Search NASA⌕ Search

SEARCH · Search NASA

Results for “complex partition function”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Antimony stable isotope fractionation during adsorption onto birnessite: A molecular perspective from X-ray absorption spectroscopy and density functional theory

Sorption of antimony (Sb) onto birnessite significantly influences the fate of Sb in oceanic and terrestrial environments and fractionates Sb isotopes. Nevertheless, little is known about Sb isotopic fractionation during its adsorption on birnessite. Here, in this study, we show the value of Δ 123 Sb adsorbed-aqueous increases from −0.398 to −0.332 ‰ in 1 h and then decreases and stabilizes at −0.384 ‰ in 72 h. The enrichment of the light Sb isotope is predominantly due to the distortion of the octahedral symmetry. X-ray absorption spectroscopy results indicate Sb first forms a double-corner-sharing complex on birnessite and then transforms to a double-edge-sharing complex during adsorption. The optimized bond distances for double-corner-sharing (3.37 Å) and double-edge-sharing (2.90 Å) complexes calculated using density functional theory (DFT) fits well with the structure (3.41 and 3.00 Å) revealed by X-ray absorption spectroscopy, respectively. The fractionation derived from reduced partition function ratios calculated using DFT aligns well with the experimental results. Therefore, the variation in Sb isotopic fractionation during adsorption is attributed to the evolving structure of Sb complexes on birnessite. Our results demonstrate the isotopic fractionation of Sb during adsorption on birnessite and provide a molecular-scale understanding of Sb behavior, contributing to the correct reconstruction of the Sb isotope composition of ancient seawater using ferromanganese crusts and nodules, and efforts to trace Sb migration in epigenetic mining environments.

Adsorption↗
NASA NTRS1984

A model of asynchronous iterative algorithms for solving large, sparse, linear systems

Solving large, sparse, linear systems of equations is one of the fundamental problems in large scale scientific and engineering computation. A model of a general class of asynchronous, iterative solution methods for linear systems is developed. In the model, the system is solved by creating several cooperating tasks that each compute a portion of the solution vector. This model is then analyzed to determine the expected intertask data transfer and task computational complexity as functions of the number of tasks. Based on the analysis, recommendations for task partitioning are made. These recommendations are a function of the sparseness of the linear system, its structure (i.e., randomly sparse or banded), and dimension.

Reed, D. A.↗
NASA NTRS2002

Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning

We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum exitation gap, gmin = O(n2(sup -n/2)), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.

Smelyanskiy, Vadius↗
DOE OSTI2023

Elucidating the speciation of extracted lanthanides by diglycolamides

Many studies over the past few decades have been devoted to addressing the application of diglycolamides (DGAs) for hydrometallurgical-based, f-element separations. Work to date has shown the molecular structure of a DGA derivative can have a significant impact on intra-lanthanide partitioning patterns. More recent studies have pushed towards probing the structure function relationship of the lanthanide-DGA complex to enable the design of more efficient lanthanide separation systems. Spectroscopic techniques, such as UV–Visible, Fourier Transformed Infrared Spectroscopy (FT-IR), Nuclear Magnetic Resonance (NMR), and Extended X-ray Absorption Fine Structure (EXAFS), provide information regarding the inner-sphere coordination of a given lanthanide-DGA complex. Scattering techniques, such as Dynamic Light Scattering (DLS), Small-Angle X-ray Scattering (SAXS), and Small-Angle Neutron Scattering (SANS), address nanoscale structures including aggregate sizes and morphology. Here, this review assesses the current state-of-knowledge regarding lanthanide-DGA hydrometallurgical (i.e., solvent extraction systems) interrogated using spectroscopic and scattering techniques to characterize the extracted Ln 3+ DGA species. Of particular interest to this review is the impact of varied diluents, inclusion and variation of phase modifiers, and DGA derivatization on system characteristics. While there has been extensive literature on the application of DGAs for f-element separations, the literature lacks a collective assessment of the speciation of Ln 3+ in the organic phase. This review provides new insights into the field of DGA separations, explicitly with an application to intra-lanthanide separations. Specifically, this review illustrates the importance of both the co-extraction anion (Cl - , NO 3 - , or ClO 4 - ) as it pertains to both the aggregate size and Ln 3+ distribution coefficient. It is evident the ability of the anion to disrupt the hydrogen bonding network limits both aggregate size and distribution coefficients according to the Hoffmeister series. This suggests the importance of the large, softer anions with a low charge-to-surface area ratio on encouraging hydrogen bond interactions. In addition, the co-extracted cation (H + vs Na + ) is important for mitigating transfer of Ln 3+ from the aqueous to the organic phase through extensive hydrogen bonding networks. These networks are responsible for forming supramolecular aggregates where a change in morphology is observed with increasing concentrations of H + and/or Ln 3+ in the organic phase.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2002

Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning

We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum excitation gap. g min, = O(n 2(exp -n/2), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to 'the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.

Smelyanskiy, V. N.↗
NASA NTRS1990

Localized basis functions and other computational improvements in variational nonorthogonal basis function methods for quantum mechanical scattering problems involving chemical reactions

The Generalized Newton Variational Principle for 3D quantum mechanical reactive scattering is briefly reviewed. Then three techniques are described which improve the efficiency of the computations. First, the fact that the Hamiltonian is Hermitian is used to reduce the number of integrals computed, and then the properties of localized basis functions are exploited in order to eliminate redundant work in the integral evaluation. A new type of localized basis function with desirable properties is suggested. It is shown how partitioned matrices can be used with localized basis functions to reduce the amount of work required to handle the complex boundary conditions. The new techniques do not introduce any approximations into the calculations, so they may be used to obtain converged solutions of the Schroedinger equation.

Schwenke, David W.↗
DOE OSTI2020

Robust, Accurate, and Efficient: Quantum Embedding Using the Huzinaga Level-Shift Projection Operator for Complex Systems

Using wave function (WF) in density functional theory (DFT) embedding methods provides a framework for performing localized, high-accuracy WF calculations on a system, while not incurring the full computational cost of the WF calculation on the full system. To effectively partition a system into localized WF and DFT subsystems, we utilize the Huzinaga level-shift projection operator within an absolutely localized basis. In this work, we study the ability of the absolutely localized Huzinaga level-shift projection operator method to study complex WF and DFT partitions, including partitions between multiple covalent bonds, a double bond, and transition-metal–ligand bonds. We find that our methodology can accurately describe all of these complex partitions. Additionally, we study the robustness of this method with respect to the WF method, specifically where the embedded systems were described using a multiconfigurational WF method. We found that the method is systematically improvable with respect to both the number of atoms in the WF region and the size of the basis set used, with energy errors less than 1 kcal/mol. Additionally, we calculated the adsorption energy of H2 to a model of an iron metal–organic framework (Fe-MOF-74) to within 1 kcal/mol compared to CASPT2 calculations performed on the full model while incurring only a small fraction of the full computational cost. In conclusion, this work demonstrates that the absolutely localized Huzinaga level-shift projection operator method is applicable to very complex systems with difficult electronic structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Adiabatic quantum decoherence in many non-interacting subsystems induced by the coupling with a common boson bath

Highlights: • System–environment quantum correlation: a main solid state NMR decoherence channel. • Non-separable system–environment model yields realistic spin decoherence rates. • New open quantum system approach explains irreversible decay of refocused NMR echoes. • Adiabatic quantum decoherence is inherently irreversible and eigen-selective. This work addresses adiabatic quantum decoherence of many-body spin systems coupled with a boson field in the framework of open quantum systems theory. We generalize the traditional spin-boson model by considering a system–environment interaction Hamiltonian that represents a partition of non-interacting subsystems and highlights the collective correlation that appears exclusively due to the coupling with a common environment. Remarkably, this simple, exactly solvable model encompasses relevant aspects of a many-body open quantum system and features the subtle quantum effects that arise when the size scales up to a macroscopic level. We derive an analytical expression for the time dependence of the density matrix elements (in the preferred basis) without assuming coarse-graining. The resulting decoherence function is eigen-selective and is a complex exponential whose exponent has a real part that introduces a decay similar to that in the spin-boson model. On the contrary, the imaginary part depends on the quantum numbers and geometry of the whole partition and does not reflect the system temperature. Motivated by decoherence in solid-state NMR, and in search of realistic numerical estimations, we apply the theoretical results to a partition of dipole-coupled spin pairs in contact with a common phonon bath, using typical parameters of hydrated salts. The proposal allows estimating the decoherence time scale in terms of the system physical constants: sound velocity and eigenvalue distribution width. As a significant novelty, the decoherence function phase depends on the eigenvalue distribution throughout the sample. It plays the leading role, overshadowing the mechanism associated with the bath thermal state. Finally, we apply the formalism to describe decoherence in the “magic echo” NMR reversal experiment. We find that the system–environment correlation explains the origin of irreversibility, and both the decoherence rate value and its dependence on the dipolar frequency, are remarkably similar to the experiment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

High Semi-Volatile Organic Aerosol Contributions Associated with Ammonium Nitrate in the Coastal Urban Environment

Organic components often contribute 50% or more of the submicron aerosol mass in coastal urban environments, but their partitioning between the gas and particle phases is controlled by a complex mixture of unidentified organic compounds that are poorly constrained by observations. This study compares daily filter organic functional groups (OFG) with online organic mass fragments from La Jolla, California, as part of the Eastern Pacific Cloud Aerosol Precipitation Experiment (EPCAPE), quantifying the contributions of four types of non-volatile (NV) organic emission sources to the submicron composition. Daily filters retained only 0.79–0.98 µg/m3 NV submicron organic mass concentration, even though 1.8–1.9 µg/m3 non-refractory (NR) submicron organic mass concentration was measured online. The 62–64% of measured NR submicron organic mass concentration that exceeded what remained on the filters after 23-hr sampling is interpreted as semi-volatile, consistent with the moderate correlation of the NR NV difference to NR ammonium, NR nitrate, and biomass burning-related NV and NR organic factors. The association between semi-volatile organic components and ammonium nitrate likely results from both co-emission and co-evaporation. Size-resolved filter analysis showed that NV organic mass concentration accounts for 68% of NR organic mass concentration for 0.5–1 µm dry diameter but account for 9.0% for 0.18–0.5 µm dry diameter showing the differences in volatility between particle modes. Importantly, volatility of organic components was size-dependent Information Classification: General and associated with ammonium nitrate and biomass burning, providing guidance for constraining atmospheric aerosol properties in global models.

Pelayo, Christian↗
DOE OSTI2021

East River Watershed Stable Water Isotope Data in Precipitation, Snowpack and Snowmelt 2016-2020

Stable water isotopes (d18O, d2H and d-excess) are important tracers in hydrologic research to understand water partitioning between vegetation, groundwater, and runoff but are rarely applied to large watersheds with persistent snowpack and complex topopgraphy. Data were collected for the Lawrence Berkeley National Laboratory Watershed Function Science Focus Area supported by the U.S Department of Energy in the East River, CO Hydrologic Unit Code (140200010) with limited data also collected in adjacent watersheds Ohio Creek and Taylor River. Data are provided in csv and includes isotopic information for precipitation (years 2014-2016), snowmelt (years 2016-2017) and snowpits (years 2016-2020). Snowpit data contain depth resolved information at 10 cm intervals for density, snow water equivalent (SWE) and stable water isotopes. Bulk isotopic data for 86 snowpits contain depth, SWE, density and SWE-weighted isotope values. Sampling locations and elevations are provided within the data files, while kmz files are provided to view sampling locations using Google Earth software.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

A Linear-Complexity Tensor Butterfly Algorithm for Compressing High-Dimensional Oscillatory Integral Operators

This paper presents a multilevel tensor compression algorithm called tensor butterfly algorithm for efficiently representing large-scale and high-dimensional oscillatory integral operators, including Green's functions for wave equations and integral transforms such as Radon transforms and Fourier transforms. The proposed algorithm leverages a tensor extension of the so-called complementary low-rank property of existing matrix butterfly algorithms. The algorithm partitions the discretized integral operator tensor into subtensors of multiple levels and factorizes each subtensor at the middle level as a Tucker-type interpolative decomposition, whose factor matrices are formed in a multilevel fashion. For a d-dimensional (d > 1) integral operator discretized into a 2d-mode tensor with n2d entries, the overall CPU time and memory requirement scale as O(nd), in stark contrast to the O(nd log n) complexity of existing matrix algorithms such as matrix butterfly algorithms and fast Fourier transforms (FFTs), where n is the number of points per direction. When comparing with other tensor algorithms such as quantized tensor train (QTT), the proposed algorithm also shows superior CPU and memory performance for tensor contraction. Remarkably, the tensor butterfly algorithm can efficiently model high-frequency Green's function interactions between two unit cubes, each spanning 512 wavelengths per direction, which represents problems of scale over 512× larger than that existing butterfly algorithms can handle, with the same amount of computation resources. On the other hand, for a problem representing 64 wavelengths per direction, which is the largest size existing algebraic matrix algorithms can handle, our tensor butterfly algorithm exhibits 200x speedups and 30× memory reduction compared with existing ones. Moreover, the tensor butterfly algorithm also permits O(nd)-complexity FFTs and Radon transforms up to d = 6 dimensions.

Kielstra, P Michael↗
DOE OSTI2020

3d-3d correspondence for mapping tori

One of the main challenges in 3d-3d correspondence is that no existent approach offers a complete description of 3d N = 2 SCFT T [ M 3 ] — or, rather, a “collection of SCFTs” as we refer to it in the paper — for all types of 3-manifolds that include, for example, a 3-torus, Brieskorn spheres, and hyperbolic surgeries on knots. The goal of this paper is to overcome this challenge by a more systematic study of 3d-3d correspondence that, first of all, does not rely heavily on any geometric structure on M 3 and, secondly, is not limited to a particular supersymmetric partition function of T [ M 3 ]. In particular, we propose to describe such “collection of SCFTs” in terms of 3d N = 2 gauge theories with “non-linear matter” fields valued in complex group manifolds. As a result, we are able to recover familiar 3-manifold invariants, such as Turaev torsion and WRT invariants, from twisted indices and half-indices of T [ M 3 ], and propose new tools to compute more recent q -series invariants Z * ( M 3 ) in the case of manifolds with b 1 > 0. Although we use genus-1 mapping tori as our “case study,” many results and techniques readily apply to more general 3-manifolds, as we illustrate throughout the paper.

Topological Field Theories↗
NASA NTRS1994

Practical and clinical nutritional concerns during spaceflight

Experience with space exploration to date has raised more questions regarding nutritional requirements for astronauts than it has answered. As mission lengths continue to increase, nutrient imbalances due to alterations in intake, dietary requirements, bioavailability, or excretion, may become more important. Factors adversely affecting intake include those as straightforward as stress and as complex as space-adaptation syndrome. Metabolic alterations induced by shifts in fluid and electrolyte balance, neuroendocrine function, and changes in hepatic protein synthesis and skeletal muscle type that result in nutrient partitioning to different biochemical pathways may also affect dietary requirements. Food processing effects on nutrient stability and digestibility, which apply to limited quantities of our usual diet on Earth, may become more important for diets that contain little fresh food during extended-length missions. Whereas nutrient and water recycling through ecosystems is taken for granted on Earth, specific effects of trace contaminant accumulation will require greater attention for prolonged space flights. Human factors, esthetics, and user-friendly operations will be necessary to facilitate the psychological as well as physiological health of the astronauts.

Review, Tutorial↗
DOE OSTI2025

Robust Multi-fidelity Bayesian Optimization with Deep Kernel and Partition

Multi-fidelity Bayesian optimization (MFBO) is a powerful approach that utilizes lowfidelity, cost-effective sources to expedite the exploration and exploitation of a high-fidelity objective function. Existing MFBO methods with theoretical foundations either lack justification for performance improvements over single-fidelity optimization or rely on strong assumptions about the relationships between fidelity sources to construct surrogate models and direct queries to low-fidelity sources. To mitigate the dependency on cross-fidelity assumptions while maintaining the advantages of low-fidelity queries, we introduce a random sampling and partition-based MFBO framework with deep kernel learning. This framework is robust to cross-fidelity model misspecification and explicitly illustrates the benefits of low-fidelity queries. Our results demonstrate that the proposed algorithm effectively manages complex cross-fidelity relationships and efficiently optimizes the target fidelity function.

Zhang, Fengxue [University of Chicago, Illinois, U↗
DOE OSTI2022

Replica symmetry breaking for the integrable two-site Sachdev–Ye–Kitaev model

We analyze a two-body non-Hermitian two-site Sachdev–Ye–Kitaev (SYK) model with the couplings of one site complex conjugated to the other site. This model, with no explicit coupling between the sites, shows an infinite number of second-order phase transitions, which is a consequence of the factorization of the partition function into a product over Matsubara frequencies. We calculate the quenched free energy in two different ways: first in terms of the single-particle energies and second by solving the Schwinger–Dyson equations of the two-site model. The first calculation can be done entirely in terms of a one-site model. The conjugate replica enters due to non-analyticities when Matsubara frequencies enter the spectral support of the coupling matrix. The second calculation is based on the replica trick of the two-site partition function. Both methods give the same result. The free-fermion partition function can also be rephrased as a matrix model for the coupling matrix. Up to minor details, this model is the random matrix model that describes the chiral phase transition of QCD, and the order parameter of the two-body model corresponds to the chiral condensate of QCD. Comparing to the corresponding four-body model, we are able to determine which features of the free energy are due to the chaotic nature of the four-body model. The high-temperature phase of both models is entropy dominated, and in both cases, the free energy is determined by the spectral density. The chaotic four-body SYK model has a low-temperature phase whose free energy is almost temperature-independent, signaling an effective gap of the theory even though the actual spectrum does not exhibit a gap. On the other hand, the low-temperature free energy of the two-body SYK model is not flat; in fact, it oscillates to arbitrarily low temperature. This indicates a less desirable feature that the entropy of the two-body model is not always positive in the low-temperature phase, which most likely is a consequence of the non-hermiticity.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Lefschetz thimble quantum Monte Carlo for spin systems

Monte Carlo simulations are useful tools for modeling quantum systems, but in some cases they suffer from a sign problem, leading to an exponential slow down in their convergence to a value. While solving the sign problem is generically NP hard, many techniques exist for mitigating the sign problem in specific cases; in particular, the technique of deforming the Monte Carlo simulation's plane of integration onto Lefschetz thimbles (complex hypersurfaces of stationary phase) has seen significant success in the context of quantum field theories. We extend this methodology to spin systems by utilizing spin coherent state path integrals to reexpress the spin system's partition function in terms of continuous variables. Using some toy systems, we demonstrate its effectiveness at lessening the sign problem in this setting, despite the fact that the initial mapping to spin coherent states introduces its own sign problem. The standard formulation of the spin coherent path integral is known to make use of uncontrolled approximations; despite this, for large spins they are typically considered to yield accurate results, so it is somewhat surprising that our results show significant systematic errors. Furthermore, possibly of independent interest, our use of Lefschetz thimbles to overcome the intrinsic sign problem in spin coherent state path integral Monte Carlo enables a novel numerical demonstration of a breakdown in the spin coherent path integral.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2014

SEU System Analysis: Not Just the Sum of All Parts

Single event upset (SEU) analysis of complex systems is challenging. Currently, system SEU analysis is performed by component level partitioning and then either: the most dominant SEU cross-sections (SEUs) are used in system error rate calculations; or the partition SEUs are summed to eventually obtain a system error rate. In many cases, system error rates are overestimated because these methods generally overlook system level derating factors. The problem with overestimating is that it can cause overdesign and consequently negatively affect the following: cost, schedule, functionality, and validation/verification. The scope of this presentation is to discuss the risks involved with our current scheme of SEU analysis for complex systems; and to provide alternative methods for improvement.

Single Event Upset (SEU) Testing↗
DOE OSTI2022

Microbial and Environmental Processes Shape the Link between Organic Matter Functional Traits and Composition

Dissolved organic matter (DOM) is a large and complex mixture of molecules that fuels biogeochemical reaction in virtually all ecosystems on Earth. However, the relative importance of deterministic and stochastic processes in structuring DOM composition remains poorly characterized. Here we develop a framework for partitioning molecular composition based on key molecular traits, including lability vs. recalcitrance and activity vs. inactivity. Within this framework, we examine the ecological processes governing the assembly of DOM fractions by deploying aquatic microcosms on mountainsides that span gradients of temperature and nutrient loading in subtropical and subarctic ecosystems. Across study regions, deterministic and stochastic processes primarily structure active and inactive fractions, respectively. However, recalcitrant molecules are more deterministically assembled than labile molecules in the inactive fraction. Deterministic processes leading to variable selection generally exhibit more variation across the energy supply gradient for inactive fractions, and their importance increases with energy supply for recalcitrant molecules in both active and inactive fractions. Together, our results indicate that active and inactive fractions of DOM assemblages are structured by contrasting ecological processes, and their recalcitrant components are sensitive to global change. In conclusion, our framework opens new avenues to understand the assembly and turnover of DOM in a changing world, which can be used to predict carbon cycling at local to global scales.

54 ENVIRONMENTAL SCIENCES↗