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 505 records · Page 28

Atom Equivalent Energies for the Rapid Estimation of the Heat of Formation of Explosive Molecules from Density Functional Tight Binding Theory

Atom equivalent energies have been derived from which the gas-phase heat of formation of explosive molecules can be estimated from fast, semiempirical density functional tight binding total energy calculations. The root-mean-square deviation and maximum deviation of the heats of formation from the experimental values for the set of 45 energetic molecules compiled by Byrd and Rice [ J. Phys. Chem. A, 2006, 110, 1005–1013] are 10.4 and 25.5 kcal/mol, respectively, using 4 atom equivalent energies and 7.4 and 15.0 kcal/mol, respectively, using 7 atom equivalent energies. These errors are around a factor of 2–3 larger than those obtained from density functional theory calculations but are smaller than those obtained from other semiempirical electronic structure methods. Heats of formation calculated with density functional tight binding theory using the 4 and 7 atom equivalent energies, the Byrd and Rice scheme, and the atom pair contribution method for a new set of 531 energetic molecules that contain only carbon, hydrogen, nitrogen, and oxygen are provided.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Calculation of spin–orbit couplings using RASCI spinless one-particle density matrices: Theory and applications

Here we present the formalism and implementation for calculations of spin–orbit couplings (SOCs) using the Breit–Pauli Hamiltonian and non-relativistic wave functions described by the restricted active space configuration interaction (RASCI) method with general excitation operators of spin-conserving spin-flipping, ionizing, and electron-attaching types. The implementation is based on the application of the Wigner–Eckart theorem within the spin space, which enables the calculation of the entire SOC matrix based on the explicit calculation of just one transition between the two spin multiplets. Numeric results for a diverse set of atoms and molecules highlight the importance of a balanced treatment of correlation and adequate basis sets and illustrate the overall robust performance of RASCI SOCs. The new implementation is a useful addition to the methodological toolkit for studying spin-forbidden processes and molecular magnetism.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Relational bulk reconstruction from modular flow

Abstract The entanglement wedge reconstruction paradigm in AdS/CFT states that for a bulk qudit within the entanglement wedge of a boundary subregion$$ \overline{A} $$ A ¯ , operators acting on the bulk qudit can be reconstructed as CFT operators on$$ \overline{A} $$ A ¯ . This naturally fits within the framework of quantum error correction, with the CFT states containing the bulk qudit forming a code protected against the erasure of the boundary subregionA. In this paper, we set up and study a framework for relational bulk reconstruction in holography: given two code subspaces both protected against erasure of the boundary regionA, the goal is to relate the operator reconstructions between the two spaces. To accomplish this, we assume that the two code subspaces are smoothly connected by a one-parameter family of codes all protected against the erasure ofA, and that the maximally-entangled states on these codes are all full-rank. We argue that such code subspaces can naturally be constructed in holography in a “measurement-based” setting. In this setting, we derive a flow equation for the operator reconstruction of a fixed code subspace operator using modular theory which can, in principle, be integrated to relate the reconstructed operators all along the flow. We observe a striking resemblance between our formulas for relational bulk reconstruction and the infinite-time limit of Connes cocycle flow, and take some steps towards making this connection more rigorous. We also provide alternative derivations of our reconstruction formulas in terms of a canonical reconstruction map we call the modular reflection operator.

Physics↗

Extending the thermodynamic form factor bootstrap program: multiple particle-hole excitations, crossing symmetry, and reparameterization invariance

In this study, we further the thermodynamic bootstrap program which involves a set of recently developed ideas used to determine thermodynamic form factors of local operators in integrable quantum field theories. These form factors are essential building blocks for dynamic correlation functions at finite temperatures or non-equilibrium stationary states. In this work we extend this program in three ways. Firstly, we demonstrate that the conjectured annihilation pole axiom is valid in the low energy particle-hole excitations. Secondly, we introduce a crossing relation, which establishes a connection between form factors with different excitation content. Typically, the crossing relation is a consequence of Lorentz invariance, but due to the finite energy density of the considered states, Lorentz invariance is broken. Nonetheless a crossing relation involving excitations with both particles and holes can established using the finite volume representation of the thermodynamic form factors. Finally, we demonstrate that the thermodynamic form factors satisfy a reparameterization invariance, an invariance which encompasses crossing. Reparameterization invariance exploits the fact that the details of the representation of the thermodynamic state are unimportant. In the course of developing these results, we demonstrate the internal consistency of the thermodynamic form factor bootstrap program in a number of ways. Finally, we provide explicit computations of form factors of conserved charges and densities with crossed excitations and show our results can be used to infer information about thermodynamic form factors in the Lieb-Liniger model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A Generalized Variational Principle with Applications to Excited State Mean Field Theory

We present a generalization of the variational principle that is compatible with any Hamiltonian eigenstate that can be specified uniquely by a list of properties. This variational principle appears to be compatible with a wide range of electronic structure methods, including mean field theory, density functional theory, multireference theory, and quantum Monte Carlo. Like the standard variational principle, this generalized variational principle amounts to the optimization of a nonlinear function that, in the limit of an arbitrarily flexible wave function, has the desired Hamiltonian eigenstate as its global minimum. Unlike the standard variational principle, it can target excited states and select individual states in cases of degeneracy or near-degeneracy. As an initial demonstration of how this approach can be useful in practice, we employ it to improve the optimization efficiency of excited state mean field theory by an order of magnitude. With this improved optimization, we are able to demonstrate that the accuracy of the corresponding second-order perturbation theory rivals that of singles-and-doubles equation-of-motion coupled cluster in a substantially broader set of molecules than could be explored by our previous optimization methodology.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quantum computation of frequency-domain molecular response properties using a three-qubit iToffoli gate

The quantum computation of molecular response properties on near-term quantum hardware is a topic of substantial interest. Computing these properties directly in the frequency domain is desirable, but the circuits require large depth if the typical hardware gate set consisting of single- and two-qubit gates is used. While high-fidelity multipartite gates have been reported recently, their integration into quantum simulation and the demonstration of improved accuracy of the observable properties remains to be shown. Here, we report the application of a high-fidelity multipartite gate, the iToffoli gate, to the computation of frequency-domain response properties of diatomic molecules. The iToffoli gate enables a ~50% reduction in circuit depth and ~40% reduction in circuit execution time compared to the traditional gate set. We show that the molecular properties obtained with the iToffoli gate exhibit comparable or better agreement with theory than those obtained with the native CZ gates. Our work is among the first demonstrations of the practical usage of a native multi-qubit gate in quantum simulation, with diverse potential applications to near-term quantum computation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Intrinsic glassy-metallic transport in an amorphous coordination polymer

Conducting organic materials, such as doped organic polymers, molecular conductors and emerging coordination polymers4, underpin technologies ranging from displays to flexible electronics. Realizing high electrical conductivity in traditionally insulating organic materials necessitates tuning their electronic structure through chemical doping6. Furthermore, even organic materials that are intrinsically conductive, such as single-component molecular conductors, require crystallinity for metallic behavior. However, conducting polymers are often amorphous to aid durability and processability. Using molecular design to produce high conductivity in undoped amorphous materials would enable tunable and robust conductivity in many applications, but there are no intrinsically conducting organic materials that maintain high conductivity when disordered. Here we report an amorphous coordination polymer, Ni tetrathiafulvalene tetrathiolate, which displays markedly high electronic conductivity (up to 1,200 S cm –1 ) and intrinsic glassy-metallic behavior. Theory shows that these properties are enabled by molecular overlap that is robust to structural perturbations. This unusual set of features results in high conductivity that is stable to humid air for weeks, pH 0–14 and temperatures up to 140 °C. Furthermore, these findings demonstrate that molecular design can enable metallic conductivity even in heavily disordered materials, raising fundamental questions about how metallic transport can exist without periodic structure and indicating exciting new applications for these materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Benchmarking nitrous oxide adsorption and activation in metal–organic frameworks bearing coordinatively unsaturated metal centers

Anthropogenic emissions of N 2 O, the third most abundant greenhouse gas after CO 2 and CH 4 , are contributing to global climate change. Although metal–organic frameworks (MOFs) have been widely studied as adsorbents for CO 2 and CH 4 , less effort has focused on the use of MOFs to remove N 2 O from emission streams or from air. Further, N 2 O activation would enable its use as an inexpensive oxidant for fine chemical synthesis. Here, in this paper, we identify features that contribute to strong binding and high uptake of N 2 O at coordinatively unsaturated metal sites in the M 2 Cl 2 (btdd) (M = Mn, Co, Ni, Cu; btdd 2– = bis(1,2,3-triazolo[4,5-b],[4',5'-i])dibenzo[1,4]dioxin) and M 2 (dobdc) (M = Mg, Mn, Fe, Co, Ni, Cu, Zn; dobdc 4– = 2,5-dioxido-1,4-benzenedicarboxylate) series of MOFs. Combined experimental and computational studies suggest that N 2 O adsorption at open-metal-sites is primarily based on electrostatic interactions, rather than π-backbonding, causing MOFs with more Lewis acidic metal centers to be superior N 2 O adsorbents. As a result, Mg 2 (dobdc) demonstrates strong binding and record-setting N 2 O uptake (8.75 mmol g –1 at 1 bar and 298 K). Using density functional theory (DFT) to characterize reactive intermediates and transition states, we demonstrate that N 2 O activation to form a M(IV)–oxo species and N 2 is thermodynamically favorable in Mn 2 (dobdc) and Fe 2 (dobdc) but appears to be kinetically limited in Mn 2 (dobdc). Our work lays a foundation for understanding N 2 O adsorption and activation in MOFs, paving the way for the design of promising next-generation materials for N 2 O capture and utilization.

36 MATERIALS SCIENCE↗

Scalable generalized screening for high-order terms in the many-body expansion: Algorithm, open-source implementation, and demonstration

The many-body expansion lies at the heart of numerous fragment-based methods that are intended to sidestep the nonlinear scaling of ab initio quantum chemistry, making electronic structure calculations feasible in large systems. In principle, inclusion of higher-order n-body terms ought to improve the accuracy in a controllable way, but unfavorable combinatorics often defeats this in practice and applications with n ≥ 4 are rare. Here, we outline an algorithm to overcome this combinatorial bottleneck, based on a bottom-up approach to energy-based screening. This is implemented within a new open-source software application (“Fragme∩t”), which is integrated with a lightweight semi-empirical method that is used to cull subsystems, attenuating the combinatorial growth of higher-order terms in the graph that is used to manage the calculations. This facilitates applications of unprecedented size, and we report four-body calculations in (H2O)64 clusters that afford relative energies within 0.1 kcal/mol/monomer of the supersystem result using less than 10% of the unique subsystems. We also report n-body calculations in (H2O)20 clusters up to n = 8, at which point the expansion terminates naturally due to screening. These are the largest n-body calculations reported to date using ab initio electronic structure theory, and they confirm that high-order n-body terms are mostly artifacts of basis-set superposition error.

Chemistry↗

Optimizing the regularization in size-consistent second-order Brillouin-Wigner perturbation theory

Despite its simplicity and relatively low computational cost, second-order Møller-Plesset perturbation theory (MP2) is well-known to overbind noncovalent interactions between polarizable monomers and some organometallic bonds. In such situations, the pairwise-additive correlation energy expression in MP2 is inadequate. Although energy-gap dependent amplitude regularization can substantially improve the accuracy of conventional MP2 in these regimes, the same regularization parameter worsens the accuracy for small molecule thermochemistry and density-dependent properties. Recently, we proposed a repartitioning of Brillouin-Wigner perturbation theory that is size-consistent to second order (BW-s2), and a free parameter ($α$) was set to recover the exact dissociation limit of H 2 in a minimal basis set. Alternatively $α$ can be viewed as a regularization parameter, where each value of $α$ represents a valid variant of BW-s2, which we denote as BW-s2($α$). In this work, we semi-empirically optimize $α$ for noncovalent interactions, thermochemistry, alkane conformational energies, electronic response properties, and transition metal datasets, leading to improvements in accuracy relative to the ab initio parameterization of BW-s2 and MP2. We demonstrate that the optimal $α$ parameter ($α$ = 4) is more transferable across chemical problems than energy-gap-dependent regularization parameters. This is attributable to the fact that the BW-s2($α$) regularization strength depends on all of the information encoded in the t amplitudes rather than just orbital energy differences. While the computational scaling of BW-s2($α$) is iterative $\mathcal{O}$($N^5$), this effective and transferable approach to amplitude regularization is a promising route to incorporate higher-order correlation effects at second-order cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Searches for baryon number violation in neutrino experiments: a white paper

Abstract Baryon number conservation is not guaranteed by any fundamental symmetry within the standard model, and therefore has been a subject of experimental and theoretical scrutiny for decades. So far, no evidence for baryon number violation has been observed. Large underground detectors have long been used for both neutrino detection and searches for baryon number violating processes. The next generation of large neutrino detectors will seek to improve upon the limits set by past and current experiments and will cover a range of lifetimes predicted by several Grand Unified Theories. In this White Paper, we summarize theoretical motivations and experimental aspects of searches for baryon number violation in neutrino experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Cosmological constraints from the cross-correlation of DESI Luminous Red Galaxies with CMB lensing from Planck PR4 and ACT DR6

Here, we infer the growth of large scale structure over the redshift range 0.4 ≲ z ≲ 1 from the cross-correlation of spectroscopically calibrated Luminous Red Galaxies (LRGs) selected from the Dark Energy Spectroscopic Instrument (DESI) legacy imaging survey with CMB lensing maps reconstructed from the latest Planck and ACT data. We adopt a hybrid effective field theory (HEFT) model that robustly regulates the cosmological information obtainable from smaller scales, such that our cosmological constraints are reliably derived from the (predominantly) linear regime. We perform an extensive set of bandpower- and parameter-level systematics checks to ensure the robustness of our results and to characterize the uniformity of the LRG sample. We demonstrate that our results are stable to a wide range of modeling assumptions, finding excellent agreement with a linear theory analysis performed on a restricted range of scales. From a tomographic analysis of the four LRG photometric redshift bins we find that the rate of structure growth is consistent with ΛCDM with an overall amplitude that is ≃ 5-7% lower than predicted by primary CMB measurements with modest (∼ 2σ) statistical significance. From the combined analysis of all four bins and their cross-correlations with Planck we obtain S 8 = 0.765 ± 0.023, which is less discrepant with primary CMB measurements than previous DESI LRG cross Planck CMB lensing results. From the cross-correlation with ACT we obtain S 8 = 0.790 +0.024 -0.027 , while when jointly analyzing Planck and ACT we find S 8 = 0.775 +0.019 -0.022 from our data alone and σ 8 = 0.772 +0.020 -0.023 with the addition of BAO data. These constraints are consistent with the latest Planck primary CMB analyses at the ≃ 1.6-2.2σ level, and are in excellent agreement with galaxy lensing surveys.

cosmological parameters from LSS↗

Band Structure and Charge Ordering of Dirac Semimetal EuAl 4 at Low Temperatures

In this article, EuAl 4 is proposed to host a topological Hall state. This material also undergoes four consecutive antiferromagnetic (AFM) transitions upon cooling below T N1 = 15.4 K in the presence of charge density wave (CDW) order that sets in below T CDW = 140 K. We use angle-resolved photoemission spectroscopy and density-functional-theory calculations to study how magnetic ordering affects the electronic properties in EuAl 4 . Here, we found changes in the band structure upon each of the four consecutive AFM transitions including band splitting, renormalizations, and appearance of new bands forming additional Fermi sheets. In addition we also found significant enhancement of the quasiparticles’ lifetime due to suppression of spin flip scattering, similar to what was previously reported for ferromagnetic EuCd 2 As 2 . Surprisingly, we observe that most significant changes in electronic properties occur not at T N1 , but instead at the AFM3 to AFM4 transition, which coincides with the largest drop in resistivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Constraints on the nuclear symmetry energy from asymmetric-matter calculations with chiral 𝑁⁢𝑁 and 3⁢𝑁 interactions

The nuclear symmetry energy is a key quantity in nuclear (astro)physics. It describes the isospin dependence of the nuclear equation of state, which is commonly assumed to be almost quadratic. Here, in this work, we confront this standard quadratic expansion of the equation of state with explicit asymmetric nuclear-matter calculations based on a set of commonly used Hamiltonians including two- and three-nucleon forces derived from chiral effective-field theory. We study, in particular, the importance of nonquadratic contributions to the symmetry energy, including the nonanalytic logarithmic term introduced by Kaiser [Phys. Rev. C 91, 065201 (2015)]. Our results suggest that the nonquadratic contribution to the symmetry energy can be systematically determined from the various Hamiltonians employed, and we obtain 0.74$^{+0.11}_{−0.08}$ MeV (or −1.02$^{+0.11}_{−0.08}$ MeV for the potential term with the effective-mass contribution) at nuclear saturation density, while the logarithmic contribution to the symmetry energy is relatively small and model-dependent. We also employ the meta-model approach to study the impact of the higher-order contributions on the neutron-star crust-core transition density, and find a 5% correction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Dynamics and Transport in Strongly-Anisotropic Quantum Magnets (Final Report)

This DOE Award has evolved from a set of projects centered on the thermal transport phenomena in quantum magnets to the broader effort in the theory of dynamical properties of complex magnets, with the focus on their enigmatic ground states, disorder-induced phenomena, and novel spectroscopic and transport effects in them. Most recent emphasis of the research under the umbrella of this Award has been on the rare-earth- and transition-metal-based strongly-anisotropic magnets, the effort that has utilized a significant experience of our group in the studies of excitations, transport, and disorder in these new materials. The studies performed in our group have advanced basic understanding of fundamental physical properties of a diverse group of materials and yielded predictions of new phenomena in them. The research under this Award has targeted the problems that are at the forefront of the modern condensed matter physics and has also addressed the need for the theoretical understanding of experiments. Our work has influenced experiments conducted at the national and international facilities and provided an impact on the DOE basic energy science missions and areas of thrust in new electronic materials, energy transport, neutron- and X-ray scattering science, and in nanoscale science.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Urban weather modeling using WRF: linking physical assumptions, code implementation, and observational needs

The Weather Research and Forecasting (WRF) model includes urban schemes that simulate the influence of urban surfaces on the atmosphere using parameterizations for flux, and radiative exchanges. Three core schemes – the Bulk urban parameterization, Single-Layer Urban Canopy Model (SLUCM), and Multi-Layer Urban Canopy Model (MLUCM) – represent increasing levels of complexity. Although the parameterizations within these urban schemes are described in the literature, their specific implementation remains poorly documented, thus slowing down model development efforts. This manuscript provides a roadmap to the three urban schemes in WRF version 4.5.2, presenting equations using the same symbols as in the model code, along with references to code lines, and including graphics and explanations that connect the code to its physical foundations. Our thorough review of the urban parameterizations implemented in WRF version 4.5.2 highlighted a handful of parameters that may introduce discontinuities in simulations: (i) in the SLUCM, a 1 mm h −1 rain rate threshold is employed to switch between two minimum moisture availability parameterizations, thus impacting latent heat flux calculations; (ii) in the SLUCM a threshold is used to partition shortwave radiation into direct and diffuse components; (iii) in all three urban schemes, the bulk Richardson number is employed to select the similarity function, which influences the vertical distribution of heat and momentum. We also identified a highly simplified treatment of the radiative balance on roof surfaces. The implications of these simplifications can be assessed through targeted observations across relevant conditions, including varying precipitation rates, cloud cover, and transitions between stability regimes. Furthermore, the widespread application of the Monin-Obukhov similarity theory in these urban schemes warrants model evaluation under highly stable and unstable conditions and in heterogeneous urban settings with variable land cover and building heights on scales finer than model resolution. To address these challenges, we offer guidance on observational strategies, emphasizing the need for multi-parametric measurements to capture potential compensating biases and multi-height measurements that align with the levels where quantities are diagnostic and prognosed in the model (i.e., the lowest atmospheric level of the WRF model). Finally, our inspection of the code revealed implementation bugs that have now been corrected in WRF versions 4.6.0 and 4.6.1. Sensitivity tests over the Atlanta urban area show that these corrections affect surface temperatures, underscoring the importance of performing rigorous documentation and verification of the implementation of parameterizations in model code.

54 ENVIRONMENTAL SCIENCES↗

End-exclusion zones in strongly stretched, molten polymer brushes of arbitrary shape

Theories of strongly stretched polymer brushes, particularly the parabolic brush theory, are valuable for providing analytically tractable predictions for the thermodynamic behavior of surface-grafted polymers in a wide range of settings. Furthermore, the parabolic brush limit fails to describe polymers grafted to convex curved substrates, such as the surfaces of spherical nanoparticles or the interfaces of strongly segregated block copolymers. It has previously been shown that strongly stretched curved brushes require a boundary layer devoid of free chain ends, requiring modifications of the theoretical analysis. While this “end-exclusion zone” has been successfully incorporated into the descriptions of brushes grafted onto the outer surfaces of cylinders and spheres, the behavior of brushes on surfaces of arbitrary curvature has not yet been studied. We present a formulation of the strong-stretching theory for molten brushes on the surfaces of arbitrary curvature and identify four distinct regimes of interest for which brushes are predicted to possess end-exclusion zones, notably including regimes of positive mean curvature but negative Gaussian curvature. Through numerical solutions of the strong-stretching brush equations, we report predicted scaling of the size of the end-exclusion zone, the chain end distribution, the chain polarization, and the free energy of stretching with mean and Gaussian surface curvatures. Through these results, we present a comprehensive picture of how the brush geometry influences the end-exclusion zones and exact strong-stretching free energies, which can be applied, for example, to model the full spectrum of brush geometries encountered in block copolymer melt assembly.

36 MATERIALS SCIENCE↗

A new phenomenological model to describe root-soil interactions based on percolation theory

In his paper on net primary productivity of terrestrial communities predicted from climatological data, Rosenzweig (1968) argued that variability in productivity is well accounted for by (evapo)-transpiration, and that water from transpiration is, on global scales, the most variable component in the photosynthesis reaction. The goal of this paper is to investigate whether variability in plant growth on local scales and within species is primarily related to transpiration under several scenarios including different terrain curvature, slope aspect, soil characteristics, and climate ranges. Here, we test the hypothesis that this relationship exists because root growth into the surface soil layers (0–2 m) tends to follow paths with minima in resistance, which in turn maximizes water flow and nutrient delivery rates that regulate growth. The set of all connected paths with individual pore-to-pore flow resistances less than a critical, percolating, value forms a cluster with mass fractal dimensionality, d f . We propose that roots follow paths through the 2D percolation cluster, defining the set of all optimal flow paths, making the 2D value of d f from percolation relevant to root fractal dimensionality. The tortuosity of such optimal paths as defined in percolation theory should then relate root length to root radial extent, linking the parameters of root tortuosity and plant productivity. Our analysis of large data sets across species implies that root radial extent and tree height are both proportional to cumulative transpiration until trees approached maximum height, and their growth rates are proportional to the transpiration rate, not to the moisture content. Local variations in tree height as functions of the variables investigated appear generally consistent with deduced variations in transpiration. Here this correlation is investigated more closely in the context of studies addressing individual tree species.

54 ENVIRONMENTAL SCIENCES↗