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DOE OSTI2015

High-intensity-beam study of O 17 ( p , γ ) F 18 and thermonuclear reaction rates for O 17 + p

Hydrogen burning of the oxygen isotopes takes place in low-mass stars, asymptotic giant branch stars, and classical novae. Observations of oxygen elemental and isotopic abundances in stellar spectra or in presolar grains provide strong constraints for stellar models if reliable thermonuclear reaction rates for hydrogen burning of oxygen are available. We present the results of a new measurement of the 17 O ( p , γ ) 18 F reaction in the laboratory bombarding energy range of 170 – 530 keV. The measurement is performed with significantly higher beam intensities ( I max ≈ 2 mA) compared to previous work and by employing a sophisticated γ -ray coincidence spectrometer. We measured the cross section at much lower energies than previous in-beam experiments. Furthermore we apply a novel data-analysis method that is based on the decomposition of different contributions to the measured pulse-height spectrum. Our measured strengths of the low-energy resonances amount to ω γ pres ( 193 keV ) = ( 1.86 ± 0.13 ) × 10 - 6 eV and ω γ pres ( 518 keV ) = ( 13.70 ± 0.96 ) × 10 - 3 eV. For the direct capture S factor at zero energy, we find a value of S DC pres ( 0 ) = 4.82 ± 0.41 keV b. We also present new thermonuclear rates for the 17 O + p reactions, taking into account all consistent results from previous measurements.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2017

Effect of ammonium-sulfide solvent on the surface passivation of GaSb (100)

X-ray photoemission spectroscopy and scanning electron microscopy are used to study the effect of a solvent on the chemical composition of a sulfide passivating layer formed on GaSb (100) surface. Treatment of the GaSb (100) surface with ammonium-sulfide solutions results in the formation of a thick (several tens of nanometers) coating composed of a mixture of various binary and ternary gallium and antimony sulfides. The chemical compositions of the passivating sulfide layers formed in aqueous and alcoholic ammonium-sulfide solutions are different. Annealing of the sulfide layer at 360°C in ultrahigh vacuum leads to the partial desorption of antimony from the surface, the decomposition of ternary sulfides into their binary constituents, and change in the surface band bending of this layer.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Flammability and thermal stability of thermoplastic-based composites filled with natural carbon

This investigation characterized flammability and thermal stability for a novel sustainable composite engineered for use in building applications. Flammability and thermal stability of coal plastic composites composed of coal (40–60 wt.%) and high-density polyethylene were compared to commercial wood–plastic composites. Pyrolysis thermogravimetric analysis results indicated that coal plastic composites possessed a single-step decomposition and higher char residue, while wood–plastic composites had two-step decomposition, with the first peak occurring at much lower temperatures. Thermogravimetric analyses in air suggest coal plastic composites, compared to wood–plastic composites and neat high-density polyethylene, were more thermally stable. Flash ignition temperatures for coal plastic composites were higher than high-density polyethylene and wood–plastic composites, while self-ignition temperatures were in the same range as wood–plastic composites. Rate of burning data indicated coal plastic composites were slower burning than wood–plastic composites, with increasing coal content slowing burning rate by 19.9%–27.6%. Cone calorimeter testing showed 27% and 59% reduction in total heat release and total smoke release as coal content increased while coal plastic composite with 60 wt.% coal possessed lower overall flammability in comparison with predominant commercially available wood–plastic composite products. Coal improved composite overall thermal stability and flammability by acting as char former and foaming agent.

Engineering↗

NASA NTRS2011

Land Surface Verification Toolkit (LVT) - A Generalized Framework for Land Surface Model Evaluation

Model evaluation and verification are key in improving the usage and applicability of simulation models for real-world applications. In this article, the development and capabilities of a formal system for land surface model evaluation called the Land surface Verification Toolkit (LVT) is described. LVT is designed to provide an integrated environment for systematic land model evaluation and facilitates a range of verification approaches and analysis capabilities. LVT operates across multiple temporal and spatial scales and employs a large suite of in-situ, remotely sensed and other model and reanalysis datasets in their native formats. In addition to the traditional accuracy-based measures, LVT also includes uncertainty and ensemble diagnostics, information theory measures, spatial similarity metrics and scale decomposition techniques that provide novel ways for performing diagnostic model evaluations. Though LVT was originally designed to support the land surface modeling and data assimilation framework known as the Land Information System (LIS), it also supports hydrological data products from other, non-LIS environments. In addition, the analysis of diagnostics from various computational subsystems of LIS including data assimilation, optimization and uncertainty estimation are supported within LVT. Together, LIS and LVT provide a robust end-to-end environment for enabling the concepts of model data fusion for hydrological applications. The evolving capabilities of LVT framework are expected to facilitate rapid model evaluation efforts and aid the definition and refinement of formal evaluation procedures for the land surface modeling community.

Kumar, Sujay V.↗

NASA NTRSDate not supplied

Identification and Study of Validation Level Test Cases for Computational Modeling of Non-Charring Ablators

Computational modeling of Thermal Protection System (TPS) materials, used for aerospace applications, provides numerous advantages in preliminary selection and design of a heatshield material and shape for atmospheric entry vehicles. However, to serve as a reliable tool for prediction of material thermal and ablative behavior, the modeling approach needs to be validated against real experimental and flight data, preferably at a range of applied conditions. The validation study is typically very complex as it requires reliable measured data not only for the material thermal response and surface recession, but also well characterized environmental conditions. The validation problem becomes even more complex when the material thermal response is dictated by multi-physics effects such as solid conduction, in-depth thermal decomposition, pyrolysis gas flow and chemical reactions. The multi-physics effects complicate not only the modeling effort, but also the experimental measurement for validation of various aspects of the highly coupled problem. In this study, an attempt is made to identify suitable experimental data that could serve as a source for validation of material thermal response modeling tools. To reduce the computational complexity, this study focuses only on non-charring ablators, where the material thermal response could be modeled with a single governing equation for solid conduction and the ablation is limited only to the surface of the material. With a well characterized and publicly available experimental data being sparse, the study is limited in presenting test cases for only three materials: camphor, graphite and FiberForm® in the sequence of increased modeling complexity. Graphite is a commonly used TPS material for aerospace applications, both for leading edges of high-speed vehicles and internal insulation of solid rocket motors. FiberForm® is a porous carbon pre-form used in preparation of the well known PICA material Tran et al. [1996]. Inclusion of camphor into the list is conditioned with the relative simplicity in modeling the material thermal and chemical response and the low-enthalpy flow environment. In addition, camphor has been used as a simple test material for study of flow transition behavior by Stock and Ginoux [1973] and assessment of a heatshield shape change at flight relevant conditions by Rotondi et al. [2022]. In this work, the identified experimental data was extracted from the public literature and test cases that yet have been published. As it was found from the review, not a single test case contains an exhaustive set of data that would validate every aspect of the material physics. However, in the data collected, various aspects of the material behavior can be still validated, such as surface and in-depth temperature, amount of recession and a shape change. The identified experimental data for each case is accompanied with a characterized flow environment and simulated boundary conditions predicted by a Data-Parallel Line Relaxation (DPLR) code Wright et al. [1998]. In addition, material thermal response numerical simulations in each test case are performed with Kentucky Aerothermodynamics and Thermal Response System (KATS-MR) Zibitsker et al. [2022] providing a comparative study and a sanity check for the proposed validation data. Sample results from the performed numerical study are shown below. Figure 1 shows distribution of surface heat flux and pressure values on a hemi-cylinder model made of FiberForm® and tested in HyMETS arc-jet facility. The results are shown for the high pressure condition among the two tests. Flow simulation was performed with DPLR code on a quarter of original geometry. In the figure, the quarter shape was mirrored across zx and xy planes to show the complete distribution. Figure 2 shows the material response results for the high pressure case (7500 Pa), simulated with KATS-MR and a comparison to the experimental data for the surface temperature and shape shape. The simulation was performed on a 2-D slice, extracted in the xy plane at the middle of the sample. Figure 3 shows the material response simulation for the low pressure case (3500 Pa) and a comparison to the experimental data for surface temperature and shape change.

ablation↗

DOE OSTI2024

From phase decomposition to evaporation: A multi-modal evaluation of thermally degraded model lightweight high-entropy alloy

Lightweight high-entropy alloys (LHEAs) have the potential to replace conventional lightweight materials due to their superior mechanical properties and thermal stability. However, the thermal degradation pattern of LHEAs from phase decomposition to evaporation is not clear. We develop a new Al-based dual phase (FCC + HCP) LHEA—AlTi 0.45 CuZn, and further investigate its thermal degradation behavior for potential high-temperature structural applications. Using multimodal advanced characterization techniques such as differential scanning calorimetry/thermogravimetric analysis, scanning/transmission electron microscopy, and synchrotron X-ray diffraction/pair distribution function (XRD/PDF), a sequence of thermal degradation events beyond the thermal phase stability limit—between 250 and 360 °C—is observed. These include phase decomposition at ~360 °C, Zn evaporation at ~750 °C, and LHEA melting at 880 °C which results in ~25% cumulative weight loss. The formation of Al-Ti phase off the AlTi 0.45 CuZn matrix is due to the largest negative mixing enthalpy for Al-Ti than other binary pairs. Similarly, Zn evaporation from AlTi 0.45 CuZn LHEA is due to its faster evaporation rate than other constituent elements. The high-resolution synchrotron XRD and PDF results support the aforementioned observations; in addition, they reveal local atomic arrangements, local strain, and sluggish grain growth in the LHEA. Among other LHEAs of close density range (5.55 ≤ ρ ≤ 5.85 g/cc), the investigated LHEA exhibits outstanding nano-indentation hardness values due to the coupled grain size effect and HCP phase strengthening of the FCC matrix. As the search for LHEAs for lightweight applications grows, this study shows the potential use of AlTi 0.45 CuZn LHEA for structural applications even at elevated temperatures.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Infrared laser ablation of poly(vinylidene fluoride): The Loss of HF

The mechanism and kinetics of infrared laser ablation of poly(vinylidene fluoride) (PVDF) in vacuum have been investigated to understand how this can be used as a polymer processing technology. The laser heats the surface and initiates decomposition of macromolecules in the molten polymer layer which rapidly leads to production of an ablative flow of polymer decomposition products. There is only a short induction period of up to 2 s before ablation begins. After the initial period, the rate of mass loss increases linearly with the time of laser exposure. Spherical particles with an average diameter of about 100 nm are formed on the surface of the powder coating obtained by laser ablation. Here, the particle distribution ranges from 50 nm to 300 nm. The main gaseous product of ablation is HF from dehydrofluorination. A second important ablation process is the formation of gaseous carbenes generated during secondary reactions. Proposed ablation reactions due to laser-induced thermal dehydrofluorination occur in two stages. In the first stage, a double bond appears in PVDF due to direct loss of HF. Subsequent detachment of HF leads to the appearance of both triple bonds and cumulene bonds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Strong Effect of B-Site Substitution on the Reactivity of Layered Perovskite Oxides Probed via Isopropanol Conversion

Perovskite oxides have exhibited promising catalytic performance in photocatalysis, electrocatalysis, and thermocatalysis, and the performance can be potentially enhanced by tuning their flexible electronic and crystal structure. The B cations play essential roles in altering the inherent electronic structure and catalytic activity of these perovskite and related layered perovskite oxides. In this work, we establish the relationship of composition (electronic structure) and activity/selectivity of layered perovskites for pure and B-site-substituted Sr 2 Sn 1–x Ru x O 4 (0 ≤ x ≤ 1). The isopropanol decomposition was chosen as the probe reaction because its divergent reaction pathways through either dehydration or dehydrogenation are sensitive to the solid-state properties of the metal oxide surface. Both parent layered perovskite oxides of Sr 2 SnO 4 and Sr 2 RuO 4 exhibited decent conversion (20%–30%) and selectivity (>80%) to acetone through dehydrogenation pathways over a temperature range of 280–320 °C under atmospheric pressure, while the substituted perovskites, even with 10 at. % substitution of Ru at the B-site showed remarkable enhancement for both activity and selectivity toward acetone. Further, by varying the dopant concentration linearly, both activity and selectivity showed a volcano-shaped dependency on the atomic concentration of the substituent. Overall, the Sr 2 Sn 0.3 Ru 0.7 O 4 had the best yield of acetone, which may be ascribed to the optimal eg filling state of the B site for appropriate B–O bond strength during oxygenate adsorption. The current research provides a guide to the rational design of perovskite oxide catalysts for efficient chemical transformation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1997

Chemical Characterization and Reactivity of Fuel-Oxidizer Reaction Product

Fuel-oxidizer reaction product (FORP), the product of incomplete reaction of monomethylhydrazine and nitrogen tetroxide propellants prepared under laboratory conditions and from firings of Shuttle Reaction Control System thrusters, has been characterized by chemical and thermal analysis. The composition of FORP is variable but falls within a limited range of compositions that depend on three factors: the fuel-oxidizer ratio at the time of formation; whether the composition of the post-formation atmosphere is reducing or oxidizing; and the reaction or post-reaction temperature. A typical composition contains methylhydrazinium nitrate, ammonium nitrate, methylammonium nitrate, and trace amounts of hydrazinium nitrate and 1,1-dimethylhydrazinium nitrate. Thermal decomposition reactions of the FORP compositions used in this study were unremarkable. Neither the various compositions of FORP, the pure major components of FORP, nor mixtures of FORP with propellant system corrosion products showed any unusual thermal activity when decomposed under laboratory conditions. Off-limit thruster operations were simulated by rapid mixing of liquid monomethylhydrazine and liquid nitrogen tetroxide in a confined space. These tests demonstrated that monomethylhydrazine, methylhydrazinium nitrate, ammonium nitrate, or Inconel corrosion products can induce a mixture of monomethylhydrazine and nitrogen tetroxide to produce component-damaging energies. Damaging events required FORP or metal salts to be present at the initial mixing of monomethylhydrazine and nitrogen tetroxide.

David, Dennis D.↗

DOE OSTI2016

Problematic projection to the in-sample subspace for a kernelized anomaly detector

We examine the properties and performance of kernelized anomaly detectors, with an emphasis on the Mahalanobis-distance-based kernel RX (KRX) algorithm. Although the detector generally performs well for high-bandwidth Gaussian kernels, it exhibits problematic (in some cases, catastrophic) performance for distances that are large compared to the bandwidth. By comparing KRX to two other anomaly detectors, we can trace the problem to a projection in feature space, which arises when a pseudoinverse is used on the covariance matrix in that feature space. Here, we show that a regularized variant of KRX overcomes this difficulty and achieves superior performance over a wide range of bandwidths.

58 GEOSCIENCES↗

DOE OSTI2022

A comprehensive experimental and kinetic modeling study of di-isobutylene isomers: Part 2

A wide variety of high temperature experimental data obtained in this study complement the data on the oxidation of the two di-isobutylene isomers presented in Part I and offers a basis for an extensive validation of the kinetic model developed in this study. Due to the increasing importance of unimolecular decomposition reactions in high-temperature combustion, we have investigated the di-isobutylene isomers in high dilution utilizing a pyrolysis microflow reactor and detected radical intermediates and stable products using vacuum ultraviolet (VUV) synchrotron radiation and photoelectron photoion coincidence (PEPICO) spectroscopy. Additional speciation data at oxidative conditions were also recorded utilizing a plug flow reactor at atmospheric pressure in the temperature range 725-1150 K at equivalence ratios of 1.0 and 3.0 and at residence times of 0.35 s and 0.22 s, respectively. Combustion products were analyzed using gas chromatography (GC) and mass spectrometry (MS). Ignition delay time measurements for di-isobutylene were performed at pressures of 15 and 30 bar at equivalence ratios of 0.5, 1.0, and 2.0 diluted in 'air' in the temperature range 900-1400 K using a high-pressure shock-tube facility. New measurements of the laminar burning velocities of di-isobutylene/air flames are also presented. The experiments were performed using the heat flux method at atmospheric pressure and initial temperatures of 298-358 K. Moreover, data consistency was assessed with the help of analysis of the temperature and pressure dependencies of laminar burning velocity measurements, which was interpreted using an empirical power-law expression. Electronic structure calculations were performed to compute the energy barriers to the formation of many of the product species formed. The predictions of the present mechanism were found to be in adequate agreement with the wide variety of experimental measurements performed.

09 BIOMASS FUELS↗

DOE OSTI2017

Phase stability, ordering tendencies, and magnetism in single-phase fcc Au-Fe nanoalloys

Bulk Au-Fe alloys separate into Au-based fcc and Fe-based bcc phases, but L1 0 and L1 2 orderings were reported in single-phase Au-Fe nanoparticles. Motivated by these observations, we study the structural and ordering energetics in this alloy by combining density functional theory (DFT) calculations with effective Hamiltonian techniques: a cluster expansion with structural filters, and the configuration-dependent lattice deformation model. The phase separation tendency in Au-Fe persists even if the fcc-bcc decomposition is suppressed. The relative stability of disordered bcc and fcc phases observed in nanoparticles is reproduced, but the fully ordered L1 0 AuFe, L1 2 Au 3 Fe, and L1 2 AuFe 3 structures are unstable in DFT. But, a tendency to form concentration waves at the corresponding [001] ordering vector is revealed in nearly-random alloys in a certain range of concentrations. Furthermore, this incipient ordering requires enrichment by Fe relative to the equiatomic composition, which may occur in the core of a nanoparticle due to the segregation of Au to the surface. Effects of magnetism on the chemical ordering are also discussed.

36 MATERIALS SCIENCE↗

DOE OSTI2014

A reduced-order modeling approach to represent subgrid-scale hydrological dynamics for land-surface simulations: application in a polygonal tundra landscape

Existing land surface models (LSMs) describe physical and biological processes that occur over a wide range of spatial and temporal scales. For example, biogeochemical and hydrological processes responsible for carbon (CO 2 , CH 4 ) exchanges with the atmosphere range from the molecular scale (pore-scale O 2 consumption) to tens of kilometers (vegetation distribution, river networks). Additionally, many processes within LSMs are nonlinearly coupled (e.g., methane production and soil moisture dynamics), and therefore simple linear upscaling techniques can result in large prediction error. In this paper we applied a reduced-order modeling (ROM) technique known as "proper orthogonal decomposition mapping method" that reconstructs temporally resolved fine-resolution solutions based on coarse-resolution solutions. We developed four different methods and applied them to four study sites in a polygonal tundra landscape near Barrow, Alaska. Coupled surface–subsurface isothermal simulations were performed for summer months (June–September) at fine (0.25 m) and coarse (8 m) horizontal resolutions. We used simulation results from three summer seasons (1998–2000) to build ROMs of the 4-D soil moisture field for the study sites individually (single-site) and aggregated (multi-site). The results indicate that the ROM produced a significant computational speedup (> 10 3 ) with very small relative approximation error (< 0.1%) for 2 validation years not used in training the ROM. We also demonstrate that our approach: (1) efficiently corrects for coarse-resolution model bias and (2) can be used for polygonal tundra sites not included in the training data set with relatively good accuracy (< 1.7% relative error), thereby allowing for the possibility of applying these ROMs across a much larger landscape. By coupling the ROMs constructed at different scales together hierarchically, this method has the potential to efficiently increase the resolution of land models for coupled climate simulations to spatial scales consistent with mechanistic physical process representation.

Pau, G. S. H.↗

NASA NTRS2005

Integrated Spectroscopic Studies of Anhydrous Sulfate Minerals

Sulfates have been identified in Martian soils and bedrock and are emerging as an important indicator for aqueous activity on Mars. Sulfate minerals can form in a variety of low-temperature (evaporitic; chemical-weathering) and high-temperature (volcanic/fumarolic; hydrothermal) environments and their formational environments can range from alkaline to acidic. Although sulfates generally form in the presence of water, not all sulfates are hydrous or contain water in their structures. Many of these anhydrous sulfates (Dana group 28; Strunz class 67A) are minerals that form as accompanying phases to the main minerals in ore deposits or as replacement deposits in sedimentary rocks. However, some form from thermal decomposition of OH or H2O-bearing sulfates, such as from the reaction [1]: jarosite = yavapaiite + Fe2O3 + H2O. Where known, the stability fields of these minerals all suggest that they would be stable under martian surface conditions [2]. Thus, anhydrous sulfate minerals may contribute to martian surface mineralogy, so they must be well-represented in spectral libraries used for interpretation of the Martian surface. We present here the preliminary results of an integrated study of emittance, reflectance, and Mossbauer spectroscopy of a suite of wel-lcharacterized anhydrous sulfates.

Lane, M. D.↗

NASA NTRS2009

Decomposition of the Mean Squared Error and NSE Performance Criteria: Implications for Improving Hydrological Modelling

The mean squared error (MSE) and the related normalization, the Nash-Sutcliffe efficiency (NSE), are the two criteria most widely used for calibration and evaluation of hydrological models with observed data. Here, we present a diagnostically interesting decomposition of NSE (and hence MSE), which facilitates analysis of the relative importance of its different components in the context of hydrological modelling, and show how model calibration problems can arise due to interactions among these components. The analysis is illustrated by calibrating a simple conceptual precipitation-runoff model to daily data for a number of Austrian basins having a broad range of hydro-meteorological characteristics. Evaluation of the results clearly demonstrates the problems that can be associated with any calibration based on the NSE (or MSE) criterion. While we propose and test an alternative criterion that can help to reduce model calibration problems, the primary purpose of this study is not to present an improved measure of model performance. Instead, we seek to show that there are systematic problems inherent with any optimization based on formulations related to the MSE. The analysis and results have implications to the manner in which we calibrate and evaluate environmental models; we discuss these and suggest possible ways forward that may move us towards an improved and diagnostically meaningful approach to model performance evaluation and identification.

Gupta, Hoshin V.↗

DOE OSTI2017

A new process sensitivity index to identify important system processes under process model and parametric uncertainty

Hydrological models are always composed of multiple components that represent processes key to intended model applications. When a process can be simulated by multiple conceptual-mathematical models (process models), model uncertainty in representing the process arises. While global sensitivity analysis methods have been widely used for identifying important processes in hydrologic modeling, the existing methods consider only parametric uncertainty but ignore the model uncertainty for process representation. To address this problem, this study develops a new method to probe multimodel process sensitivity by integrating the model averaging methods into the framework of variance-based global sensitivity analysis, given that the model averaging methods quantify both parametric and model uncertainty. A new process sensitivity index is derived as a metric of relative process importance, and the index includes variance in model outputs caused by uncertainty in both process models and model parameters. For demonstration, the new index is used to evaluate the processes of recharge and geology in a synthetic study of groundwater reactive transport modeling. The recharge process is simulated by two models that converting precipitation to recharge, and the geology process is also simulated by two models of different parameterizations of hydraulic conductivity; each process model has its own random parameters. The new process sensitivity index is mathematically general, and can be applied to a wide range of problems in hydrology and beyond.

Dai, Heng↗

DOE OSTI2022

Thermodynamic re-modelling of the Cu–Nb–Sn system: Integrating the nausite phase

Currently available Cu–Nb–Sn phase diagrams lack the recently discovered nausite phase (Cu,Nb)Sn 2 , which is an important intermediate in the course of thermal processing of superconducting Nb 3 Sn wires. Processing decisively determines the resulting microstructure of Nb 3 Sn and, thus, its superconducting properties. Lack of suitable and complete phase diagrams, however, obstructs rational design of such thermal processing procedures. To close this gap and to obtain valid knowledge of homogeneity and stability range of nausite, various Cu–Nb–Sn samples, which are heat-treated between 300 °C and 500 °C, are investigated. By means of energy-dispersive X-ray spectroscopy (EDX), a temperature-dependent homogeneity range of nausite is observed, which covers average mole fractions of Cu between 0.09 and 0.15. This is correlated with a change in the mean atomic volume and can be seen in the lattice parameters determined by X-ray diffraction (XRD). Additionally performed first-principles calculations on different CuSn 2 and NbSn 2 model structures confirm this trend. Furthermore, the peritectic decomposition of nausite to NbSn 2 and liquid at 586 °C is determined by means of in situ XRD and differential scanning calorimetry (DSC). By using the CALPHAD (CALculation of PHase Diagrams) approach, all these findings are used to extend a previous thermodynamic description of the Cu–Nb–Sn system by including the nausite as an additional phase. Finally, with this noteworthy integration, the updated modelling of the Cu–Nb–Sn system can be used for optimizing the multistage heat-treatment steps during processing superconducting Nb 3 Sn wires.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Weighted Composition Operators for Learning Nonlinear Dynamics

Operator theoretic methods in dynamical system have been dominated by the use of Koopman operators and their continuous time counterparts, such as Koopman Generators and Liouville Operators. The advantage gained from their use primarily stems from the ability to extract subspaces and eigenfunctions within a space of observables that are invariant with respect to the Koopman operator over that space. When this occurs, a dynamic mode decomposition of the systems state provides a linear model for the dynamical system. Not all Koopman operators have eigenfunctions that may be exploited in this manner. However, the framework can still be leveraged for approximations using other operators. In this setting, we present a different operator for the study of dynamical systems, the weighted composition operator. These operators are compact for a wide range of dynamics and spaces, and through their interactions with occupation kernels and vector valued kernels, they admit an estimation of the underlying dynamics. Here, this manuscript presents a new algorithm for the data driven study of dynamical systems from data, and also provides two numerical experiments where convergence is achieved as a proof of concept.

97 MATHEMATICS AND COMPUTING↗