Search NASA⌕ Search

SEARCH · Search NASA

Results for “Numerical methods”

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 181 records · Page 10

Ground-state-based model reduction with unitary circuits

Here, we present a method to numerically obtain low-energy effective models based on a unitary transformation of the ground state. The algorithm finds a unitary circuit that transforms the ground state of the original model to a projected wavefunction with only the low-energy degrees of freedom. The effective model can then be derived using the unitary transformation encoded in the circuit. We test our method on the one-dimensional and two-dimensional square-lattice Hubbard model at half-filling, and obtain more accurate effective spin models than the standard perturbative approach.

Hubbard model↗

Classifying photonic topology using the spectral localizer and numerical K -theory

Recently, the spectral localizer framework has emerged as an efficient approach for classifying topology in photonic systems featuring local nonlinearities and radiative environments. In nonlinear systems, this framework provides rigorous definitions for concepts such as topological solitons and topological dynamics, where a system’s occupation induces a local change in its topology due to nonlinearity. For systems embedded in radiative environments that do not possess a shared bulk spectral gap, this framework enables the identification of local topology and shows that local topological protection is preserved despite the lack of a common gap. However, as the spectral localizer framework is rooted in the mathematics of C*-algebras, and not vector bundles, understanding and using this framework requires developing intuition for a somewhat different set of underlying concepts than those that appear in traditional approaches for classifying material topology. In this tutorial, we introduce the spectral localizer framework from a ground-up perspective and provide physically motivated arguments for understanding its local topological markers and associated local measure of topological protection. In doing so, we provide numerous examples of the framework’s application to a variety of topological classes, including crystalline and higher-order topology. We then show how Maxwell’s equations can be reformulated to be compatible with the spectral localizer framework, including the possibility of radiative boundary conditions. To aid in this introduction, we also provide a physics-oriented introduction to multi-operator pseudospectral methods and numerical K-theory, two mathematical concepts that form the foundation for the spectral localizer framework. Finally, we provide some mathematically oriented comments on the C*-algebraic origins of this framework, including a discussion of real C*-algebras and graded C*-algebras that are necessary for incorporating physical symmetries. Looking forward, we hope that this tutorial will serve as an approachable starting point for learning the foundations of the spectral localizer framework.

97 MATHEMATICS AND COMPUTING↗

Unraveling Electronic and Vibrational Coherences Following a Charge Transfer Process in a Photosystem II Reaction Center

A reaction center is a unique biological system that performs the initial charge separation within a Photosystem II (PSII) multiunit enzyme, which eventually drives the catalytic water-splitting in plants and algae. The possible role of quantum coherences coinciding with the energy and charge transfer processes in PSII reaction center is one of the active areas of research. Here, we study these quantum coherences by using a numerically exact method on an excitonic dimer model, including linear vibronic coupling and employing optimal parameters from experimental two-dimensional coherent spectroscopic measurements. This enables us to precisely capture the excitonic interaction between pigments and the dissipation of the energy from electronic and charge-transfer (CT) states to the protein environment. We employ the time nonlocal (TNL) quantum master equation to calculate the population dynamics, which yields numerically reliable results. The calculated results show that, due to the strong dissipation, the lifetime of electronic coherence is too short to have direct participation in the charge transfer processes. However, there are long-lived vibrational coherences present in the system at frequencies close to the excitionic energy gap. These are strongly coupled with the electronic coherences, which makes the detection of the electronic coherences with conventional techniques very challenging. Additionally, we unravel the strong excitonic interaction of radical pair (PD1 and PD2) in the reaction center, which results in a long-lived electronic coherence of >100 fs, even at room temperature. Our work provide important physical insight to the charge separation process in PSII reaction center, which may be helpful for better understanding of photophysical processes in other natural and artificial light-harvesting systems.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Non-local transport in radiation-hydrodynamics codes for ICF by efficient coupling to an external Vlasov–Fokker–Planck code

Accurately incorporating non-local transport into radiation-hydrodynamics codes, and indeed any fluid system, has long been elusive. To date, a simplified and accurate theory that can be easily integrated has not been available. This limitation affects modeling in inertial confinement fusion (ICF) and magnetic confinement fusion systems, among others, where non-local transport is well-known to be present. Here, we present a coupling methodology between a full Vlasov–Fokker–Planck (VFP) electron kinetic code and radiation-hydrodynamics (rad-hydro) codes. The VFP code is used to adjust native electron transport in the rad-hydro code, thus enabling improved transport without the need to integrate a full electron VFP solver into the rad-hydro code. This approach necessitates only occasional invocation of the VFP code, reducing computational intensity compared to following the dynamic evolution entirely with the VFP code on fluid time scales. We illustrate that the methodology is more accurate than other simplified methods in thermal decay systems relevant to ICF and can replicate standard theoretical results with high accuracy.

Electronic transport↗

ComPort: Rigorous Testing Methods to Safeguard Software Porting (Final Technical Report)

This is a technical report from the lead institution – University of Utah, Kahlert School of Computing – funded under the Department of Energy, Office of Science, Office of Advanced Scientific Computing Research under award number DE-SC0022252. We summarize our work done over the three years of funding received. The relevant papers and software have already been uploaded at the DOE site.

97 MATHEMATICS AND COMPUTING↗

Hybrid Basis and Multi-Center Grid Method for Strong-Field Processes

We present a time-dependent framework that combines a hybrid basis, consisting of Gaussian-type orbitals (GTOs) and finite-element discrete-variable representation (FEDVR) functions, with a multicenter grid to simulate strong-field and attosecond dynamics in atoms and molecules. The method incorporates the construction of the orthonormal hybrid basis, the evaluation of electronic integrals, a unitary time-propagation scheme, and the extraction of optical and photoelectron observables. Its accuracy and robustness are benchmarked on one-electron systems such as atomic hydrogen and the dihydrogen cation (H$^+_2$) through comparisons with essentially-exact reference results for bound-state energies, high-harmonic generation spectra, photoionization cross sections, and photoelectron momentum distributions. This work establishes the groundwork for its integration with quantum-chemistry methods, which is already operational but will be detailed in future work, thereby enabling ab initio simulations of correlated polyatomic systems in intense ultrafast laser fields.

74 ATOMIC AND MOLECULAR PHYSICS↗

Comparison between explicit and implicit discretization strategies for a dissipative thermal environment

We investigate strategies for simulating open quantum systems coupled to dissipative baths by comparing explicit wave function-based discretization [via multi-layer multi-configuration time-dependent Hartree (ML-MCTDH)] and the implicit density matrix-based master equation method [via tree tensor network hierarchical equations of motion (TTN-HEOM)]. For dissipative baths characterized by exponentially decaying bath correlation functions, the implicit discretization approach of HEOM—rooted in bath correlation function decompositions—proves significantly more efficient than explicit discretization of the bath into discrete harmonic modes. Explicit methods, like ML-MCTDH, require extensive mode discretization to approximate continuum baths, leading to computational bottlenecks. Case studies for two-level systems and a Fenna–Matthews–Olson complex model highlight TTN-HEOM’s superiority in capturing dissipative dynamics with relaxations with a minimal number of auxiliary modes, while the explicit methods are as exact as the HEOM in pure dephasing regimes. This comparison is enabled by the TENSO package, which has both ML-MCTDH and TTN-HEOM implemented using the same computational structure and propagation strategy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An infrasound source analysis of the OSIRIS-REx sample return capsule hypersonic re-entry

The OSIRIS-REx sample return capsule's hypersonic re-entry into the atmosphere is a rare opportunity to test a variety of sonic boom source models since the projectile dimensions are well characterized. While the as-flown flight path is unknown, the predicted flight path enables a rough approximation of the source Mach number and location. Six infrasound microphones deployed in the boom carpet along the predicted flight path recorded impulsive signals from the OSIRIS-REx re-entry. Using a suite of atmosphere profiles and the geometric acoustics approximation, we estimate locations with uncertainty estimates along the flight path from which the signals were emitted. Acoustic overpressure and signal duration predictions from Whitham's far field theory, Carlson's simplified sonic boom prediction method, and a drag-dominated hypersonic model are analyzed with uncertainty estimates from the location estimate. While the Carlson simplified sonic boom prediction method could be accurate, our preference is for the drag-dominated source model. Using this source model with an inviscid Burgers's equation solver for propagation, we obtained an excellent match to the recorded data. In conclusion, these results will help better inform future sample return capsule re-entry observation campaigns as well as contribute to a better understanding of high altitude infrasonic sources.

58 GEOSCIENCES↗

Dark Energy Survey Deep Field photometric redshift performance and training incompleteness assessment

Context. The determination of accurate photometric redshifts (photo-zs) in large imaging galaxy surveys is key for cosmological studies. One of the most common approaches are machine learning techniques. These methods require a spectroscopic or reference sample to train the algorithms. Attention has to be paid to the quality and properties of these samples since they are key factors in the estimation of reliable photo-zs. Aims. The goal of this work is to calculate the photo-zs for the Y3 DES Deep Fields catalogue using the DNF machine learning algorithm. Moreover, we want to develop techniques to assess the incompleteness of the training sample and metrics to study how incompleteness affects the quality of photometric redshifts. Finally, we are interested in comparing the performance obtained with respect to the EAzY template fitting approach on Y3 DES Deep Fields catalogue. Methods. We have emulated -- at brighter magnitude -- the training incompleteness with a spectroscopic sample whose redshifts are known to have a measurable view of the problem. We have used a principal component analysis to graphically assess incompleteness and to relate it with the performance parameters provided by DNF. Finally, we have applied the results about the incompleteness to the photo-z computation on Y3 DES Deep Fields with DNF and estimated its performance. Results. The photo-zs for the galaxies on DES Deep Fields have been computed with the DNF algorithm and added to the Y3 DES Deep Fields catalogue. They are available at https://des.ncsa.illinois.edu/releases/y3a2/Y3deepfields. Some techniques have been developed to evaluate the performance in the absence of "true" redshift and to assess completeness. We have studied... (Partial abstract)

79 ASTRONOMY AND ASTROPHYSICS↗

Micropolar Elastoplasticity Using a Fast Fourier Transform‐Based Solver

ABSTRACT This work presents a micromechanical spectral formulation for obtaining the full‐field and homogenized response of elastoplastic micropolar composites. A closed‐form radial‐return mapping is derived from thermodynamics‐based micropolar elastoplastic constitutive equations to determine the increment of plastic strain necessary to return the generalized stress state to the yield surface, and the algorithm implementation is verified using the method of numerically manufactured solutions. Then, size‐dependent material response and micro‐plasticity are shown as features that may be efficiently simulated in this micropolar elastoplastic framework. The computational efficiency of the formulation enables the generation of large datasets in reasonable computing times.

42 ENGINEERING↗

Generalized boost transformations in finite volumes and application to Hamiltonian methods

The investigation of hadron interactions within lattice QCD has been facilitated by the well-known quantisation condition, linking scattering phase shifts to finite-volume energies. Additionally, the ability to utilise systems at finite total boosts has been pivotal in smoothly charting the energy-dependent behaviour of these phase shifts. The existing implementations of the quantization condition at finite boosts rely on momentum transformations between rest and moving frames, defined directly in terms of the energy eigenvalues. This energy dependence is unsuitable in the formulation of a Hamiltonian. In this work, we introduce a novel approach to generalise the three-momentum boost prescription, enabling the incorporation of energy-independent finite-volume Hamiltonians within moving frames. We demonstrate the application of our method through numerical comparisons, employing a phenomenological ππ scattering example.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Calculation of machine precision second order derivatives using dual-complex numbers

It is well known that both complex and dual numbers can be employed to obtain machine precision first-order derivatives; however, neither, on their own, can compute machine precision 2nd order derivatives. To address this limitation, it is demonstrated in this paper that combined dual-complex numbers can be used to compute machine precision 1st and 2nd order derivatives. The dual-complex approach is simpler than utilizing multicomplex or hyper-dual numbers as existing dual libraries can be used as is or easily augmented to accept complex numbers, and the complexity of developing, integrating, and deploying multicomplex or hyper-dual libraries is avoided. The efficacy of this approach is demonstrated for both univariate and multivariate functions. Finally, source code examples using the Python, Julia, and Mathematica languages are provided as supplemental material.

97 MATHEMATICS AND COMPUTING↗

Numerical investigation of mixing and heat transfer in a 7.9 m JP-8 pool fire

The response of objects engulfed in, and adjacent to, large-scale pool fires is of interest in accident and safety assessments. In this study, Fuego, a low-Mach turbulent reacting flow code was used to study conjugate heat transfer in a 7.9 m diameter JP-8 pool fire. Simulations were designed to replicate past experimental measurements (Blanchat et al., 2006) of incident heat flux to three cylindrical calorimeters in and around the pool fire. Two turbulent combustion models were compared directly - the eddy dissipation concept and a more recently developed unsteady flamelet model. First and second order spatial and temporal discretization schemes were also compared to assess the performance of low-dissipation numerical operators. Heat flux predictions to the transportation size calorimeter outside the fire were within experimental uncertainties. Inside the fire, experimental measurements were higher than predicted values and may have been a consequence of soot deposition and augmented participating media radiation from soot and fuel vapor. Simulation predictions improved in cases where turbulent kinetic energy and mixing were more resolved. This work, and others referenced herein, suggest that spatial resolution on the order of 0.5–1.0 cm may be required to fully resolve fluid instabilities, vortex production between fire plumes and crosswind, soot production, and fuel-air mixing. This presents a substantial computational challenge for safety assessments of engulfed objects in fully turbulent pool fires.

Conjugate heat transfer↗

Leveraging large language models to address data scarcity in machine learning for graphene synthesis

Machine learning in experimental materials science faces significant challenges due to the scarcity of data, which are costly and time-consuming to generate, particularly when relying on in-house experiments. Literature data mining offers a potential solution but introduces issues like mixed data quality, inconsistent formats, and non-uniform reporting of synthesis parameters, resulting in partially missing and heterogeneous features across the dataset. Here, we propose data imputation and feature engineering methods that employ pre-trained large language models (LLMs) to enhance machine learning performance on scarce, heterogeneous datasets, demonstrated on graphene CVD synthesis data and the ML-HydPARK hydrogen storage dataset. GPT models perform data imputation via tailored prompting and semantic normalization of inconsistently reported features through embeddings, for example, to harmonize the complex nomenclature of CVD substrates. Beyond yielding more diverse and richer feature representations than traditional methods such as K-nearest neighbors (KNN) and Multivariate Imputation by Chained Equations (MICE), LLM-based data imputation is evaluated against dataset characteristics and prompting strategies. We vary the level of autonomy granted to the LLM, from generic prompting that leverages pre-trained knowledge for autonomous data generation to data-informed prompting that constrains outputs using target-specific information, and demonstrate which level of autonomy yields superior imputation performance across datasets and feature types. The proposed data engineering methods markedly improve downstream performance; for example, in graphene layer number classification using a support vector machine (SVM), binary accuracy increases from 39% to 65% and ternary accuracy from 52% to 72%. Fine-tuning experiments on both datasets show that combining our proposed LLM-based data imputation and feature encoding methods with numerical machine learning predictors outperforms standalone fine-tuned LLM predictors in data-scarce settings. The proposed strategies emphasize data enhancement techniques rather than refining learning architectures or regularizing loss functions, offering a broadly applicable framework for improving machine learning performance on scarce, inhomogeneous datasets.

Chemical vapor deposition↗

Process intensification in hydrothermal liquefaction of biomass: A review

Hydrothermal liquefaction (HTL) presents a promising pathway for converting wet biomass resources into biofuels, offering significant advantages over conventional methods. However, numerous challenges must be addressed for HTL scale-up, including energy provision for the endothermic process, heat and mass transfer limitations, slurry concentration and pumpability challenges, char and coke formation, and continuous phase separation. This review explores key strategies such as autothermal HTL, which improves process efficiency and reduces external energy requirements by coupling exothermic and endothermic reactions within the same reactor, thereby simplifying reactor design and reducing operational costs. Additionally, multistage HTL processes are highlighted for their ability to optimize biocrude quality and yield by fractionating biomass conversion stages, resulting in higher energy returns on investment and better-quality biocrude. Solvothermal HTL and integration techniques for aqueous phase are also discussed. Furthermore, the HTL patent landscape is discussed to provide insights into current technological advancements. This review aims to offer a comprehensive understanding of process intensification in HTL, highlighting innovative solutions to enhance the efficiency and scalability of the process for sustainable biofuel production.

Biocrude oil↗

The influence of kinematics of deformation on polycrystalline halite dynamic recrystallization: Full-field simulation of simple shear versus pure shear

Rock salt, composed mainly of halite, flows viscoplastically over a wide range of geological conditions, strongly impacting the dynamic evolution of sedimentary basins and orogens. Understanding how dislocation creep, which involves dislocation glide, intracrystalline recovery and dynamic recrystallization, influences the microstructure and rheology of halite under various deformation kinematics and temperatures is crucial for enhancing knowledge of salt flow dynamics. Here, this study employs a full-field numerical simulation method to compare the viscoplastic deformation of polycrystalline halite under simple shear and pure shear conditions up to a natural strain of ε = 1.5 at temperatures ranging from 100 °C to 300 °C. The results are presented in terms of crystallographic preferred orientation (CPO), grain shape preferred orientation (SPO), subgrain boundary direction, grain size and strain rate distribution. The results indicate that the crystallographic anisotropy of individual halite crystals is transferred to the polycrystalline scale, resulting in strain localization, particularly in simple shear simulations. The kinematics of deformation affect the evolution and distribution of high strain-rate bands, determining the direction of intragranular substructures and the morphology of strain-induced grain boundaries, with minimal impact on grain size. The intensity of grain boundary migration increases with temperature, significantly influencing grain morphology and size, thereby obscuring strain localization, while having little effect on CPOs. At low strain (ε < 1.0), CPOs relative to both the maximum shortening direction and the grain SPO are similar regardless of the deformation kinematics. At high strain (ε > 1.0), simple shear CPOs exhibit three stronger {100} maxima with a monoclinic symmetry relative to the grain SPO compared to the six {100} maxima with an orthotropic symmetry relative to the grain SPO generated under pure shear. Therefore, microstructures and CPOs can serve as indicators of the strain path in polycrystalline halite under various conditions, aiding in determining the shear sense and elucidating the deformation kinematics of salt structures.

58 GEOSCIENCES↗