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Computer implemented empirical mode decomposition method apparatus, and article of manufacture utilizing curvature extrema

A computer implemented physical signal analysis method is includes two essential steps and the associated presentation techniques of the results. All the steps exist only in a computer: there are no analytic expressions resulting from the method. The first step is a computer implemented Empirical Mode Decomposition to extract a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals based on local extrema and curvature extrema. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform. The final result is the Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum.

Huang, Norden Eh

Empirical mode decomposition apparatus, method and article of manufacture for analyzing biological signals and performing curve fitting

A computer implemented physical signal analysis method includes four basic steps and the associated presentation techniques of the results. The first step is a computer implemented Empirical Mode Decomposition that extracts a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform which produces a Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum. The third step filters the physical signal by combining a subset of the IMFs. In the fourth step, a curve may be fitted to the filtered signal which may not have been possible with the original, unfiltered signal.

Huang, Norden E.

Combustion of Organic Molecules by the Thermal Decomposition of Perchlorate Salts: Implications for Organics at the Mars Phoenix Scout Landing Site

The Mars 2007 Phoenix Scout Mission successfully landed on May 25, 2008 and operated on the northern plains of Mars for 150 sols. The primary mission objective was to study the history of water and evaluate the potential for past and present habitability in Martian arctic ice-rich soil [1]. Phoenix landed near 68 N latitude on polygonal terrain created by ice layers that are a few centimeters under loose soil materials. The Phoenix Mission is assessing the potential for habitability by searching for organic molecules in the ice or icy soils at the landing site. Organic molecules are necessary building blocks for life, although their presence in the ice or soil does not indicate life itself. Phoenix searched for organic molecules by heating soil/ice samples in the Thermal and Evolved-Gas Analyzer (TEGA, [2]). TEGA consists of 8 differential scanning calorimeter (DSC) ovens integrated with a magnetic-sector mass spectrometer with a mass range of 2-140 daltons [2]. Endothermic and exothermic reactions are recorded by the TEGA DSC as samples are heated from ambient to ~1000 C. Evolved gases, including any organic molecules and their fragments, are simultaneously measured by the mass spectrometer during heating. Phoenix TEGA data are still under analysis; however, no organic fragments have been identified to date in the evolved gas analysis (EGA). The MECA Wet Chemistry Lab (WCL) discovered a perchlorate salt in the Phoenix soils and a mass 32 peak evolved between 325 and 625 C for one surface sample dubbed Baby Bear [3]. The mass 32 peak is attributed to evolved O2 generated during the thermal decomposition of the perchlorate salt. Perchlorates are very strong oxidizers when heated, so it is possible that organic fragments evolved in the temperature range of 300-600 C were combusted by the O2 released during the thermal decomposition of the perchlorate salt. The byproduct of the combustion of organic molecules is CO2. There is a prominent release of CO2 between 200-600 C for several of the Phoenix soils analyzed by TEGA. This low temperature release of CO2 might be any combination of 1) desorption of adsorbed CO2, 2) thermal decomposition of Fe- and Mg-carbonates, and 3) combustion of organic molecules [2].

Ming, D.W.

Thermal Decomposition of an Impure (Roxbury) Siderite: Relevance to the Presence of Chemically Pure Magnetite Crystals in ALH84001 Carbonate Disks

The question of the origin of nanophase magnetite in Martian meteorite ALH84001 has been widely debated for nearly a decade. Golden et al. have reported producing nearly chemically pure magnetite from thermal decomposition of chemically impure siderite [(Fe, Mg, Mn)CO3]. This claim is significant for three reasons: first, it has been argued that chemically pure magnetite present in the carbonate disks in Martian meteorite ALH84001 could have formed by the thermal decomposition of the impure carbonate matrix in which they are embedded; second, the chemical purity of magnetite has been previously used to identify biogenic magnetite; and, third, previous studies of thermal decomposition of impure (Mg,Ca,Mn)-siderites, which have been investigated under a wide variety of conditions by numerous researchers, invariably yields a mixed metal oxide phase as the product and not chemically pure magnetite. The explanation for this observation is that these siderites all possess the same crystallographic structure (Calcite; R3c) so solid solutions between these carbonates are readily formed and can be viewed on an atomic scale as two chemically different but structurally similar lattices.

McKay, D.S.

Isothermal Decomposition of Hydrogen Peroxide Dihydrate

We present a new method of growing pure solid hydrogen peroxide in an ultra high vacuum environment and apply it to determine thermal stability of the dihydrate compound that forms when water and hydrogen peroxide are mixed at low temperatures. Using infrared spectroscopy and thermogravimetric analysis, we quantified the isothermal decomposition of the metastable dihydrate at 151.6 K. This decomposition occurs by fractional distillation through the preferential sublimation of water, which leads to the formation of pure hydrogen peroxide. The results imply that in an astronomical environment where condensed mixtures of H2O2 and H2O are shielded from radiolytic decomposition and warmed to temperatures where sublimation is significant, highly concentrated or even pure hydrogen peroxide may form.

Loeffler, M. J.

A Structural Model Decomposition Framework for Systems Health Management

Systems health management (SHM) is an important set of technologies aimed at increasing system safety and reliability by detecting, isolating, and identifying faults; and predicting when the system reaches end of life (EOL), so that appropriate fault mitigation and recovery actions can be taken. Model-based SHM approaches typically make use of global, monolithic system models for online analysis, which results in a loss of scalability and efficiency for large-scale systems. Improvement in scalability and efficiency can be achieved by decomposing the system model into smaller local submodels and operating on these submodels instead. In this paper, the global system model is analyzed offline and structurally decomposed into local submodels. We define a common model decomposition framework for extracting submodels from the global model. This framework is then used to develop algorithms for solving model decomposition problems for the design of three separate SHM technologies, namely, estimation (which is useful for fault detection and identification), fault isolation, and EOL prediction. We solve these model decomposition problems using a three-tank system as a case study.

Roychoudhury, Indranil

Synthesis, Decomposition and Characterization of Fe and Ni Sulfides and Fe and CO Nanoparticles for Aerospace Applications

We describe several related studies where simple iron, nickel, and cobalt complexes were prepared, decomposed, and characterized for aeronautics (Fischer-Tropsch catalysts) and space (high-fidelity lunar regolith simulant additives) applications. We describe the synthesis and decomposition of several new nickel dithiocarbamate complexes. Decomposition resulted in a somewhat complicated product mix with NiS predominating. The thermogravimetric analysis of fifteen tris(diorganodithiocarbamato)iron(III) has been investigated. Each undergoes substantial mass loss upon pyrolysis in a nitrogen atmosphere between 195 and 370 C, with major mass losses occurring between 279 and 324 C. Steric repulsion between organic substituents generally decreased the decomposition temperature. The product of the pyrolysis was not well defined, but usually consistent with being either FeS or Fe2S3 or a combination of these. Iron nanoparticles were grown in a silica matrix with a long-term goal of introducing native iron into a commercial lunar dust simulant in order to more closely simulate actual lunar regolith. This was also one goal of the iron and nickel sulfide studies. Finally, cobalt nanoparticle synthesis is being studied in order to develop alternatives to crude processing of cobalt salts with ceramic supports for Fischer-Tropsch synthesis.

Cowen, Jonathan E.

The Relative Importance of Methanogenesis in the Decomposition of Organic Matter in Northern Peatlands

Using an isotope-mass balance approach and assuming the equimolar production of CO2 and CH4 from methanogenesis (e.g., anaerobic decomposition of cellulose), we calculate that the proportion of total CO2 production from methanogenesis varies from 37 to 83% across a variety of northern peatlands. In a relative sense, methanogenesis was a more important pathway for decomposition in bogs (80 +/- 13% of CO2 production) than in fens (64 +/- 5.7% of CO2 production), but because fens contain more labile substrates they may support higher CH4 production overall. The concentration of CO2 produced from methanogenesis (CO2-meth) can be considered equivalent to CH4 concentration before loss due to ebullition, plant-mediated transport, or diffusion. Bogs produced slightly less CO2-meth than fens (2.9 +/- 1.3 and 3.7 +/- 1.4 mmol/L, respectively). Comparing the quantity of CH4 present to CO2-meth, fens lost slightly more CH4 than bogs (89 +/- 2.8% and 82 +/- 5.3%, respectively) likely due to the presence of vascular plant roots. In collapsed permafrost wetlands, bog moats produced half the amount of CO2-meth (0.8 +/- 0.2mmol/L) relative to midbogs (1.6 +/- 0.6 mmol/L) and methanogenesis was less important (42 +/- 6.6% of total CO2 production relative to 55 +/- 8.1%).We hypothesize that the lower methane production potential in collapsed permafrost wetlands occurs because recently thawed organic substrates are being first exposed to the initial phases of anaerobic decomposition following collapse and flooding. Bog moats lost a comparable amount of CH4 as midbogs (63 +/- 7.0% and 64 +/- 9.3%).

bacteria

Applicability of Spectral Decomposition by Varimax-Rotated, Principal Component Analysis to the Surface Biology and Geology (SBG) VNIR Mission Concept

Cyanobacterial and Harmful Algal Blooms (CyanoHABs) are a growing concern in coastal and inland waters. But, spectral interference from multiple constituents in optically complex waters can hamper application of remote sensing using traditional image processing methods. The Kent State University (KSU) spectral decomposition method can be applied to multispectral and hyperspectral remote sensing images (e.g. HICO and the NASA Glenn HSI2) to partition and identify signals related to cyanobacteria, algae, pigment degradation products and suspended sediment in each pixel. Fundamental to the use of remote sensing data is the ability to extract independent signals from correlated hyperspectral VNIR data cubes. The Kent State University varimax-rotated, principal component analysis method (VPCA) is important to integrate into the SBG VNIR mission concept because it provides greater specificity, a software-based SNR boost relative to hardware performance, and can assist with Cal/Val, Modeling and Applications. We present examples of the hyperspectral application of the KSU VPCA method with relevance to SBG. The information extracted by VPCA can be validated spectrally or spatially with laboratory and/or in situ sensors, which capture spatial or time series of information at discrete points within remote sensing images. Comparisons show hyperspectral sensors extract more components than multispectral ones, but more independent information can be extracted from multispectral sensors by VPCA than traditional band ratio approaches. The spectral decomposition method is capable of enhancing the signal to noise ratio (SNR) of the NASA Glenn, second-generation hyperspectral imager by a factor of 7x to 20x, with a spectral reproducibility of ±3%. The spectral decomposition method, when compared against existing remote sensing monitoring methods exhibits both greater specificity and a lower detection limit. The method has been validated with multispectral images in Lake Erie to quantify the Microcystis CyanoHAB and from the Indian River Lagoon, Florida to quantify the Brown Tide resulting from A. lagunesnsis. Field operations in the Western Basin of Lake Erie were conducted using a bbe Fluoroprobe to collect vertical profiles and horizontal tows along a transect from the Toledo to the Detroit Lighthouse during coincident satellite overpasses. Extraction of pixel values from the MODIS Aqua sensor yields agreement between in situ field and lab-based measures of cyanobacterial, cryptophyte, diatoms and green algae, suspended sediment and pigment degradation products with R2>0.8.

hyperspectral

A Phenomenon-Based Decomposition of Model-Based Estimates of Boreal Winter ENSO Variability

Climate models are now routinely being used to simulate and predict climate variability on time scales ranging from sub-seasonal to seasonal and longer. As such, there are now long histories of such simulations and predictions spanning multiple decades and multiple ensemble members, both of which are crucial for separating climate signal from climate noise. A key focus of such runs has been the El Niño-Southern Oscillation (ENSO), spurred by recent improvements in our ability to predict such events, though questions remain as to how well climate models do beyond simply always predicting the “canonical” atmospheric response to an ENSO event—something simple statistical models already do reasonably well. This is a critical issue that needs addressing, given the importance of event-to-event differences for predicting regional impacts of ENSO teleconnections, and the need to justify the expense of running sophisticated climate models. Unfortunately, current diagnostic tools are not well suited for quantifying the different sources of variability associated with specific phenomena such as ENSO. More generally, while much effort has focused on addressing model bias, less has been done to address errors in second moment statistics—an issue whose importance is gaining increased attention particularly as we build climate prediction systems capable of taking advantage of forecasts of opportunity—a capability that requires reliable estimates of forecast uncertainty. In this report, we outline a phenomenon-based statistical decomposition of climate variance(in essence a detailed variance budget)that is specifically tailored to address the above questions by separating the variability (both the signal and noise) into that tied to the long-term average impact of a particular phenomenon(the composite mean) and the event-to-event(E2E) variability about the composite mean. In addition, we provide related decompositions of the correlations that allow us to quantify how much of the agreement with observations (the skill) comes from the composite mean as opposed to from the E2Evariability. As an example, we present the results of such a decomposition for ENSO based on simulations with the GEOS atmospheric general circulation model (AGCM), with a focus on the monthly mean impacts over North America during boreal winter(December –March). Here we take advantage of existing GEOS AGCM simulations that were produced as companion simulations to MERRA-2for the period 1980-2016. Comparisons are made throughout with MERRA-2.

ENSO

SNoGloDe: A Structured Nonlinear Global Decomposition Solver

Large-scale optimization problems often require decomposition strategies and customized algorithms to achieve optimal solutions within a reasonable time. Building on the work of Cao and Zavala (2019) for solving nonlinear two-stage stochastic programs to global optimality, we implement and extend their approach. We generalize to optimization problems reformulated with a block-angular constraint structure (e.g., temporal decomposition). Our framework, written in Python using Pyomo, is highly customizable and enables parallel execution of the decomposition. SNoGloDe allows tailored branching strategies, lower bounding problems, and candidate generators to leverage problem-specific knowledge. To demonstrate effectiveness, we compare SNoGloDe’s performance with Gurobi on a temporally decomposed produced water case study.

algorithms

SPRUCE FT-ICR MS, Bulk Chemistry, and Mass Loss from Litter Decomposition Study in Experimental Plots, Marcell Experimental Forest, Minnesota, 2015-2017

This dataset contains molecular, bulk chemical, and mass loss measurements from a litter decomposition study at the Spruce and Peatland Responses Under Changing Environments (SPRUCE) experimental site within the Marcell Experimental Forest in northern Minnesota, USA. This site is in a Sphagnum spp. ombrotrophic bog forest. Litterbags were deployed into the peat in September 2015 across three warming levels (+0, +4.5, and +9°C) under ambient and elevated carbon dioxide (CO₂ - +500 ppm) and retrieved after roughly 0.5, 1, and 2 years of field incubation (2015-09-23 to 2017-08-02). Litterbags containing six peatland litter types: black spruce needles (Picea mariana - SPL), spruce fine roots (SPR), Sphagnum angustifolium (ANG), Sphagnum magellanicum (MAG), Labrador tea leaves (Rhododendron groenlandicum - LTL), and Labrador tea roots (LTR). Molecular composition of water-soluble organic matter extracts was characterized using Fourier Transform Ion Cyclotron Resonance Mass Spectrometry (FT-ICR MS) at 9.4 Tesla, operated in negative ion mode with electrospray ionization, providing molecular formula assignments and compound-class distributions across the decomposition time series. Bulk chemical characterization included elemental analysis (percent carbon, nitrogen, and phosphorus) and Fourier Transform Infrared Spectroscopy (FTIR) to quantify functional group composition. Litter mass loss was tracked gravimetrically at each retrieval interval, expressed as percent mass remaining relative to initial dry mass for each litter type and treatment combination. These data are valuable for understanding how vegetation shifts driven by increased atmospheric CO2 and temperature in peatlands alter litter inputs and organic matter stabilization trajectories, with implications for projecting and modeling peatland carbon cycling. This dataset contains two data files in comma-separated value (.csv) format. Additional metadata are provided: two data dictionaries and a file-level metadata file in comma separate (.csv) format and a user guide in PDF (*.pdf) format.

decomposition

New Synthetic Route to 4,6‐Diamino‐5,7‐dinitro‐benzo‐furazan, Important Decomposition Product of 1,3,5‐Triamino‐2,4,6‐trinitrobenzene

The important 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) decomposition byproduct, 4,6-diamino-5,7-dinitro-benzo-furazan (F 1 ), was prepared in a four-step reaction sequence starting with commercially available materials through a key intermediate, 4,6-dichloro-5,7-dinitro-benzo-furazan. The introduction of azido to 4,6-dichloro-benzo-furazan, followed by nitration and amination gave F 1 in good yield. This new method showed a greatly improved yield and ease of purification than previous methods (the total yield was 30%–40% in seven steps). F 1 is a stable yellow solid with a melting point of 308.7°C and a thermal decomposing temperature of 310.3°C (differential scanning calorimetry at 10°C/min heating rate). The solid-state structure was solved by single-crystal X-ray analyses at low temperatures (100 K). The compound crystallizes in a P 2 1 c space group with the formula C 6 H 4 N 6 O 5 •H 2 O with 12 molecules of F 1 /H 2 O in the unit cell. This compound has eluded complete characterization for almost 50 years. With this information, more advanced decomposition models can be created to further improve critical safety margins in handling the energetic material, TATB.

decomposition

Graph-Based Modeling and Decomposition of Hierarchical Optimization Problems

We present a graph-theoretic modeling approach for hierarchical optimization that leverages the OptiGraph abstraction implemented in the Julia package Plasmo.jl. We show that the abstraction is flexible and can effectively capture complex hierarchical connectivity that arises from decision-making over multiple spatial and temporal scales (e.g., integration of planning, scheduling, and operations in manufacturing and infrastructures). We also show that the graph abstraction facilitates the conceptualization and implementation of decomposition and approximation schemes. Specifically, we propose a graph-based Benders decomposition (gBD) framework that enables the exploitation of hierarchical (nested) structures and that uses graph aggregation/partitioning procedures to discover such structures. In addition, we provide a Julia implementation of gBD, which we call PlasmoBenders.jl. We illustrate the capabilities using examples arising in the context of energy and power systems.

97 MATHEMATICS AND COMPUTING

Online randomized interpolative decomposition with a posteriori error estimator for temporal PDE data reduction

Traditional low-rank approximation is a powerful tool for compressing large data matrices that arise in simulations of partial differential equations (PDEs), but suffers from high computational cost and requires several passes over the PDE data. The compressed data may also lack interpretability thus making it difficult to identify feature patterns from the original data. Here, to address these issues, we present an online randomized algorithm to compute the interpolative decomposition (ID) of large-scale data matrices in situ. Compared to previous randomized IDs that used the QR decomposition to determine the column basis, we adopt a streaming ridge leverage score-based column subset selection algorithm that dynamically selects proper basis columns from the data and thus avoids an extra pass over the data to compute the coefficient matrix of the ID. In particular, we adopt a single-pass error estimator based on the non-adaptive Hutch++ algorithm to provide real-time error approximation for determining the best coefficients. As a result, our approach only needs a single pass over the original data and thus is suitable for large and high-dimensional matrices stored outside of core memory or generated in PDE simulations. A strategy to improve the accuracy of the reconstructed data gradient, when desired, within the ID framework is also presented. We provide numerical experiments on turbulent channel flow and ignition simulations, and on the NSTX Gas Puff Image dataset, comparing our algorithm with the offline ID algorithm to demonstrate its utility in real-world applications.

Column subset selection

Optimizing the design and operation of water networks: Two decomposition approaches

We consider the design and operation of water networks simultaneously. Water network problems can be divided into two categories: the design problem and the operation problem. The design problem involves determining the appropriate pipe sizing and placements of pump stations, while the operation problem involves scheduling pump stations over multiple time periods to account for changes in supply and demand. Our focus is on networks that involve water co-produced with oil and gas. While solving the optimization formulation for such networks, we found that obtaining a primal (feasible) solution is more challenging than obtaining dual bounds using off-the-shelf mixed-integer nonlinear programming solvers. Therefore, we propose two methods to obtain good primal solutions. One method involves a decomposition framework that utilizes a convex reformulation, while the other is based on time decomposition. To test our proposed methods, we conduct computational experiments on a network derived from the PARETO case study.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Local reduced-order modeling for electrostatic plasmas by physics-informed solution manifold decomposition

Despite advancements in high-performance computing and modern numerical algorithms, computational cost remains prohibitive for multi-query kinetic plasma simulations. Here, in this work, we develop data-driven reduced-order models (ROMs) for collisionless electrostatic plasma dynamics, based on the kinetic Vlasov-Poisson equation. Our ROM approach projects the equation onto a linear subspace defined by the proper orthogonal decomposition (POD) modes. We introduce an efficient tensorial method to update the nonlinear term using a precomputed third-order tensor. We capture multiscale behavior with a minimal number of POD modes by decomposing the solution manifold into multiple time windows and creating temporally local ROMs. We consider two strategies for decomposition: one based on the physical time and the other based on the electric field energy. Applied to the 1D1V Vlasov–Poisson simulations, that is, prescribed E-field, Landau damping, and two-stream instability, we demonstrate that our ROMs accurately capture the total energy of the system both for parametric and time extrapolation cases. The temporally local ROMs are more efficient and accurate than the single ROM. In addition, in the two-stream instability case, we show that the energy-windowing reduced-order model (EW-ROM) is more efficient and accurate than the time-windowing reduced-order model (TW-ROM). With the tensorial approach, EW-ROM solves the equation approximately 90 times faster than Eulerian simulations while maintaining a maximum relative error of 7.5% for the training data and 11% for the testing data.

Electrostatic plasmas

Multi-Scale Modeling for Plasma-Enhanced Ammonia Decomposition over Carbides and Nitrides

Ammonia is a carbon-free hydrogen carrier, but its decomposition typically requires high temperatures over costly Ru-based catalysts due to the large barrier for N≡N bond formation. We develop a multiscale framework combining density functional theory, zero-dimensional plasma kinetics, and microkinetic modeling to elucidate how non-thermal plasma (NTP) enables low-temperature NH 3 decomposition over Co-based carbides and nitrides, benchmarked against Ru and Co. Under thermal conditions, all catalysts are limited by N≡N bond formation, with Co 3 C(001) most active owing to its negatively charged surface, strong N* binding, and low activation barriers of N≡N bond formation. Plasma-induced vibrational excitation of NH 3 and its reactive radicals promotes a radical-driven •NH 2 –N* coupling pathway that dominates on Co 3 C(001) and Co 3 N(001), shifting the rate-limiting step to NH 3 (v1) dissociation, increasing turnover frequencies by up to 6 orders of magnitude, and reducing the temperature needed to reach a turnover frequency of 5 s –1 from >680 °C (Ru and Co under thermal condition) to 267 °C (Co 3 C) and 415 °C (Co 3 N). These results identify Co-based carbides and nitrides as promising plasma-active catalysts for energy-efficient hydrogen production from ammonia.

ammonia decomposition