links, generalizing the graph/hypergraph entropy cone program. We demonstrate that there exist link representations of entropy vectors which provably cannot be represented by graphs or hypergraphs. Furthermore, we show that the contraction map proof method generalizes to the topological setting, though now requiring oracular solutions to well-known but difficult problems in knot theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Ground and excited state properties of ThB − and ThB: a theoretical study

In the present work, we studied a series of electronic and spin–orbit states of ThB − and ThB using high-level multireference and coupled-cluster theories. We report the potential energy curves (PECs), equilibrium electron configurations, spectroscopic constants, energetics, and spin–orbit coupling effects of 17 and 19 electronic states of ThB − and ThB, respectively. The ground state of ThB − is a single-reference 1 3 Π with a 1σ 2 2σ 2 3σ 1 1π 3 electron configuration. Detachment of an electron from the doubly occupied 1π orbital of ThB − (1 3 Π) produces the single-reference ground electronic state of ThB (1 4 Σ − ). The ground spin–orbit states of ThB − and of ThB are 1 3 Π + 0 and 1 4 Σ − 3/2 , respectively. The vertical electron detachment energy (VDE) of ThB − and the adiabatic electron attachment energy (AEA) of ThB at our largest CBS-C-CCSD(T)+δT(Q)+δSO (complete basis set effect, spin–orbit effect, and triple and perturbative quadruple electron correlation effect added coupled-cluster theory with single, double, and perturbative triple excitations) level are 1.473 eV and 1.459, respectively. The reaction of Th( 3 F) + B( 2 P o ) produces the ground state of ThB with a bond energy of 2.843 eV. Finally, we estimated a heat of formation, Δ H 0 f (298 K), of 891.01 kJ mol −1 for the ThB molecule. The high-level findings of this work are expected to aid and motivate future experimental spectroscopic investigations of ThB and ThB − species.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

On negative induced polarization in frequency domain measurements

SUMMARY Induced polarization (IP) has been widely used to non-invasively characterize electrical conduction and polarization in the subsurface resulting from an applied electric field. Earth materials exhibit a lossy capacitance defined by a negative intrinsic phase in frequency-domain IP (FDIP) or a positive intrinsic chargeability in time-domain IP (TDIP). However, error-free positive apparent phase or negative apparent chargeability (i.e. negative IP effects) can occur in IP measurements over heterogeneous media. While negative IP effects in TDIP data sets have been discussed, no studies have addressed this topic in detail for FDIP measurements. We describe theory and numerical modelling to explain the origin of negative IP effects in FDIP measurements. A positive apparent phase may occur when a relatively high polarizability feature falls into negative sensitivity zones of complex resistivity measurements. The polarity of the apparent phase is determined by the distribution of subsurface intrinsic phase and resistivity, with the resistivity impacting the apparent phase polarity via its control on the sensitivity distribution. A physical explanation for the occurrence of positive apparent phase data is provided by an electric circuit model representing a four-electrode measurement. We also show that the apparent phase polarity will be frequency dependent when resistivity changes significantly with frequency (i.e. in the presence of significant IP effects). Consequently, negative IP effects manifest themselves in the shape of apparent phase spectra recorded with multifrequency (spectral IP) data sets. Our results imply that positive apparent phase measurements should be anticipated and should be retained during inversion and interpretation of single frequency and spectral IP data sets.

Geochemistry & Geophysics↗