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At least 19 records

Order conditions for nonlinearly partitioned Runge-Kutta methods

Recently, a new class of nonlinearly partitioned Runge–Kutta (NPRK) methods was proposed for nonlinearly partitioned systems of autonomous ordinary differential equations y' = F(y, y). The target class of problems are those in which different scales, stiffnesses, or physics are coupled in a nonlinear way, wherein the desired partition cannot be written in a classical additive or component-wise fashion. Here we use a rooted-tree analysis to derive full-order conditions for NPRKM methods, where M denotes the number of nonlinear partitions. Due to the nonlinear coupling and thereby the mixed product differentials, it turns out that the standard node-colored rooted tree analysis used in analyzing ODE integrators does not naturally apply. Instead we develop a new edge-colored rooted-tree framework to address the nonlinear coupling. The resulting order conditions are enumerated, are provided directly for up to fourth order with M = 2 and third order with M = 3, and are related to existing order conditions of additive and partitioned RK methods. We conclude with an example that shows how the nonlinear order conditions can be used to obtain an embedded estimate of the state-dependent nonlinear coupling strength in a dynamical system.

97 MATHEMATICS AND COMPUTING↗

Eu speciation in apatite at 1 bar: An experimental study of valence-state partitioning by XANES, lattice strain, and Eu/Eu* in basaltic systems

Abstract Partition coefficients for rare earth elements (REEs) between apatite and basaltic melt were determined as a function of oxygen fugacity (fO2; iron-wüstite to hematite-magnetite buffers) at 1 bar and between 1110 and 1175 °C. Apatite-melt partitioning data for REE3+ (La, Sm, Gd, Lu) show near constant values at all experimental conditions, while bulk Eu becomes more incompatible (with an increasing negative anomaly) with decreasing fO2. Experiments define three apatite calibrations that can theoretically be used as redox sensors. The first, a XANES calibration that directly measures Eu valence in apatite, requires saturation at similar temperature-composition conditions to experiments and is defined by: ( E u 3 + ∑ E u ) Apatite = 1 1 + 10 - 0.10 ± 0.01 × l o g ⁡ ( f o 2 ) - 1.63 ± 0.16 . The second technique involves analysis of Sm, Eu, and Gd in both apatite and coexisting basaltic melt (glass), and is defined by: ( Eu E u * ) D Sm × Gd = 1 1 + 10 - 0.15 ± 0.03 × l o g ⁡ ( f o 2 ) - 2.46 ± 0.41 . The third technique is based on the lattice strain model and also requires analysis of REE in both apatite and basalt. This calibration is defined by ( Eu E u * ) D lattice strain = 1 1 + 10 - 0.20 ± 0.03 × l o g ⁡ ( f o 2 ) - 3.03 ± 0.42 . The Eu valence-state partitioning techniques based on (Sm×Gd) and lattice strain are virtually indistinguishable, such that either methodology is valid. Application of any of these calibrations is best carried out in systems where both apatite and coexisting glass are present and in direct contact with one another. In holocrystalline rocks, whole rock analyses can be used as a guide to melt composition, but considerations and corrections must be made to either the lattice strain or Sm×Gd techniques to ensure that the effect of plagioclase crystallization either prior to or during apatite growth can be removed. Similarly, if the melt source has an inherited either a positive or negative Eu anomaly, appropriate corrections must also be made to lattice strain or Sm×Gd techniques that are based on whole rock analyses. This being the case, if apatite is primary and saturates from the parent melt early during the crystallization sequence, these corrections may be minimal. The partition coefficients for the REE between apatite and melt range from a maximum DEu3+ = 1.67 ± 0.25 (as determined by lattice strain) to DLu3+ = 0.69 ± 0.10. The REE partition coefficient pattern, as observed in the Onuma diagram, is in a fortuitous situation where the most compatible REE (Eu3+) is also the polyvalent element used to monitor fO2. These experiments provide a quantitative means of assessing Eu anomalies in apatite and how they be used to constrain the oxygen fugacity of silicate melts.

Geochemistry & Geophysics↗

Stage-local partitioned two-step runge-kutta methods for large systems of ordinary differential equations

We introduce stage-local partitioned two-step Runge-Kutta methods are an extension of standard two-step Runge-Kutta methods, which are an alternative to the standard additive two-step Runge-Kutta methods currently existing in the literature. Furthermore, these new schemes are designed with an eye towards truly N-partitioned systems and leverage local stage approximations to make several computationally interesting approximations viable. Specifically, the focus on local stage approximations makes possible the construction of truly asynchronous schemes, in the parallel sense, possible. In addition, we show that an implicit-explicit approach to these schemes can lead to methods that require the inversion of only local nonlinear systems.

Applied Dynamical Systems↗

Spectral Clustering-Based Partitioning of Large-Scale Power Electronics-Based Power Systems for Small-Signal Stability Analysis

The nodal admittance matrix (NAM)-based approach is well-suited for small-signal stability analysis of large-scale power electronics-based power systems (PEPSs), as it preserves the system structure through its admittance matrix. Previous studies have explored partitioning such systems into subareas and interconnections to reduce computational burden; however, they lacked a formal algorithmic procedure for determining feasible partitions. While several grid partitioning methods, such as those based on graph theory or machine learning, exist in the literature, they cannot be directly applied to NAM-based analysis due to differing objectives and constraints. Here, this paper addresses this gap by presenting a systematic, step-by-step procedure for applying a spectral partitioning algorithm that yields a division of the system into subareas suitable for NAM-based analysis. The computational complexity of the proposed method is also derived to demonstrate its efficiency and justify the practicality of the resulting subarea decomposition. The performance of the partitioning method is evaluated by applying the spectral clustering-derived subareas and interconnections to the NAM-based partitioning approach on a 140-bus system. Computational times for the full-system and partitioned NAM analyses are compared using MATLAB. Additionally, PSCAD simulations of the complete system and partitioned subareas are carried out to verify the effectiveness of the proposed method.

Nupur [Univ. of Tennessee, Knoxville, TN (United S↗

Analysis of Dynamical Peculiarities in Nanoalloys at Subsystems Level: Dynamical Degrees of Freedom, Temperature Differences, and the Chameleon Effect

Abstract A novel analysis of the dynamical behavior of nanoalloy systems, as represented by model Ni/Al 13‐atom clusters, over a broad range of energies that cover the stage‐wise transition of the systems from their solid‐like to liquid‐like state is presented. Conceptually, the analysis is rooted in partitioning the systems into judiciously chosen subsystems and characterizing the latter in terms of subsystem‐specific dynamical descriptors that include dynamical degrees of freedom , root‐mean‐square bond‐length fluctuation , and element‐specific subsystem temperature . The analysis reveals a host of intriguing new peculiarities in the dynamical behavior of the Ni/Al 13‐mers, among which are what we call the chameleon effect and the difference in the temperatures of the Ni and Al subsystems at high energies, a difference that strongly depends on the cluster composition and also changes with energy. These do not have an analog in pure Ni 13 and Al 13 and are explained in terms of the coupled effects of the difference between the masses of the Ni and Al atoms (the mass effect) and of the difference in the anharmonicity of the overall interaction potential as experienced by the Ni and Al subsystems of the clusters (the potential effect).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Multireference Embedding and Fragmentation Methods for Classical and Quantum Computers: From Model Systems to Realistic Applications

One of the primary challenges in quantum chemistry is the accurate modeling of strong electron correlation. While multireference methods effectively capture such correlation, their steep scaling with system size prohibits their application to large molecules and extended materials. Quantum embedding offers a promising solution by partitioning complex systems into manageable subsystems. In this Review, we highlight recent advances in multireference density matrix embedding and localized active space self-consistent field approaches for complex molecules and extended materials. We discuss both classical implementations and the emerging potential of these methods on quantum computers. Here, by extending classical embedding concepts to the quantum landscape, these algorithms have the potential to expand the reach of multireference methods in quantum chemistry and materials.

Algorithms↗

The unitary dependence theory for characterizing quantum circuits and states

Abstract Most existing quantum algorithms are discovered accidentally or adapted from classical algorithms, and there is the need for a systematic theory to understand and design quantum circuits. Here we develop a unitary dependence theory to characterize the behaviors of quantum circuits and states in terms of how quantum gates manipulate qubits and determine their measurement probabilities. Compared to the conventional entanglement description of quantum circuits and states, the unitary dependence picture offers more practical information on the measurement and manipulation of qubits, easier generalization to many-qubit systems, and better robustness upon partitioning of the system. The unitary dependence theory can be applied to systematically understand existing quantum circuits and design new quantum algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Incorporating the molecular-scale into a hydrodynamic description of confined aqueous systems

Hydrodynamics provides a continuum-level description of fluid motion, but its applicability at the nanoscale becomes uncertain due to the emerging importance of molecular-level effects such as spatial heterogeneity. Hydrodynamic boundary conditions that incorporate molecular details allow us to partition the system into a near-wall region and a bulk fluid region. We identify a hydrodynamic wall located inside the fluid that determines where slip begins. By extending the hydrodynamic wall with the slip length, the position of the extrapolated wall is established. This offers a unified description of both slip and stagnant flow behaviors, with wall hydrophobicity characterized by the relative location of the extrapolated wall with respect to the physical wall. Employing this concept in analyses of equilibrium molecular dynamics (MD) and non-equilibrium MD simulations of Couette and Poiseuille flows, our results demonstrate consistency between equilibrium and non-equilibrium approaches across different flow types and confinement levels. This demonstrates the robust nature of linear response theory. We then explore the effects of fluid-wall and bulk fluid interactions on the hydrodynamic properties. These findings enhance the effectiveness of molecular-based simulations for investigating complex confined systems in nanofluidics, biology, and colloidal science, offering a complementary molecular-scale perspective to traditional continuum approaches.

flow simulations↗

Investigation of Mercury Compound Partitioning Through the Solvent Extraction System

Savannah River National Laboratory (SRNL) has been requested by Savannah River Mission Completion (SRMC)/ Salt Waste Processing Facility (SWPF) personnel to investigate the potential routes for titanium and mercury accumulations within the SWPF Flowsheet. This report documents work performed to examine how various forms of mercury can migrate through the multiple flowsheets of a solvent extraction system. This entailed 29 single stage distribution tests, a multi-stage Extraction-Scrub-Strip (ESS) test, and a detailed speciation analysis of several salt batch feed samples.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Range‐separated density functional theory using multiresolution analysis and quantum computing

Quantum computers are expected to outperform classical computers for specific problems in quantum chemistry. Such calculations remain expensive, but costs can be lowered through the partition of the molecular system. In the present study, partition was achieved with range-separated density functional theory (RS-DFT). The use of RS-DFT reduces both the basis set size and the active space size dependence of the ground state energy in comparison with the use of wave function theory (WFT) alone. The utilization of pair natural orbitals (PNOs) in place of canonical molecular orbitals (MOs) results in more compact qubit Hamiltonians. To test this strategy, a basis-set independent framework, known as multiresolution analysis (MRA), was employed to generate PNOs. Tests were conducted with the variational quantum eigensolver for a number of molecules. The results show that the proposed approach reduces the number of qubits needed to reach a target energy accuracy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Partitioning of Large-Scale Power Electronics-Based Power Systems for Small-Signal Stability Analysis

The nodal admittance matrix (NAM)-based approach is suitable for analyzing the small-signal stability of large-scale power electronics-based power systems (PEPSs) as it preserves the system structure by utilizing the admittance matrix. Previously, NAM-based area partition has been proposed, which divides the system into various subareas and interconnections for easier analysis of the low-dimension matrix compared to the entire system-based high-dimension matrix. However, no partition algorithm has been presented for the NAM-based area partition method. This paper focuses on implementing the spectral partitioning algorithm for partitioning large-scale PEPSs into a low-dimension matrix to reduce the computation complexity of the analysis. These spectral components facilitate data transformation into a new space, enabling the application of traditional clustering methods like k-means. To evaluate the performance of the partitioning method, the subareas and interconnections obtained from the spectral clustering algorithm are incorporated into the NAM-based area partition method for a large system with 140 buses. The computational times of the original method, where the NAM-based criterion is directly applied to the entire system, are compared with those of the NAM-based partition method in MATLAB. PSCAD simulations of the whole system and the obtained subareas are conducted to validate the effectiveness of the proposed algorithm.

Nupur, Nupur↗

Hierarchical Truncations for Many-Body Expansion Potentials

In this work, a new strategy to truncate high-order terms in the many-body expansion (MBE) is proposed. This new approach, which we call a hierarchical many-body expansion (HMBE), is based on a hierarchical partition of the system into multitier fragments and can in principle be applied to any large molecular system. Numerical tests on a series of (H 2 O) 64 structures are presented, demonstrating satisfactory relative energies between the clusters and binding energies of individual clusters compared with full-cluster calculations, with significantly fewer high-order terms computed than conventional MBE. The hierarchical truncation can be augmented by certain many-body terms for fragments at the interface between the partitions (called “Schengen terms”) to further improve accuracy. This work establishes the HMBE scheme as a promising framework to model very large systems (e.g., proteins), which are naturally built on a hierarchical structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Updates to the Hanford Soil Inventory Model (SIM Version 2) for FY 2023

The purpose of this environmental calculation file (ECF) is to document the updates made to the Soil Inventory Model version 2.1 (SIM-v2.1) (ECF-HANFORD-21-0073, Updates to the Hanford Soil Inventory Model (SIM Version 2) for FY 2021) in FY 2023. These updates to SIM-v2.1 are referred to as the SIM-v2.2 version. The following updates have been made: • Include inventory estimate for a new analyte • hexavalent chromium (Cr(VI)), separate from total chromium inventory • Revise the inventory discharged to the 216-U-10 and 216-T-4 Pond systems based on partitioning of waste streams discharges over time and space among influent ditches and ponds • Enhance the preprocessing and postprocessing of the input and output files Note that the methodology for estimating Cr(VI) inventories is based on ECF-200W-23-0040, Recommendations for Updating Liquid Discharged Inventory and Transport Modeling Parameters for Cumulative Impacts Evaluation of Hexavalent Chromium in the 200 West Area while the revision of inventory discharged to the 216-U-10 and 216-T-4 Pond systems is based on ECF-HANFORD-19-0032, Distribution of Infiltration in the 216-U-10, 216-B-3 Pond, and 216-T-4 Pond Systems 1944-1997.

54 ENVIRONMENTAL SCIENCES↗

Coupled Aerodynamic and Hydrodynamic Hybrid Simulation of Floating Offshore Wind Turbines

The development and innovation of floating offshore wind energy in the U.S. requires detailed high-fidelity observations and measurements of turbine and platform loading due to wind, waves, and currents. However, full-scale and quasi-full-scale experiments require significant financial and temporal investments for construction, experimental testing, and long-term field campaigns. To support the commercial advancement of the offshore wind energy industry, specialized wind tunnel and wave basin experimental facilities are critical to be able to test FOWT designs at small scale under controlled conditions prior to full-scale deployment. Oregon State University (OSU) is internationally known as a leader in water and energy research, development, and testing. The O.H. Hinsdale Wave Research Laboratory (HWRL) and the Wallace Energy Systems and Renewables Facility (WESRF) at OSU have extensive experience building, modeling, monitoring, controlling, and actuating scaled systems. Experiments on wave-structure interaction have been performed at the HWRL since its establishment in 1972. Studies have included the interaction of waves with coastal structures (breakwaters, seawalls, buildings, cylinders, bridges, fixed foundations of offshore wind turbines, etc.) and with floating structures (e.g., wave energy converters, maneuvering of vessels, etc.). Hinsdale is actively used by marine energy technology developers, both for private testing and OSU-collaborative research projects. However, despite the availability of several large-scale facilities for hydrodynamic testing (at OSU and elsewhere in the U.S.), existing experimental laboratories are generally limited in their ability to accurately generate combined wind and wave conditions. The simulation of both wind and waves in experimental testing is complicated due to a number of constraints, including: [i] incompatible similitude laws governing the wind and waves for scaled experiments, [ii] producing accurate wind over a large enough control volume via fans, and [iii] generating wind that reasonably represents the atmospheric boundary layer in existing wave basins/flumes. Hence, physical test data providing insight into the simultaneous wave- and wind-structure response of floating offshore wind components can be difficult to generate. Given the aforementioned challenges in classic hydrodynamic experiments, the motivation of this project is to establish a real-time hybrid simulation (RTHS) approach that can apply aero- and hydro-dynamic loading by augmenting wave-only experimental facilities with virtual aerodynamic forces through numerical models representing the remaining dynamic forces. RTHS is a physical-numerical approach that partitions a prototype system into physical and numerical sub-assemblies that interact with each other through actuators and sensors in real time. In coupling physical and numerical models, the hybrid simulation approach applied herein is ideal for problems with: (1) structures subjected to different scaling laws, such as floating offshore wind turbines subjected to combined aero/hydro-dynamic loading, (2) structures that are too large or complex to be tested entirely in a laboratory setting, such as deep-water mooring applications, and (3) component testing, where the behavior of a portion of the assembly is uncertain but still interacts with other portions of the structure, such as testing the fatigue life of turbine blades. Few U.S. experimental facilities are able to test simultaneous aero- and hydro-dynamic loading and none can accurately produce aero/hydro-dynamic response on scaled FOWT models due to conflicting similitude laws between the wind (commonly Reynolds) and the waves (commonly Froude). To aid in accelerating the development of the U.S. floating offshore industry, there is a significant need to develop a flexible, modular framework that can expand the capacities of existing wave-only laboratories. The project goal is to demonstrate a hydrodynamic real-time hybrid simulation (hydro-RTHS) framework that couples numerical wind and physical waves acting on a FOWT, thus representing simultaneous aero/hydro-dynamic loading. The FOWT is partitioned into a full-scale numerical sub-assembly associated with the aerodynamics and a model-scale physical sub-assembly associated with the hydrodynamics. The numerical-physical partition associated with hydro-RTHS mitigates scaling constraints by supplying different scaling laws to the physical and numerical sub-assemblies. Herein, length, force, and time are scaled and exchanged between the sub-assemblies using Froude scaling to represent the open-channel flow in the physical sub-assembly. Other similitude laws could also be utilized depending on the problem definition. It is envisioned that the ability to model FOWTs under waves and wind, with mitigation of similitude distortions, would result in reduced development costs (currently, FOWT concept development is performed with full-size pro- totypes at enormous expense and risk) and increase the reliability of the FOWT industry (since extreme wave and wind conditions and contingency events can be tested safely in a controlled environment).

16 TIDAL AND WAVE POWER↗

Applications of the Dulmage–Mendelsohn decomposition for debugging nonlinear optimization problems

Nonlinear modeling and optimization is a valuable tool for aiding decisions by engineering practitioners, but programming an optimization problem based on a complex electrical, mechanical, or chemical process is a time-consuming and error-prone activity. Therefore, there is a need for model analysis and debugging tools that can detect and diagnose modeling errors. One such tool is the Dulmage–Mendelsohn decomposition, which identifies structurally under- and over-determined subsets in systems of equations and variables by partitioning the bipartite graph of the system. This work provides the necessary background to understand the Dulmage–Mendelsohn decomposition and its application to the analysis of nonlinear optimization problems, demonstrates its use in diagnosing a variety of modeling errors, and introduces software implementations for analyzing nonlinear optimization problems in the Pyomo and JuMP algebraic modeling languages.

42 ENGINEERING↗

Strategies to Obtain Reliable Energy Landscapes from Embedded Multireference Correlated Wavefunction Methods for Surface Reactions

Embedded correlated wavefunction (ECW) theory is a powerful tool for studying ground- and excited-state reaction mechanisms and associated energetics in heterogeneous catalysis. Several factors are important to obtaining reliable ECW energies, critically the construction of consistent active spaces (ASs) along reaction pathways when using a multireference correlated wavefunction (CW) method that relies on a subset of orbital spaces in the configuration interaction expansion to account for static electron correlation, e.g., complete AS self-consistent field theory, in addition to the adequate partitioning of the system into a cluster and environment, as well as the choice of a suitable basis set and number of states included in excited-state simulations. Here, in this work, we conducted a series of systematic studies to develop best-practice guidelines for ground- and excited-state ECW theory simulations, utilizing the decomposition of NH 3 on Pd(111) as an example. We determine that ECW theory results are relatively insensitive to cluster size, the aug-cc-pVDZ basis set provides an adequate compromise between computational complexity and accuracy, and that a fixed-clean-surface approximation holds well for the derivation of the embedding potential. Additionally, we demonstrate that a merging approach, which involves generating ASs from the molecular fragments at each configuration, is preferable to a creeping approach, which utilizes ASs from adjacent structures as an initial guess, for the generation of consistent potential energy curves involving open-d-shell metal surfaces, and, finally, we show that it is essential to include bands of excited states in their entirety when simulating excited-state reaction pathways.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Performance Evaluation of Gray-box and Machine Learning Models of a Thermal Energy Storage System with Active Insulation

An interior partition wall integrated with active thermal storage and a dynamic insulation system was built and then installed in an office building in Oak Ridge, Tennessee, TN. This smart wall, termed the Empower Wall, was equipped with embedded pipes in the building envelope core component and an additional pipe network enclosing rigid insulation to switch on and off the active insulation dynamically. The performance of the wall's contribution to cooling load reduction under different parameters has been investigated in previous publications. Aiming to be deployed into model predictive control and other optimization methods, simplified and reliable models for the developed wall and the room accommodating it are required. They are needed to characterize the properties and thermal response of both Empower Wall and building envelope, which form an essential component for accurate indoor temperature or cooling/heating demand prediction. In this study, simplified gray-box and regression models as well as machine learning model were developed and the performance of them were compared and analyzed.

Cui, Borui↗