Search NASASearch

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 19 records

Causal sets and an emerging continuum

Abstract Causal set theory offers a simple and elegant picture of discrete physics. But the vast majority of causal sets look nothing at all like continuum spacetimes, and must be excluded in some way to obtain a realistic theory. I describe recent results showing that almost all non-manifoldlike causal sets are, in fact, very strongly suppressed in the gravitational path integral. This does not quite demonstrate the emergence of a continuum—we do not yet understand the remaining unsuppressed causal sets well enough—but it is a significant step in that direction.

Astronomy & Astrophysics

Scale setting of SU⁡(𝑁) Yang–Mills theory, topology and large-𝑁 volume independence

We set the scale of SU⁡(𝑁) Yang-Mills theories for 𝑁 =3, 5, 8 and in the large-𝑁 limit via gradient flow, as a first step towards the computation of the large-𝑁 Λ-parameter using step scaling. We adopt twisted boundary conditions to achieve large-𝑁 volume reduction and the Parallel Tempering on Boundary Conditions algorithm to tame topological freezing. This setup allows accurate determinations of the gradient-flow scales down to lattice spacings as fine as ∼0.025 fm for all the explored values of 𝑁, a regime that has never been reached with ergodic algorithms. Moreover, we are able to precisely estimate the finite-size systematics related to topological freezing, and to show the suppression of finite-volume effects expected by virtue of large-𝑁 twisted volume reduction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Final Results of the M AJORANA D EMONSTRATOR ’s Search for Double-Beta Decay of 76 Ge to Excited States of 76 Se

76 Ge can 𝛽⁢𝛽 decay into three possible excited states of 76 Se , with the emission of two or, if the neutrino is Majorana, zero neutrinos. None of these six transitions have yet been observed. The M AJORANA D EMONSTRATOR was designed to study 𝛽⁢𝛽 decay of 76 Ge using a low background array of high purity germanium detectors. With 98.2 kg-y of isotopic exposure, the demonstrator sets the strongest half-life limits to date for all six transition modes. For 2⁢𝜈⁢𝛽⁢𝛽 to the 0$^+_1$ state of 76 Se , this search has begun to probe for the first time half-life values predicted using modern many-body nuclear theory techniques, setting a limit of 𝑇 1/2 > 1.5 × 10 24 y (90% CL).

Majorana neutrinos

Second‐ and Third‐Order Elastic Constants of Inert and Energetic Molecular Crystals From Density Functional Theory

Complete tensors of the second- and third-order elastic constants of the organic molecular crystals acetaminophen, pentaerythritol tetranitrate (PETN), cyclotrimethylene trinitramine (RDX), cyclotetramethylene tetranitramine (HMX), 1,1-diamino-2,2-dinitroethylene (FOX-7), hexanitrohexaazaisowurtzitane (CL-20), and erythritol tetranitrate (ETN) have been calculated using dispersion-corrected density functional theory. The sets of second- and third-order elastic constants are expected to provide a more accurate and reliable description of the behavior of these materials under nonhydrostatic loads than pressure- and volume-dependent second-order elastic constants. The tensors of second-order constants have been compared with experimental data and/or other calculations when possible, and with the exception of results for CL-20 from Brillouin scattering experiments, we find good agreement. The calculated third-order elastic constants of PETN are in very good agreement with the subset of third-order constants derived from experimental wave speed measurements. The elastic anisotropies of the crystals have been estimated using the universal elastic anisotropy index, which shows that the crystals fall into three groups with low anisotropy (PETN, RDX, and CL-20), moderate anisotropy (acetaminophen, HMX, and ETN), and high elastic anisotropy (FOX-7).

36 MATERIALS SCIENCE

Modeling ethanol/water adsorption in all-silica zeolites using the real adsorbed solution theory

A comprehensive set of single-component and binary isotherms were collected for ethanol/water adsorption into the siliceous forms of 185 known zeolites using grand-canonical Monte Carlo simulations. Using these data, a systematic analysis of ideal/real adsorbed-solution theory (IAST/RAST) was conducted and activity coefficients were derived for ethanol/water mixtures adsorbed in different zeolites based on RAST. It was found that activity coefficients of ethanol are close to unity while activity coefficients of water are larger in most zeolites, indicating a positive excess free energy of the mixture. This observation can be attributed to water/ethanol interactions being less favorable than water/water interactions in the single-component adsorption of water at comparable loadings. The deviation from ideal behavior can be highly structure-dependent but no clear correlation with pore diameters was identified. Furthermore, our analysis also demonstrates the following: (1) accurate unary isotherms in the low-loading regime are critical for obtaining physically sensible activity coefficients; (2) the global regression scheme to solve for activity model parameters performs better than fitting activity models to activity coefficients calculated locally at each binary state point; and (3) including the dependence on adsorption potential offers only a minor benefit for describing binary adsorption at the lowest fugacities. Finally, the Margules activity model was found incapable of capturing the non-ideal adsorption behavior over the entire range of fugacities and compositions in all zeolites, but for conditions typical of solution-phase adsorption, RAST predictions using zeolite-specific or even bulk Margules parameters provide an improved description compared to IAST.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Transversely pumped laser driven particle accelerator

We present a novel acceleration scheme capable of accelerating electrons and ions in an underdense plasma. Transversely Pumped Acceleration (TPA) uses multiple arrays of counter-propagating laser beamlets that focus onto a central acceleration axis. Tuning the injection timing and the spacing between the adjacent beamlets allows for precise control over the position and velocity of the intersection point of the counter-propagating beam arrays. This results in an accelerating structure that propagates orthogonal to the direction of laser propagation. We present the theory that sets the injection timing of the incoming pulses to accelerate electrons and ions with a tunable phase velocity plasma wave. Simulation results are also presented which demonstrate 1.12 GeV proton beams accelerated in 3.6 mm of plasma and electron acceleration gradients on the order of 1 TeV/m in a scheme that circumvents dephasing. This work has potential applications as a compact accelerator for medical physics and high energy physics colliders.

Laser-produced plasmas

Control and Real-Time Simulation of Microgrids with EV Fast-Charging and Grid-Forming Resources

Fast charging stations (FCSs) for electric vehicles (EVs) can behave as constant power loads, which is problematic for the operation of grid-forming (GFM) inverter-based resources (IBRs). To tackle this problem, this paper proposes a control suite that makes FCSs responsive to ac voltage and frequency disturbances. To test the performance of the FCS controls, the paper also sets forth theory to compensate for time-delays appearing in the real-time simulation of microgrid models divided into several central processing units (CPUs). Furthermore, these contributions are showcased via multi-CPU real-time simulations of a faulted microgrid having EV FCSs and GFM IBRs powered by photovoltaic solar arrays as well as power hardware-in-the-loop experiments. These contributions are significant to address NERC recommendations and IEEE standards.

14 SOLAR ENERGY

Thermal relaxation and the complete set of second-order transport coefficients for the unitary Fermi gas from kinetic theory

We compute the complete set of second-order transport coefficients of the unitary Fermi gas, a dilute gas of spin-1/2 particles interacting via an 𝑠 -wave interaction tuned to infinite scattering length. The calculation is based on kinetic theory and the Chapman-Enskog method at second order in the Knudsen expansion. We take into account the exact two-body collision integral. We extend previous results on second-order coefficients related to shear stress by including terms related to heat flow and gradients of the fugacity. We confirm that the thermal relaxation time is given by the simple estimate 𝜏 𝜅 = 𝜅⁢𝑚/(𝑐 𝑃 ⁢𝑇) even if the full collision kernel is taken into account. Furthermore, 𝜅 is the thermal conductivity, 𝑚 is the mass of the particles, 𝑐𝑃 is the specific heat at constant pressure, and 𝑇 is the temperature.

Kinetic theory

Dynamic probabilistic risk assessment and game theory for cyber security risk analysis in nuclear power plants

Nuclear Power Plants and energy systems have become more prone to cyber-attacks with their digitalization and the increased use of smart equipment. Hence, it is important to quantify the risk associated with cyber-attacks in such systems. Dynamic Probabilistic Risk Assessment which involves studying the evolution of a system due to random events and operator and attacker actions during a cyber-attack by employing a physics-based model of the system is a suitable framework to quantify cybersecurity risk in nuclear power plants. In addition to the plant dynamics, it is also important to model the strategies of the attackers and plant operators for an effective cybersecurity risk assessment. Game theory provides a set of necessary tools to model such strategic interactions. In this research, a framework that integrates dynamic probabilistic risk assessment with game theory for cybersecurity risk analysis in nuclear power plants is presented. The mathematical formulation is derived based on the theory of continuous event trees. We propose a game theory based action model, that utilizes physics-based rewards to define the strategies of attackers and operators at every decision epoch. As a case study, the risk associated with cyber-attacks on the digital components in the secondary side of a pressurized water reactor is studied using a reduced order model. A set of attacker actions and a set of operator actions are defined for the system. The operator and attacker interactions were modelled using simultaneous game, their action policies were computed using the concept of mixed strategy Nash equilibrium and the evolution of the system was studied.

97 MATHEMATICS AND COMPUTING

Observation of VVZ production at $\sqrt{s}$ = 13 TeV with the ATLAS detector

A search for the production of three massive vector bosons, VVZ(V = W, Z) , in proton-proton collisions at $\sqrt{s}$ = 13 TeV is performed using data with an integrated luminosity of 140 fb -1 recorded by the ATLAS detector at the Large Hadron Collider. Events produced in the leptonic final states WWZ → ℓvℓvℓℓ (ℓ = e,μ), WZZ → ℓvℓℓℓℓ, ZZZ → ℓℓℓℓℓ, and the semileptonic final states WWZ → qq ℓvℓℓ and WZZ → ℓv qq ℓℓ, are analysed. The measured cross section for the pp → VVZ process is 660$^{+93}_{-90}$(stat.)$^{+80}_{-81}$(syst.) fb, and the observed (expected) significance is 6.4 (4.7) standard deviations, representing the observation of VVZ production. In addition, the measured cross section for the pp → WWZ process is 442 ± 94(stat.)$^{+60}_{-52}$(syst.) fb, and the observed (expected) significance is 4.4 (3.6) standard deviations, representing evidence of WWZ production. The measured cross sections are consistent with the Standard Model predictions. Constraints on physics beyond the Standard Model are also derived in the effective field theory framework by setting limits on Wilson coefficients for dimension-8 operators describing anomalous quartic gauge boson couplings.

Aad, G. (ORCID:0000000266654934)

Convergent Protocols for Computing Protein–Ligand Interaction Energies Using Fragment-Based Quantum Chemistry

Fragment-based quantum chemistry methods offer a way to sidestep the steep nonlinear scaling of electronic structure calculations so that large molecular systems can be investigated using high-level methods. Here, we use fragmentation to compute protein–ligand interaction energies in systems with several thousand atoms, using a new software platform for managing fragment-based calculations that implements a screened many-body expansion. Convergence tests using a minimal-basis semiempirical method (HF-3c) indicate that two-body calculations, with single-residue fragments and simple hydrogen caps, are sufficient to reproduce interaction energies obtained using conventional supramolecular electronic structure calculations, to within 1 kcal/mol at about 1% of the computational cost. We also demonstrate that the HF-3c results are illustrative of trends obtained with density functional theory in basis sets up to augmented quadruple-ζ quality. Strategic deployment of fragmentation facilitates the use of converged biomolecular model systems alongside high-quality electronic structure methods and basis sets, bringing ab initio quantum chemistry to systems of hitherto unimaginable size. This will be useful for generation of high-quality training data for machine learning applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

High-Yield Room-Temperature Aryl 211 At Radiolabeling via Redox-Activated Column-Shipped 211 At

Efficient late-stage formation of aryl– 211 At bonds is relevant to expanding the scope of targeted α-therapy radiopharmaceuticals. In this work, a catalyst-enabled astatodeboronation approach is evaluated using wet chemically regenerated 211 At recovered from shipped 3-octanone-impregnated columns. A series of aryl boronic esters bearing electron-donating and electron-withdrawing substituents were radiolabeled under mild conditions, with reaction parameters examined through time-dependent studies. Radiochemical conversions ranging from 68–97% were observed across the substrate set. Density functional theory calculations were employed as a qualitative framework to contextualize relative B–C and At–C bonding descriptors. Overall, this study demonstrates that wet chemically regenerated 211 At can be applied to the late-stage labeling of aryl boronic esters under mild conditions and provides guidance for future exploration of 211 At radiolabeling strategies.

211At-aryl labeling

Burn mode signatures enabled by high dynamic range fusion reaction history

The evolution of the fusion burn of a compressed inertial confinement fusion (ICF) implosion gives information about the evolution of the temperature, mass, and volume of the hot spot. Currently, the fusion reaction history has been measured with about a decade of dynamic range, giving information about just the peak of the fusion burn. There are proposals for extending the dynamic range to 1000×, measuring the rising edge of the burn earlier in time. Using fusion hot spot theory and a set of ICF simulations, we identify and categorize different stages of fusion burn and what signatures could be measured. For ice layered implosions, the details, conditions, and dynamics of the fusion burn propagation could be observed. For double shell and OMEGA scale implosions, the evolution of the final compression and rebounding shock before ignition could be observed. Higher dynamic range expands investigation into the logarithmic derivative, α, as a signature of various mechanisms.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Multi-fidelity learning for interatomic potentials: low-level forces and high-level energies are all you need

The promise of machine learning interatomic potentials (MLIPs) has led to an abundance of public quantum mechanical (QM) training datasets. The quality of an MLIP is directly limited by the accuracy of the energies and atomic forces in the training dataset. Unfortunately, most of these datasets are computed with relatively low-accuracy QM methods, e.g. density functional theory with a moderate basis set. Due to the increased computational cost of more accurate QM methods, e.g. coupled-cluster theory with a complete basis set (CBS) extrapolation, most high-accuracy datasets are much smaller and often do not contain atomic forces. The lack of high-accuracy atomic forces is quite troubling, as training with force data greatly improves the stability and quality of the MLIP compared to training to energy alone. Because most datasets are computed with a unique level of theory, traditional single-fidelity (SF) learning is not capable of leveraging the vast amounts of published QM data. In this study, we apply multi-fidelity learning (MFL) to train an MLIP to multiple QM datasets of different levels of accuracy, i.e. levels of fidelity. Specifically, we perform three test cases to demonstrate that MFL with both low-level forces and high-level energies yields an extremely accurate MLIP—far more accurate than a SF MLIP trained solely to high-level energies and almost as accurate as a SF MLIP trained directly to high-level energies and forces. Therefore, MFL greatly alleviates the need for generating large and expensive datasets containing high-accuracy atomic forces and allows for more effective training to existing high-accuracy energy-only datasets. Indeed, low-accuracy atomic forces and high-accuracy energies are all that are needed to achieve a high-accuracy MLIP with MFL.

36 MATERIALS SCIENCE

ReaxFF Parameter Set for Boron Clusters and Icosahedral Boron Crystals: Comparison with Density Functional Theory and Machine-Learning Potentials

Icosahedral boron materials, which include regular icosahedra of 12 boron atoms have gained increasing attention due to their potential applications as superhard materials, semiconductors, and energy storage media. However, the synthesis of high quality crystals of these materials has been a major barrier to the development of these applications. To enable computational prediction of synthesis conditions yielding high-quality icosahedral boron crystals, herein we tested and refined a set of ReaxFF parameters for the nucleation and growth of such crystals. We focused on matching the relative energies of small boron clusters obtained by density functional theory since such small clusters and similar motifs are likely present in crystal nuclei and at the interface of growing crystals. Using a training set of B 80 clusters, including a low-energy core–shell structure containing a B 12 icosahedron core and a high-energy single-shell structure produced in preliminary ReaxFF simulations, the ReaxFF parameter set was refined to better reproduce energies calculated by density functional theory (DFT). Among existing ReaxFF parameter sets and the machine-learning interatomic potentials MACE-MP-0, MACE-MP-0b3, MACE-MPA-0, PFP v7.0.0, and SevenNet-MF-ompa, only our new parameter set and PFP v7.0.0 correctly ranked these B 80 clusters. This refinement led to improved agreement with DFT for a test set of 58 clusters consisting of 8–103 boron atoms. Furthermore, our refined parameter set yielded greater local icosahedral structure than the previously existing ReaxFF parameter set for larger scale simulations of crystallization from supercooled liquid boron. Additionally, simulations of solid boron in contact with molten nickel using our refined ReaxFF parameters yielded a boron solubility value that agrees moderately well with experimental expectations, while the previous boron parameters gave a value that was much too low.

boron

Embedding space approach to Lorentzian CFT amplitudes and causal spherical functions

Conformal field theory in a Minkowski setting is discussed in an embedding space approach, paying special attention to causality constraints for four-point amplitudes. The physics of dilatation and Lorentz boost is emphasized in specifying the noncompact maximal Abelian subgroup of S O ( d , 2 ) . Reduction of a conformal field theory four-point amplitudes as functions of cross ratios is shown to be equivalent to enforcing H bi-invariance, i.e., F ( h g h ′ ) = F ( g ) , with g ∈ S O ( d , 2 ) and H an appropriate subgroup. Causality is imposed by introducing appropriate semigroups. Causal zonal spherical functions are constructed, making contact with Minkowski conformal blocks introduced previously. Published by the American Physical Society 2024

Agarwal, Pulkit (ORCID:0000000346581691)

Redox Potentials for Hydrogen Species in Acetonitrile and Tetrahydrofuran

The properties of the fundamental hydrogen species, proton (H+), hydrogen atom (H•), and hydride anion (H-) are critical to a vast range of chemical processes, yet their thermodynamic properties in nonaqueous solvents are not well established. A hybrid supermolecule-continuum approach is used to predict the Gibbs free energies of solvation (?G°solv) and standard redox potentials (E°) for the 2H+/H2 and H•/H- couples in acetonitrile (MeCN) and tetrahydrofuran (THF) following the approach previously used for water. Gas phase geometry optimizations were done using density functional theory (DFT) with the ?B97XD functional, Møller-Plesset second-order perturbation theory (MP2) with augmented correlation-consistent basis sets and composite-correlated molecular orbital theory (G3MP2 and G3MP2B3). Additional single point calculations in gas phase were performed for H- affinity for MeCN and THF at the coupled cluster CCSD(T) level using MP2 geometries. Solvation was included using the self-consistent reaction field SMD model. For H+, the ?G°solv values are predicted to be -252.2 kcal/mol in MeCN and -261.0 kcal/mol in THF. The redox potentials for the 2H+/H2 couple are +0.49 V in MeCN and +0.11 V in THF relative to the aqueous SHE, consistent with the available experimental data. The ?G°solv for H- is predicted to be -80 kcal/mol in MeCN and -68 in THF, and for H•, ?G°solv is predicted to be -1.3 kcal/mol in THF and -2.0 kcal/mol in MeCN. These solvation energies yield respective calculated redox potentials for the H•/H- couple of -0.14 V in MeCN and -0.68 V in THF relative to the aqueous SHE. H2 solvation is slightly exergonic in MeCN (-3.3 kcal/mol) and near thermoneutral in THF (+1.3 kcal/mol). The pKa(H2) is predicted to be 45.4 in MeCN and 47.8 in THF. The proton-coupled electron transfer (PCET) accounting term CG was evaluated giving values on the ferrocene scale within approximately 2 kcal/mol of literature in both solvents. These results provide benchmarks for hydrogen redox chemistry in MeCN and THF and improve consistency across E°, ?G°solv, pKa, and CG. These results provide benchmarks for hydrogen redox chemistry in nonaqueous media challenging previous estimates based on indirect extrapolations and assumptions.

Duda, Damian P.

An Algorithm for Atom-Centered Lossy Compression of the Atomic Orbital Basis in Density Functional Theory Calculations

Large atomic-orbital (AO) basis sets of at least triple and preferably quadruple-ζ (QZ) size are required to adequately converge Kohn–Sham density functional theory (DFT) calculations toward the complete basis set limit. However, incrementing the cardinal number by one nearly doubles the AO basis dimension, and the computational cost scales as the cube of the AO dimension, so this is very computationally demanding. Here, in this work, we develop and test a threshold-based natural atomic orbital (NAO) scheme in which ϵ-NAOs are obtained as eigenfunctions of atomic blocks of the density matrix in a one-center orthogonalized representation. This enables compression of the AO basis that is optimal for a given threshold, 10 –ϵ , by discarding NAOs with occupation numbers below that threshold. Extensive pilot test calculations using the Hartree–Fock functional and taking the converged density matrix as input suggest that a threshold of 10 –5 can yield a compression factor (ratio of AO to compressed ϵ-NAO dimension) between 2.5 and 4.5 for the QZ pc-3 basis. The errors in relative energies are typically less than 0.1 kcal/mol when the compressed basis is used instead of the uncompressed basis. Between 10 and 100 times smaller errors (i.e., usually less than 0.01 kcal/mol) can be obtained with a threshold 10 –7 , while the compression factor is typically between 2 and 2.5.

basis sets