Search NASA⌕ Search

SEARCH · Search NASA

Results for “Set theory”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 199 records · Page 11

Threshold Collision-Induced Dissociation of Hydrated Thorium(IV) Trihydroxide Cation: Experimental and Theoretical Investigation of the Binding Energies for Th(OH) 3 + (H 2 O) n Complexes ( n = 1–4)

Threshold collision-induced dissociation of Th(OH) 3 + (H 2 O) n Complexes ( n = 1–4) with xenon was performed using a guided ion beam tandem mass spectrometer. The primary dissociation pathway for all complexes is a loss of a single water molecule followed by the sequential loss of additional water molecules at higher collision energies. Here, the data were analyzed using a statistical model after accounting for lifetime effects and reactant internal and kinetic energy distributions to obtain 0 K bond dissociation energies (BDEs). These were also converted using rigid rotor/harmonic oscillator approximations to yield thermodynamic values at room temperature. The 0 K BDEs of H 2 O ligands to Th(OH) 3 + (IV) are experimentally determined for the first time as 106 ± 6, 89 ± 6, 76 ± 4, and 51 ± 4 kJ/mol for the first, second, third, and fourth water ligand added. These values agree reasonably well with values calculated at the B3LYP, B3PW91, and PBE0 levels of theory with aug-cc-pVQZ basis sets, whereas B3LYP-GD3BJ, MP2, and CCSD(T) single point energies with (without) counterpoise corrections systematically overestimate the bond energies by about 15 (20), 19 (25), and (18) kJ/mol, respectively.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Transferability of data-driven, many-body models for CO 2 simulations in the vapor and liquid phases

Here, extending on the previous work by Riera et al. [J. Chem. Theory Comput. 16, 2246–2257 (2020)], we introduce a second generation family of data-driven many-body MB-nrg models for CO 2 and systematically assess how the strength and anisotropy of the CO 2 –CO 2 interactions affect the models’ ability to predict vapor, liquid, and vapor–liquid equilibrium properties. Building upon the many-body expansion formalism, we construct a series of MB-nrg models by fitting one-body and two-body reference energies calculated at the coupled cluster level of theory for large monomer and dimer training sets. Advancing from the first generation models, we employ the charge model 5 scheme to determine the atomic charges and systematically scale the two-body energies to obtain more accurate descriptions of vapor, liquid, and vapor–liquid equilibrium properties. Challenges in model construction arise due to the anisotropic nature and small magnitude of the interaction energies in CO 2 , calling for the necessity of highly accurate descriptions of the multidimensional energy landscape of liquid CO 2 . These findings emphasize the key role played by the training set quality in the development of transferable, data-driven models, which, accurately representing high-dimensional many-body effects, can enable predictive computer simulations of molecular fluids across the entire phase diagram.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Propagating sample variance uncertainties in redshift calibration: simulations, theory, and application to the COSMOS2015 data

ABSTRACT Cosmological analyses of galaxy surveys rely on knowledge of the redshift distribution of their galaxy sample. This is usually derived from a spectroscopic and/or many-band photometric calibrator survey of a small patch of sky. The uncertainties in the redshift distribution of the calibrator sample include a contribution from shot noise, or Poisson sampling errors, but, given the small volume they probe, they are dominated by sample variance introduced by large-scale structures. Redshift uncertainties have been shown to constitute one of the leading contributions to systematic uncertainties in cosmological inferences from weak lensing and galaxy clustering, and hence they must be propagated through the analyses. In this work, we study the effects of sample variance on small-area redshift surveys, from theory to simulations to the COSMOS2015 data set. We present a three-step Dirichlet method of resampling a given survey-based redshift calibration distribution to enable the propagation of both shot noise and sample variance uncertainties. The method can accommodate different levels of prior confidence on different redshift sources. This method can be applied to any calibration sample with known redshifts and phenotypes (i.e. cells in a self-organizing map, or some other way of discretizing photometric space), and provides a simple way of propagating prior redshift uncertainties into cosmological analyses. As a worked example, we apply the full scheme to the COSMOS2015 data set, for which we also present a new, principled SOM algorithm designed to handle noisy photometric data. We make available a catalogue of the resulting resamplings of the COSMOS2015 galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗

Measuring the growth of Alfvén wave parametric decay instability using counter-propagating waves: Theory and simulations

The parametric decay instability (PDI) of Alfvén waves—where a pump Alfvén wave decays into a backward-propagating child Alfvén wave and a forward ion acoustic wave—is a fundamental nonlinear wave-wave interaction and holds significant implications for space and laboratory plasmas. However, to date there has been no direct experimental measurement of PDI. Here, we propose a novel and experimentally viable scheme to quantify the growth of Alfvén wave PDI on a linear device using a large pump Alfvén wave and a small counter-propagating seed Alfvén wave, with the seed-wave frequency tuned to match the backward Alfvén wave generated by standard PDI. Using hybrid simulations, we show that energy transfer from the pump to the seed reduces the latter's spatial damping. By comparing seed-wave amplitudes with and without the pump wave, this damping reduction can be used as a direct and reliable proxy for PDI growth. The method is validated in our simulations across a range of plasma and wave parameters and agrees well with theoretical predictions. Notably, the scheme exhibits no threshold for PDI excitation and is, in principle, readily implementable under current laboratory conditions. Finally, this scheme is a critical step toward solving the challenge of experimentally accessing Alfvén wave PDI and provides an elegant method that may be used to validate fundamental theories of parametric instabilities in controlled laboratory settings.

heliosphere↗

Self-interacting neutrinos: Solution to Hubble tension versus experimental constraints

Exotic self-interactions among the Standard-Model neutrinos have been proposed as a potential reason behind the tension in the expansion rate, H 0 , of the universe inferred from different observations. We constrain this proposal using electroweak precision observables, rare meson decays, and neutrinoless double-β decay. In contrast to previous works, we emphasize the importance of carrying out this study in a framework with full Standard-Model gauge invariance. We implement this first by working with a relevant set of Standard- Model-Effective-Field-Theory operators and subsequently by considering a UV completion in the inverse See-Saw model. We find that the scenario in which all flavors of neutrinos self-interact universally is strongly constrained, disfavoring a potential solution to the H 0 problem in this case. The scenario with self-interactions only among tau neutrinos is the least constrained and can potentially be consistent with a solution to the H 0 problem.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Does the Z boson have a lighter cousin?

In the quenched electroweak theory on the lattice I construct a set of physical states which overlap the physical photon and Z boson states. This is done by employing eigenstates of the covariant lattice Laplacian, in addition to the Higgs and lattice link variables, to construct gauge invariant vector boson creation operators. Diagonalizing the transfer matrix in the subspace of Hilbert space spanned by this set yields a massless photon and massive Z particle, as expected. But in the numerical data there is evidence for more vector bosons in the spectrum, albeit with considerable uncertainty in their masses, with the lowest finite mass particle in the range of 3–4 GeV. Published by the American Physical Society 2025

Greensite, Jeff (ORCID:0000000317209436)↗

Search for production of four top quarks in final states with same-sign or multiple leptons in proton–proton collisions at $\sqrt{s}=13$ ${TeV}$

The standard model (SM) production of four top quarks ($\text {t} {}{\overline{\text {t}}} \text {t} {}{\overline{\text {t}}} $) in proton–proton collisions is studied by the CMS Collaboration. The data sample, collected during the 2016–2018 data taking of the LHC, corresponds to an integrated luminosity of 137$\,\text {fb}^{-1}$ at a center-of-mass energy of 13$\,\text {TeV}$. The events are required to contain two same-sign charged leptons (electrons or muons) or at least three leptons, and jets. The observed and expected significances for the $\text {t} {}{\overline{\text {t}}} \text {t} {}{\overline{\text {t}}} $ signal are respectively 2.6 and 2.7 standard deviations, and the $\text {t} {}{\overline{\text {t}}} \text {t} {}{\overline{\text {t}}} $ cross section is measured to be $12.6^{+5.8}_{-5.2}\,\text {fb} $. The results are used to constrain the Yukawa coupling of the top quark to the Higgs boson, $y_{\text {t}}$, yielding a limit of $|y_{\text {t}}/y_{\text {t}}^{\mathrm {SM}} | < 1.7$ at $95\%$ confidence level, where $y_{\text {t}}^{\mathrm {SM}}$ is the SM value of $y_{\text {t}}$. They are also used to constrain the oblique parameter of the Higgs boson in an effective field theory framework, $\hat{H}<0.12$. Limits are set on the production of a heavy scalar or pseudoscalar boson in Type-II two-Higgs-doublet and simplified dark matter models, with exclusion limits reaching 350–470$\,\text {GeV}$ and 350–550$\,\text {GeV}$ for scalar and pseudoscalar bosons, respectively. Upper bounds are also set on couplings of the top quark to new light particles.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Erratum to: Higgs boson production cross-section measurements and their EFT interpretation in the $4\ell $ decay channel at $\sqrt{s}=$13 TeV with the ATLAS detector

When quoting the final cross section result in the text of the paper (Eur. Phys. J. C 80 (2020) 957), the theory component of the uncertainty was incorrectly set to 0.04 pb while the correct value of 0.03 pb was given in Table 8 and in all other results reported in this paper.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Quantum Optimization: Potential, Challenges, and the Path Forward

Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization being one of the most pronounced domains. Across computer science and physics, there are a number of algorithmic approaches, often with little linkage. This is further complicated by the fragmented nature of the field of mathematical optimization, where major classes of optimization problems, such as combinatorial optimization, convex optimization, non-convex optimization, and stochastic extensions, have devoted communities. With these aspects in mind, this work draws on multiple approaches to study quantum optimization. Provably exact versus heuristic settings are first explained using computational complexity theory — highlighting where quantum advantage is possible in each context. Then, the core building blocks for quantum optimization algorithms are outlined to subsequently define prominent problem classes and identify key open questions that, if answered, will advance the field. The effects of scaling relevant problems on noisy quantum devices are also outlined in detail, alongside meaningful benchmarking problems. We underscore the importance of benchmarking by proposing clear metrics to conduct appropriate comparisons with classical optimization techniques. Lastly, we highlight two domains – finance and sustainability – as rich sources of optimization problems that could be used to benchmark, and eventually validate, the potential real-world impact of quantum optimization.

97 MATHEMATICS AND COMPUTING↗

Coherent optical imaging of moving objects hidden in a heavily scattering random medium

Experimental results are presented that provide insight into the physics of statistical imaging in heavily scattering random media based on measured speckle correlations as a function of the change in position of a moving object. In this way, definitive interpretation of a rather complex and earlier theory is achieved, making this work an experimental complement to that theory paper []. Motion could be natural, where the set of positions is estimated or separately obtained, or directed, where a mechanical stage can be used to adjust the object's position. In the experiment, a coherent laser illuminates two scattering diffusers, while an object is translated between them in the resulting speckled field and images are collected in a transmission configuration. Results are shown for various objects of differing size and geometry, allowing the theory to be validated and interpreted with new understanding. This work demonstrates imaging opportunities, and applications include material characterization, environmental imaging and sensing, and deep-tissue imaging. Published by the American Physical Society 2025

Hastings, Ryan L. (ORCID:0009000095977807)↗

Ecologically-Informed Precision Conservation: A framework for increasing biodiversity in intensively managed agricultural landscapes with minimal sacrifice in crop production

Conservation actions are urgently needed to tackle biodiversity loss in intensively managed agricultural landscapes. Production lands are usually heterogeneous and contain low-yield areas that can be set aside for biodiversity conservation without serious yield losses. Here, we introduce Ecologically-Informed Precision Conservation, a framework that integrates yield mapping and ecological theory to select the best areas to create new set-asides while ensuring high crop yields at the farm/landscape level. Long-term yield maps can be generated using globally available satellite data and basic information on field/farm crop yield from farmers. Ecological principles are then used to select the subset of areas with the highest potential for biodiversity conservation by prioritising those that increase connectivity, maximise habitat heterogeneity and decrease landscape grain size. Here, the created non-crop habitats can be permanent and thus ensure biodiversity support over time. In addition, agricultural management efficiency can be enhanced by improving field shapes. The framework provides the basis for a practical, user-friendly tool that informs all interested stakeholders on how to rationalise existing agricultural landscapes using already-existing farming systems and available technologies. High cost-effectiveness from an economic and conservation perspective, along with the creation of heterogeneous non-crop habitats, make our framework a promising solution to re-design agricultural landscapes.

Precision agriculture↗

Quantum Hamilton-Jacobi theory, spectral path integrals, and exact WKB analysis

We propose a new way to perform path integrals in quantum mechanics by using a quantum version of Hamilton-Jacobi (HJ) theory. In classical mechanics, Hamilton-Jacobi theory is a powerful formalism, however, its utility is not explored in quantum theory beyond approximation schemes. The canonical transformation enables one to set the new Hamiltonian to constant or zero, but keeps the information about solution in Hamilton’s characteristic function. To benefit from this in quantum theory, one must work with a formulation in which classical Hamiltonian is used. This uniquely points to phase space path integral. However, the main variable in HJ formalism is energy, not time. Thus, we are led to consider the Fourier transform of the path integral, the spectral path integral Z ˜ ( E ) . The evaluation of path integrals reduces to determining the quantum Hamilton characteristic functions (which can be achieved via an asymptotic analysis) and a discrete sum over the quantum period lattice, generalizing Gutzwiller’s sum. Published by the American Physical Society 2025

Türe, Mustafa (ORCID:0009000975968618)↗

Obstacles to constructing de Sitter space in string theory

There have been many attempts to construct de Sitter space-times in string theory. While arguably there have been some successes, this has proven challenging, leading to the de Sitter swampland conjecture: quantum theories of gravity do not admit stable or metastable de Sitter space. Here we explain that, within controlled approximations, one lacks the tools to construct de Sitter space in string theory. Such approximations would require the existence of a set of (arbitrarily) small parameters, subject to severe constraints. But beyond this one also needs an understanding of big-bang and big-crunch singularities that is not currently accessible to standard approximations in string theory. The existence or non-existence of metastable de Sitter space in string theory remains a matter of conjecture.

79 ASTRONOMY AND ASTROPHYSICS↗

Langevin Dynamics modeling of gas-phase ion-ion recombination (Final Technical Report)

A self-consistent trajectory simulation approach to model MN reactions (Fig. 1) which incorporates the probability of electron transfer as a Monte Carlo operator (Fig. 2) was developed and published as Liu et al. J. Chem. Phys. 159, 114111 (2023). The electron transfer probability p ET estimated using the two-state Landau-Zener (LZ) theory was incorporated into classical trajectory simulations to elicit predictions of MN reaction cross-section σ (vacuum) or rate constant β (finite pressure). Electronic structure calculations with multireference configuration interaction (MRCI) and large correlation consistent basis sets were used to derive inputs to the LZ theory. The key advance of our trajectory simulation approach is the incorporation of electron transfer probability and the inclusion of the effect of ion-neutral interactions on MN using a Langevin representation of the effect of neutral gas on ions. For H + – H - and Li + – H(D) - pairs, our approach quantitatively agrees with measured speed-dependent cross-sections for up to ~10 5 m/s. For the ion pair Ne + – Cl - , our predictions of the MN rate constant at ~1 torr are a factor of ~2 – 3 higher than the experimentally measured value. Similarly, for Xe + – F - in the pressure range of ~20000 – 80000 Pa, our predictions of the MN rate constant are ~20% lower but are in excellent qualitative agreement with experimental data. The paradigm of using trajectory simulations to self-consistently model MN reactions is the basis for inclusion of additional non-classical, and static magnetic and electric field effects. Subsequent work, published as Roy et al. focused on modeling recombination rate constant for three ion pairs (rare gas Ar + cation and halide anions): Ar + – Cl - , Ar + – Br - , Ar + – I - , 2) considering spin-orbit couplings in the electronic structure calculations to obtain high-fidelity estimates of the electron transfer probability and incorporated within the classical trajectory simulations to elicit predictions. In addition to calculations of ion-ion recombination rate constants, a classical trajectory simulation technique (published as Roy et al. J. Chem. Phys. 162(9), 094104 (2023)) that uses quaternions to represent orientation of non-spherical particles (ions or aerosol particles) was developed to simulate the recombination of diatomic or more generally, polyatomic molecules. Finally, several other ion pairs such as Ne + – Cl - , Kr + – Cl - , were explored using the developed semi-classical trajectory simulations to understand various challenges in tackling electronic structure calculations. Using empirical approaches to parameterize the electron transfer radius, trajectory simulations were also used to probe the effect of ion number density on MN rate constant.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Hidden conformal symmetry from the lattice

We analyze newly expanded and refined data from lattice studies of an SU(3) gauge theory with eight Dirac fermions in the fundamental representation. We focus on the light composite states emerging from these studies, consisting of a set of pseudoscalars and a single light scalar. We first consider the view that this theory is just outside the conformal window. In this case, the pseudoscalars arise from spontaneous breaking of chiral symmetry. Identifying the scalar in this case as an approximate dilaton, we fit the lattice data to a dilaton effective field theory, finding that it yields a good fit even at lowest order. For comparison, we then consider the possibility that the theory is inside the conformal window. The fermion mass provides a deformation, triggering confinement. We employ simple scaling laws to fit the lattice data, and find that it is of lesser quality.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Active learning for robust, high-complexity reactive atomistic simulations

Machine learned reactive force fields based on polynomial expansions have been shown to be highly effective for describing simulations involving reactive materials. Nevertheless, the highly flexible nature of these models can give rise to a large number of candidate parameters for complicated systems. In these cases, reliable parameterization requires a well-formed training set, which can be difficult to achieve through standard iterative fitting methods. In this paper, we present an active learning approach based on cluster analysis and inspired by Shannon information theory to enable semi-automated generation of informative training sets and robust machine learned force fields. The use of this tool is demonstrated for development of a model based on linear combinations of Chebyshev polynomials explicitly describing up to four-body interactions, for a chemically and structurally diverse system of C/O under extreme conditions. We show that this flexible training database management approach enables development of models exhibiting excellent agreement with Kohn–Sham density functional theory in terms of structure, dynamics, and speciation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Finite-temperature many-body perturbation theory for anharmonic vibrations: Recursions, algebraic reduction, second-quantized reduction, diagrammatic rules, linked-diagram theorem, finite-temperature self-consistent field, and general-order algorithm

A unified theory is presented for finite-temperature many-body perturbation expansions of the anharmonic vibrational contributions to thermodynamic functions, i.e., the free energy, internal energy, and entropy. The theory is diagrammatically size-consistent at any order, as ensured by the linked-diagram theorem proved in this study, and, thus, applicable to molecular gases and solids on an equal footing. It is also a basis-set-free formalism, just like its underlying Bose–Einstein theory, capable of summing anharmonic effects over an infinite number of states analytically. It is formulated by the Rayleigh–Schrödinger-style recursions, generating sum-over-states formulas for the perturbation series, which unambiguously converges at the finite-temperature vibrational full-configuration-interaction limits. Two strategies are introduced to reduce these sum-over-states formulas into compact sum-over-modes analytical formulas. One is a purely algebraic method that factorizes each many-mode thermal average into a product of one-mode thermal averages, which are then evaluated by the thermal Born–Huang rules. Canonical forms of these rules are proposed, dramatically expediting the reduction process. The other is finite-temperature normal-ordered second quantization, which is fully developed in this study, including a proof of thermal Wick’s theorem and the derivation of a normal-ordered vibrational Hamiltonian at finite temperature. The latter naturally defines a finite-temperature extension of size-extensive vibrational self-consistent field theory. These reduced formulas can be represented graphically as Feynman diagrams with resolvent lines, which include anomalous and renormalization diagrams. Two order-by-order and one general-order algorithms of computing these perturbation corrections are implemented and applied up to the eighth order. The results show no signs of Kohn–Luttinger-type nonconvergence.

74 ATOMIC AND MOLECULAR PHYSICS↗

Substitution Reactions in the Pyrolysis of Acetone Revealed through a Modeling, Experiment, Theory Paradigm

The development of high-fidelity mechanisms for chemically reactive systems is a challenging process that requires the compilation of rate descriptions for a large and somewhat ill-defined set of reactions. The present unified combination of modeling, experiment, and theory provides a paradigm for improving such mechanism development efforts. Here we combine broadband rotational spectroscopy with detailed chemical modeling based on rate constants obtained from automated ab initio transition state theory-based master equation calculations and high-level thermochemical parametrizations. Broadband rotational spectroscopy offers quantitative and isomer-specific detection by which branching ratios of polar reaction products may be obtained. Using this technique, we observe and characterize products arising from H atom substitution reactions in the flash pyrolysis of acetone (CH 3 C(O)CH 3 ) at a nominal temperature of 1800 K. The major product observed is ketene (CH 2 CO). Minor products identified include acetaldehyde (CH 3 CHO), propyne (CH 3 CCH), propene (CH 2 CHCH 3 ), and water (HDO). Literature mechanisms for the pyrolysis of acetone do not adequately describe the minor products. The inclusion of a variety of substitution reactions, with rate constants and thermochemistry obtained from automated ab initio kinetics predictions and Active Thermochemical Tables analyses, demonstrates an important role for such processes. Furthermore, the pathway to acetaldehyde is shown to be a direct result of substitution of acetone's methyl group by a free H atom, while propene formation arises from OH substitution in the enol form of acetone by a free H atom.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗