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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.

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At least 883 records · Page 49
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Vibrational levels of a generalized Morse potential

A Generalized Morse Potential (GMP) is an extension of the Morse Potential (MP) with an additional exponential term and an additional parameter that compensate for MP’s erroneous behavior in the long range part of the interaction potential. Because of the additional term and parameter, the vibrational levels of the GMP cannot be solved analytically, unlike the case for the MP. We present several numerical approaches for solving the vibrational problem of the GMP based on Galerkin methods, namely, the Laguerre Polynomial Method (LPM), the Symmetrized LPM, and the Polynomial Expansion Method (PEM), and apply them to the vibrational levels of the homonuclear diatomic molecules B 2 , O 2 , and F 2 , for which high level theoretical near full configuration interaction (CI) electronic ground state potential energy surfaces and experimentally measured vibrational levels have been reported. Overall, the LPM produces vibrational states for the GMP that are converged to within spectroscopic accuracy of 0.01 cm –1 in between 1 and 2 orders of magnitude faster and with much fewer basis functions/grid points than the Colbert–Miller Discrete Variable Representation (CN-DVR) method for the three homonuclear diatomic molecules examined in this study.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

On the Cauchy problem for Boltzmann equation modeling a polyatomic gas

In the present article, we consider the Boltzmann equation that models a polyatomic gas by introducing one additional continuous variable, referred to as microscopic internal energy. We establish existence and uniqueness theory in the space homogeneous setting for the full non-linear case, under an extended Grad-type assumption on transition probability rates, which comprises hard potentials for both the relative speed and internal energy with the rate in the interval 0,2, multiplied by an integrable angular part and integrable partition functions. The Cauchy problem is resolved by means of an abstract ordinary differential equation (ODE) theory in Banach spaces for the initial data with finite and strictly positive gas mass and energy, finite momentum, and additionally finite K* polynomial moment, with K* depending on the rate of the transition probability and the structure of a polyatomic molecule or its internal degrees of freedom. Moreover, we prove that polynomially and exponentially weighted Banach space norms associated with the solution are both generated and propagated uniformly in time.

Physics↗
DOE OSTI2023

Subspace recursive Fermi-operator expansion strategies for large-scale DFT eigenvalue problems on HPC architectures

Quantum mechanical calculations for material modeling using Kohn–Sham density functional theory (DFT) involve the solution of a nonlinear eigenvalue problem for N smallest eigenvector-eigenvalue pairs, with N proportional to the number of electrons in the material system. Here, these calculations are computationally demanding and have asymptotic cubic scaling complexity with the number of electrons. Large-scale matrix eigenvalue problems arising from the discretization of the Kohn–Sham DFT equations employing a systematically convergent basis traditionally rely on iterative orthogonal projection methods, which are shown to be computationally efficient and scalable on massively parallel computing architectures. However, as the size of the material system increases, these methods are known to incur dominant computational costs through the Rayleigh–Ritz projection step of the discretized Kohn–Sham Hamiltonian matrix and the subsequent subspace diagonalization of the projected matrix. This work explores the potential of polynomial expansion approaches based on recursive Fermi-operator expansion as an alternative to the subspace diagonalization of the projected Hamiltonian matrix to reduce the computational cost. Subsequently, we perform a detailed comparison of various recursive polynomial expansion approaches to the traditional approach of explicit diagonalization on both multi-node central processing unit and graphics processing unit architectures and assess their relative performance in terms of accuracy, computational efficiency, scaling behavior, and energy efficiency.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Second harmonic generation for estimating state of charge of lithium-ion batteries

This study applied the nonlinear ultrasonic method, second harmonic generation, to precisely estimate the state of charge (SoC) in lithium-ion batteries. The second harmonic of the longitudinal wave is generated on a pouch cell battery at 5 MHz with a through-transmission setup. The relative nonlinear parameter β' is determined by analyzing the amplitudes at the fundamental and second harmonic frequencies. To enhance the nonlinear parameter's measurement accuracy, multiple excitation amplitudes are employed. Two separate charge/discharge tests (four-cycle and eight-cycle) are conducted on the battery at a rate of C/10. The nonlinear parameter is measured periodically during the charge/discharge process, and temperature compensation is applied to the measurement. The correlation curves between the nonlinear parameter and the actual SoC align well for the four-cycle and eight-cycle tests, and a robust linear relationship is observed for both correlation curves. A linear model and a second-order polynomial model are applied to fit the correlation using all data points from both tests. The two models are employed to validate the SoC prediction on a second battery by using a four-cycle test. Furthermore, the results indicate that both models can predict the SoC with an accuracy of approximately 3%, whereas the polynomial model demonstrates smaller errors in the regions near 0% and 100% SoC. Therefore, the nonlinear parameter β', measured through the second harmonic generation, can effectively predict lithium-ion battery SoC with an accuracy of less than 3%.

25 ENERGY STORAGE↗
DOE OSTI2024

An enrichment wall modeling framework for spectral element methods

In the present work, a first-of-its-kind enrichment wall-model is developed within the spectral element method (SEM) framework for large-eddy simulations (LES) of wall-bounded turbulent flows. The method augments the polynomial solution in the wall-adjacent elements with an analytical law-of-the-wall enrichment function representing the mean velocity near the wall. In the solution representation, this enrichment function captures the large gradients in the boundary layer, which allows the polynomial modes to represent the turbulent fluctuations. The enriched solution is able to resolve the shear stress at the wall without any modification to the no-slip wall boundary conditions, which allows for greater accuracy in the near-wall region compared to traditional methods. The enrichment wall modeling approach is implemented in a high-order SEM computational fluid dynamics solver, Nek5000, and its performance is assessed in turbulent channel flow wall-modeled LES for a range of Reynolds numbers. It is demonstrated that the enrichment wall-model improves solution accuracy on under-resolved near-wall grids as compared to traditional shear stress wall-models.

42 ENGINEERING↗
DOE OSTI2025

An eigenvalue-based method for computing the relaxed pressure in compressible multiphase flow with N phases

The modeling of compressible multiphase flows is a decades-old area of study with many applications across various fields. Many of these application areas use stiff pressure relaxation. This process involves the solution of a nonlinear system with N + 1 equations and N + 1 unknowns, where N is the number of phases. The resolution of this system with general equations of state (EOSs) is difficult. Furthermore, nonlinear systems can admit multiple solutions, and current solution methods do not address this possibility. Very recently, a thermodynamic relaxation method was introduced, which effectively maps a relatively simple predictor equation of state onto a more complex target equation of state. In this context, the target EOSs are the chosen EOSs for the thermodynamic model. Furthermore, this thermodynamic relaxation has the benefit of simplifying the stiff pressure relaxation system of equations. In this article, we show this system reduces to a polynomial of degree N, which can be recast as an eigenvalue problem through the use of the associated companion matrix. We show that although this eigenvalue method is generally less efficient than Newton–Raphson iteration, it does not suffer from convergence issues and finds all N roots of the polynomial. Hence, the method provides a fail-safe for root-finding iterative methods and a way to address the issue of multiple solutions to the nonlinear system of equations in stiff pressure relaxation.

Eigenvalue algorithm↗
DOE OSTI2025

Circuit complexity and functionality: A statistical thermodynamics perspective

Circuit complexity, defined as the minimum circuit size required for implementing a particular Boolean computation, is a foundational concept in computer science. Determining circuit complexity is believed to be a hard computational problem. Recently, in the context of black holes, circuit complexity has been promoted to a physical property, wherein the growth of complexity is reflected in the time evolution of the Einstein-Rosen bridge (“wormhole”) connecting the two sides of an anti-de Sitter “eternal” black hole. Here, we are motivated by an independent set of considerations and explore links between complexity and thermodynamics for functionally equivalent circuits, making the physics-inspired approach relevant to real computational problems, for which functionality is the key element of interest. In particular, our thermodynamic framework provides an alternative perspective on the obfuscation of programs of arbitrary length—an important problem in cryptography—as thermalization through recursive mixing of neighboring sections of a circuit, which can be viewed as the mixing of two containers with “gases of gates.” This recursive process equilibrates the average complexity and leads to the saturation of the circuit entropy, while preserving functionality of the overall circuit. The thermodynamic arguments hinge on ergodicity in the space of circuits which we conjecture is limited to disconnected ergodic sectors due to fragmentation. The notion of fragmentation has important implications for the problem of circuit obfuscation as it implies that there are circuits of same size and functionality that cannot be connected via a polynomial number of local moves. Furthermore, we argue that fragmentation is unavoidable unless the complexity classes NP and coNP coincide, a statement that implies the collapse of the polynomial hierarchy of computational complexity theory to its first level.

Science & Technology - Other Topics↗
DOE OSTI2022

Characterizing Tradeoffs in Memory, Accuracy, and Speed for Chemistry Tabulation Techniques

Chemistry tabulation is a common approach in practical simulations of turbulent combustion at engineering scales. Linear interpolants have traditionally been used for accessing precomputed multidimensional tables but suffer from large memory requirements and discontinuous derivatives. Higher-degree interpolants address some of these restrictions but are similarly limited to relatively low-dimensional tabulation. Artificial neural networks (ANNs) can be used to overcome these limitations but cannot guarantee the same accuracy as interpolants and introduce challenges in reproducibility and reliable training. These challenges are enhanced as the physics complexity to be represented within the tabulation increases. Here, we assess the efficiency, accuracy, and memory requirements of Lagrange polynomials, tensor product B-splines, and ANNs as tabulation strategies. We analyze results in the context of nonadiabatic flamelet modeling where higher dimension counts are necessary. While ANNs do not require structuring of data, providing benefits for complex physics representation, interpolation approaches often rely on some structuring of the table. Interpolation using structured table inputs that are not directly related to the variables transported in a simulation can incur additional query costs. This is demonstrated in the present implementation of heat losses. We show that ANNs, despite being difficult to train and reproduce, can be advantageous for high-dimensional, unstructured datasets relevant to nonadiabatic flamelet models. Furthermore we demonstrate that Lagrange polynomials show significant speedup for similar accuracy compared to B-splines.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Impact of Sequential Ammonia Fiber Expansion (AFEX) Pretreatment and Pelletization on the Moisture Sorption Properties of Corn Stover

Combining ammonia fiber expansion (AFEX™) pretreatment with a depot processing facility is a promising option for delivering high-value densified biomass to the emerging bioenergy industry. However, because the pretreatment process results in a high moisture material unsuitable for pelleting or storage (40% wet basis), the biomass must be immediately dried. If AFEX pretreatment results in a material that is difficult to dry, the economics of this already costly operation would be at risk. This work tests the nature of moisture sorption isotherms and thin-layer drying behavior of corn (Zea mays L.) stover at 20°C to 60°C before and after sequential AFEX pretreatment and pelletization to determine whether any negative impacts to material drying or storage may result from the AFEX process. The equilibrium moisture content to equilibrium relative humidity relationship for each of the materials was determined using dynamic vapor sorption isotherms and modeled with modified Chung-Pfost, modified Halsey, and modified Henderson temperature-dependent models as well as the Double Log Polynomial (DLP), Peleg, and Guggenheim Anderson de Boer (GAB) temperature-independent models. Drying kinetics were quantified under thin-layer laboratory testing and modeled using the Modified Page's equation. Water activity isotherms for non-pelleted biomass were best modeled with the Peleg temperature-independent equation while isotherms for the pelleted biomass were best modeled with the Double Log Polynomial equation. Thin-layer drying results were accurately modeled with the Modified Page's equation. The results of this work indicate that AFEX pretreatment results in drying properties more favorable than or equal to that of raw corn stover, and pellets of superior physical stability in storage.

09 BIOMASS FUELS↗
DOE OSTI2020

Toward an international practical pressure scale: A proposal for an IPPS ruby gauge (IPPS-Ruby2020)

At the 26 th AIRAPT conference in 2017, a task group was formed to work on an International Practical Pressure Scale (IPPS). This report summarizes the activities of the task group toward an IPPS ruby gauge. We have selected three different approaches to establishing the relation between pressure ( P ) and ruby R1-line shift ( Δλ ) with three groups of optimal reference materials for applying these approaches. Using a polynomial form of the second order, the recommended ruby gauge (referred as Ruby2020) is expressed by: P [ G P a ] = 1.87 ( ± 0.01 ) × 10 3 Δ λ λ 0 1 + 5.63 ( ± 0.03 ) Δ λ λ 0 , where λ 0 is the wavelength of the R1-line near 694.25 nm at ambient condition. In June of 2020, the Executive Committee of AIRAPT endorsed the proposed Ruby2020. Finally, we encourage high-pressure practitioners to utilize Ruby2020 within its applicable pressure range (up to 150 GPa), so that pressure data can be directly compared across laboratories and amended consistently as better scales emerge in the future.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2013

AN ACCURATE FLUX DENSITY SCALE FROM 1 TO 50 GHz

We develop an absolute flux density scale for centimeter-wavelength astronomy by combining accurate flux density ratios determined by the Very Large Array between the planet Mars and a set of potential calibrators with the Rudy thermophysical emission model of Mars, adjusted to the absolute scale established by the Wilkinson Microwave Anisotropy Probe. The radio sources 3C123, 3C196, 3C286, and 3C295 are found to be varying at a level of less than {approx}5% per century at all frequencies between 1 and 50 GHz, and hence are suitable as flux density standards. We present polynomial expressions for their spectral flux densities, valid from 1 to 50 GHz, with absolute accuracy estimated at 1%-3% depending on frequency. Of the four sources, 3C286 is the most compact and has the flattest spectral index, making it the most suitable object on which to establish the spectral flux density scale. The sources 3C48, 3C138, 3C147, NGC 7027, NGC 6542, and MWC 349 show significant variability on various timescales. Polynomial coefficients for the spectral flux density are developed for 3C48, 3C138, and 3C147 for each of the 17 observation dates, spanning 1983-2012. The planets Venus, Uranus, and Neptune are included in our observations, and we derive their brightness temperatures over the same frequency range.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Quantum Algorithm for Approximating Maximum Independent Sets

We present a quantum algorithm for approximating maximum independent sets of a graph based on quantum non-Abelian adiabatic mixing in the sub-Hilbert space of degenerate ground states, which generates quantum annealing in a secondary Hamiltonian. For both sparse and dense random graphs G , numerical simulation suggests that our algorithm on average finds an independent set of size close to the maximum size α ( G ) in low polynomial time. The best classical algorithms, by contrast, produce independent sets of size about half of α ( G ) in polynomial time.

Physics↗
DOE OSTI2020

Key Questions for the Quantum Machine Learner to Ask Themselves

Within the last several years quantum machine learning (QML) has begun to mature; however, many open questions remain. Rather than review open questions, in this perspective piece I will discuss my view about how we should approach problems in QML. In particular I will list a series of questions that I think we should ask ourselves when developing quantum algorithms for machine learning. These questions focus on what the definition of quantum ML is, what is the proper quantum analogue of QML algorithms is, how one should compare QML to traditional ML and what fundamental limitations emerge when trying to build QML protocols. As an illustration of this process I also provide information theoretic arguments that show that amplitude encoding can require exponentially more queries to a quantum model to determine membership of a vector in a concept class than classical bit-encodings would require; however, if the correct analogue is chosen then both the quantum and classical complexities become polynomially equivalent. This example underscores the importance of asking ourselves the right questions when developing and benchmarking QML algorithms.

Wiebe, Nathan O.↗
DOE OSTI2020

Tractable minor-free generalization of planar zero-field Ising models

In this work, we present a new family of zero-field Ising models over N binary variables/spins obtained by consecutive 'gluing' of planar and O(1)-sized components and subsets of at most three vertices into a tree. The polynomial time algorithm of the dynamic programming type for solving exact inference (computing partition function) and exact sampling (generating i.i.d. samples) consists of sequential application of an efficient (for planar) or brute-force (for O(1)-sized) inference and sampling to the components as a black box. To illustrate the utility of the new family of tractable graphical models, we first build a polynomial algorithm for inference and sampling of zero-field Ising models over K 33 -minor-free topologies and over K 5 -minor-free topologies—both of which are extensions of the planar zero-field Ising models—which are neither genus- nor treewidth-bounded. Second, we empirically demonstrate an improvement in the approximation quality of the NP-hard problem of inference over the square-grid Ising model in a node-dependent nonzero 'magnetic' field.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Application of State Quantization-Based Methods in HEP Particle Transport Simulation

Simulation of particle-matter interactions in complex geometries is one of the main tasks in high energy physics (HEP) research. An essential aspect of it is an accurate and efficient particle transportation in a non-uniform magnetic field, which includes the handling of volume crossings within a predefined 3D geometry. Quantized State Systems (QSS) is a family of numerical methods that provides attractive features for particle transportation processes, such as dense output (sequences of polynomial segments changing only according to accuracy-driven discrete events) and lightweight detection and handling of volume crossings (based on simple root-finding of polynomial functions). In this work we present a proof-of-concept performance comparison between a QSS-based standalone numerical solver and an application based on the Geant4 simulation toolkit, with its default Runge-Kutta based adaptive step method. In a case study with a charged particle circulating in a vacuum (with interactions with matter turned off), in a uniform magnetic field, and crossing up to 200 volume boundaries twice per turn, simulation results showed speedups of up to 6 times in favor of QSS while it being 10 times slower in the case with zero volume boundaries.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Chronically underestimated: a reassessment of US heat waves using the extended heat index

Abstract The heat index, or apparent temperature, was never defined for extreme heat and humidity, leading to the widespread adoption of a polynomial extrapolation designed by the United States National Weather Service. Recently, however, the heat index has been extended to all combinations of temperature and humidity, presenting an opportunity to reassess past heat waves. Here, three-hourly temperature and humidity are used to evaluate the extended heat index over the contiguous United States during the years 1984–2020. It is found that the 99.9th percentile of the daily maximum heat index is highest over the Midwest. Identifying and ranking heat waves by the spatially integrated exceedance of that percentile, the Midwest once again stands out as home to the most extreme heat waves, including the top-ranked July 2011 and July 1995 heat waves. The extended heat index can also be used to evaluate the physiological stress induced by heat and humidity. It is found that the most extreme Midwest heat waves tax the cardiovascular system with a skin blood flow that is elevated severalfold, approaching the physiological limit. These effects are not captured by the National Weather Service’s polynomial extrapolation, which also underestimates the heat index by as much as 10 ∘ C (20 ∘ F) during severe heat waves.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Potts-model critical manifolds revisited

We compute the critical polynomials for the q-state Potts model on all Archimedean lattices, using a parallel implementation of the algorithm of Ref. [1] that gives us access to larger sizes than previously possible. The exact polynomials are computed for bases of size 6 6 unit cells, and the root in the temperature variable v = e K -1 is determined numerically at q = 1 for bases of size 8 8. This leads to improved results for bond percolation thresholds, and for the Potts-model critical manifolds in the real (q; v) plane. In the two most favourable cases, we find now the kagome-lattice threshold to eleven digits and that of the (3; 12 2 ) lattice to thirteen. Our critical manifolds reveal many interesting features in the antiferromagnetic region of the Potts model, and determine accurately the extent of the Berker-Kadano phase for the lattices studied.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Superresolution without separation

Abstract This article provides a theoretical analysis of diffraction-limited superresolution, demonstrating that arbitrarily close point sources can be resolved in ideal situations. Precisely, we assume that the incoming signal is a linear combination of $M$ shifted copies of a known waveform with unknown shifts and amplitudes, and one only observes a finite collection of evaluations of this signal. We characterize properties of the base waveform such that the exact translations and amplitudes can be recovered from $2M+1$ observations. This recovery can be achieved by solving a weighted version of basis pursuit over a continuous dictionary. Our analysis shows that $\ell_1$-based methods enjoy the same separation-free recovery guarantees as polynomial root finding techniques, such as de Prony’s method or Vetterli’s method for signals of finite rate of innovation. Our proof techniques combine classical polynomial interpolation techniques with contemporary tools from compressed sensing.

Schiebinger, Geoffrey↗