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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

Neutron Assay System for Confinement Vessel Disposition

Waste will be removed from confinement vessels remaining from 1970s-era experiments. Los Alamos has 9+ spherical confinement vessels remaining from experiments. Each vessel contains {approx} 500 lbs of radioactive debris such as actinide metals and oxides, metals, powdered silica, graphite, and wires and hardware. In order to dispose of the vessels, debris and contamination must be removed. Neutron assay system was designed to assay vessels before and after cleanout. System requirements are: (1) Modular and moveable; (2) Capable of detecting {approx}100g {sup 239}Pu equivalent in a 2-inch thick steel sphere with 6 foot diameter; and (3) Capable of safeguards-quality assays. Initial design parameters arethe use of 4-atm {sup 3}He tubes with length of 6 feet, and {sup 3}He tubes embedded in polyethelene for moderation. This paper describes the calibration of the Confinement Vessel Assay System (CVAS) and quantification of its uncertainties. Assay uncertainty depends on five factors: (1) Statistical uncertainty in the assay measurement; (2) Statistical uncertainty in the background measurement; (3) Statistical uncertainty in the isotopics determination - This should be much smaller than the other uncertainties; (4) Systematic uncertainty due to position bias; and (5) Systematic uncertainty due to fluctuations in cosmic ray spallation. This one can be virtually eliminated by performing the background measurement with an empty vessel - but that may not be possible. We used modeling and experiments to quantify the systematic uncertainties. The calibration assumes a uniform distribution of material, but reality will be different. MCNPX modeling was used to quantify the positional bias. The model was benchmarked to build confidence in its results. Material at top of vessel is 44% greater than amount assayed, according to singles. Material near 19-tube detector is 38% less than amount assayed, according to singles. Cosmic ray spallation contributes significantly to the background. Comparing rates with and without a vessel showed that spallation adds an average of 27.27 singles/s and 5.45 doubles/s to background. Errors in the background rates were estimated at 20%.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Clinical knowledge extraction via sparse embedding regression (KESER) with multi-center large scale electronic health record data

The increasing availability of electronic health record (EHR) systems has created enormous potential for translational research. However, it is difficult to know all the relevant codes related to a phenotype due to the large number of codes available. Traditional data mining approaches often require the use of patient-level data, which hinders the ability to share data across institutions. In this project, we demonstrate that multi-center large-scale code embeddings can be used to efficiently identify relevant features related to a disease of interest. We constructed large-scale code embeddings for a wide range of codified concepts from EHRs from two large medical centers. We developed knowledge extraction via sparse embedding regression (KESER) for feature selection and integrative network analysis. We evaluated the quality of the code embeddings and assessed the performance of KESER in feature selection for eight diseases. Besides, we developed an integrated clinical knowledge map combining embedding data from both institutions. The features selected by KESER were comprehensive compared to lists of codified data generated by domain experts. Features identified via KESER resulted in comparable performance to those built upon features selected manually or with patient-level data. The knowledge map created using an integrative analysis identified disease-disease and disease-drug pairs more accurately compared to those identified using single institution data. Analysis of code embeddings via KESER can effectively reveal clinical knowledge and infer relatedness among codified concepts. KESER bypasses the need for patient-level data in individual analyses providing a significant advance in enabling multi-center studies using EHR data.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2016

Comparative Performance Analysis of Coarse Solvers for Algebraic Multigrid on Multicore and Manycore Architectures

In this paper, we study the performance of a two-level algebraic-multigrid algorithm, with a focus on the impact of the coarse-grid solver on performance. We consider two algorithms for solving the coarse-space systems: the preconditioned conjugate gradient method and a new robust HSS-embedded low-rank sparse-factorization algorithm. Our test data comes from the SPE Comparative Solution Project for oil-reservoir simulations. We contrast the performance of our code on one 12-core socket of a Cray XC30 machine with performance on a 60-core Intel Xeon Phi coprocessor. To obtain top performance, we optimized the code to take full advantage of fine-grained parallelism and made it thread-friendly for high thread count. We also developed a bounds-and-bottlenecks performance model of the solver which we used to guide us through the optimization effort, and also carried out performance tuning in the solver’s large parameter space. Finally, as a result, significant speedups were obtained on both machines.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Structural changes and variability of the ITCZ induced by radiation–cloud–convection–circulation interactions: inferences from the Goddard Multi-scale Modeling Framework (GMMF) experiments

In this paper, we have investigated the impact of radiation–cloud–convection–circulation interaction (RC3I) on structural changes and variability of the Inter-tropical Convergence Zone (ITCZ) using the Goddard Multi-scale Modeling Framework, where cloud processes are super-parameterized, i.e., explicitly resolved with 2-D cloud resolving models embedded in each coarse grid of the host Goddard Earth Observing System-Version 5 global climate model. Experiments have been conducted under prescribed sea surface temperature conditions for 10 years (2007–2016), with and without cloud radiation feedback in the atmosphere, respectively. Diagnostic analyses separately for January and July show that RC3I leads to an enhanced and expanded Hadley Circulation characterized by (1) a quasi-uniform warming and moistening of the tropical atmosphere and a sharpening of the ITCZ with enhanced deep convection, more intense precipitation and higher clouds, (2) extended drying of the tropical marginal convective zones, and extratropical mid- to lower troposphere, and (3) a cooling of the polar regions, with increased baroclinicity and midlatitude storm track activities. Computations based on the zonal mean thermodynamic energy balance equation show that the radiative warming and cooling are strongly balanced by local adiabatic processes associated with changes in large-scale vertical motions, as well as horizontal atmospheric heat transport. In the tropics, enhanced short-wave absorption and longwave water vapor greenhouse effects by high clouds play key roles in providing strong positive feedback to the tropospheric warming. In the extratropics, increased atmospheric heat transport associated with changes in the Hadley circulation is balanced by strong longwave cooling above, and warming below due to increased high clouds. We also find a strong positive correlation between daily and pentad heavy rain in the ITCZ core, and expansion of the drier zones coupled to a contraction of the highly convective zones in the ITCZ, indicating a strong tendency RC3I-induced convective aggregation in tropical clouds i.e., wet-regions-get-wetter and contracted, and dry-areas-get-drier and expanded.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Electrospun Conjugated Polymer/Fullerene Hybrid Fibers: Photoactive Blends, Conductivity through Tunneling-AFM, Light Scattering, and Perspective for Their Use in Bulk-Heterojunction Organic Solar Cells

Hybrid conjugated polymer/fullerene filaments based on MEH-PPV/PVP/PCBM were prepared by electrospinning, and their properties were assessed by scanning electron, atomic and lateral-force, tunneling, and confocal microscopies, as well as by attenuated-total-reflection Fourier transform infrared spectroscopy, photoluminescence quantum yield, and spatially resolved fluorescence. Highlighted features include the ribbon shape of the realized fibers and the persistence of a network serving as a template for heterogeneous active layers in solar cell devices. A set of favorable characteristics is evidenced in this way in terms of homogeneous charge-transport behavior and formation of effective interfaces for diffusion and dissociation of photogenerated excitons. The interaction of the organic filaments with light, exhibiting specific light-scattering properties of the nanofibrous mat, might also contribute to spreading incident radiation across the active layers, thus potentially enhancing photovoltaic performance. Finally, this method might be applied to other electron donor–electron acceptor material systems for the fabrication of solar cell devices enhanced by nanofibrillar morphologies embedding conjugated polymers and fullerene compounds.

14 SOLAR ENERGY↗
DOE OSTI2018

Highly Stable, Ultrasmall Polymer-Grafted Nanobins (usPGNs) with Stimuli-Responsive Capability

In this work, highly stable and stimuli/pH-responsive ultrasmall polymer-grafted nanobins (usPGNs) have been developed by grafting a small amount (10 mol %) of short (4.3 kDa) cholesterol-terminated poly(acrylic acid) (Chol-PAA) into an ultrasmall unilamellar vesicle (uSUV). The usPGNs are stable against fusion and aggregation over several weeks, exhibiting over 10-fold enhanced cargo retention in biologically relevant media at pH 7.4 in comparison with the parent uSUV template. Coarse-grained molecular dynamics (CGMD) simulations confirm that the presence of the cholesterol moiety can greatly stabilize the lipid bilayer. They also show extended PAA chain conformations that can be interpreted as causing repulsion between colloidal particles, thus stabilizing them against fusion. Notably, CGMD predicted a clustering of the Chol-PAA chains on the lipid bilayer under acidic conditions due to intra- and interchain hydrogen bonding, leading to the destabilization of local membrane areas. This explains the experimental observation that usPGNs can be triggered to release a significant amount of cargo upon acidification to pH 5. These developments put the lipid-bilayer-embedded Chol-PAA in stark contrast with traditional poly(acrylic acid) systems where the molar mass (M n ) of the polymer chains must exceed 16.5 kDa to achieve stimuli-responsive changes in conformation. They also distinguish the small usPGNs from the much-larger polymer-caged nanobin platform where the Chol-PAA chains must be covalently cross-linked to engender stimuli-responsive behaviors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

GaAs/AlGaAs quantum wells with indirect-gap AlGaAs barriers for solar cell applications

We have fabricated GaAs/AlGaAs quantum well (QW) solar cells in which 3 nm-thick QWs and indirect-gap Al{sub 0.78}Ga{sub 0.22}As barriers are embedded, and we studied extraction processes of photogenerated carriers in this QW system. The photocurrent under 700 nm light illumination at voltages close to the open-circuit voltage shows only a small reduction, indicating that the carrier recombination inside QWs is largely suppressed. We attribute this result to an efficient extraction of electrons from the QWs through the X-valley of AlGaAs. The insertion of QWs is shown to be effective in extending the absorption wavelengths and in enhancing the photocurrent. The use of indirect-gap materials as barriers is found to enhance carrier extraction processes, and result in an improved performance of QW solar cells.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

On energetic prerequisites of attracting electrons

The internal reorganization energy and the zero-point vibrational energy (ZPE) of fractionally charged molecules embedded in molecular materials are discussed. The theory for isolated open quantum systems is taken as the starting point. It is shown that for isolated molecules the internal reorganization-energy function and its slope, i.e., the chemical potential of an open molecular system are monotonically decreasing functions with respect to increasing amount of negative excess charge (q) in the range of q = [0, 1]. Calculations of the ZPE for fractionally charged molecules show that the ZPE may have a minimum for fractional occupation. The calculations show that the internal reorganization energy and changes in the ZPE are of the same order of magnitude with different behavior as a function of the excess charge. The sum of the contributions might favor molecules with fractional occupation of the molecular units and partial delocalization of the excess electrons in solid-state materials also when considering Coulomb repulsion between the excess electrons. The fractional electrons are then coherently distributed on many molecules of the solid-state material forming a condensate of attracting electrons, which is crucial for the superconducting state.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Communication: Embedded fragment stochastic density functional theory

We develop a method in which the electronic densities of small fragments determined by Kohn-Sham density functional theory (DFT) are embedded using stochastic DFT to form the exact density of the full system. The new method preserves the scaling and the simplicity of the stochastic DFT but cures the slow convergence that occurs when weakly coupled subsystems are treated. It overcomes the spurious charge fluctuations that impair the applications of the original stochastic DFT approach. We demonstrate the new approach on a fullerene dimer and on clusters of water molecules and show that the density of states and the total energy can be accurately described with a relatively small number of stochastic orbitals.

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

Effect of surface free energies on the heterogeneous nucleation of water droplet: A molecular dynamics simulation approach

Heterogeneous nucleation of water droplet on surfaces with different solid-liquid interaction intensities is investigated by molecular dynamics simulation. The interaction potentials between surface atoms and vapor molecules are adjusted to obtain various surface free energies, and the nucleation process and wetting state of nuclei on surfaces are investigated. The results indicate that near-constant contact angles are already established for nano-scale nuclei on various surfaces, with the contact angle decreasing with solid-liquid interaction intensities linearly. Meanwhile, noticeable fluctuation of vapor-liquid interfaces can be observed for the nuclei that deposited on surfaces, which is caused by the asymmetric forces from vapor molecules. The formation and growth rate of nuclei are increasing with the solid-liquid interaction intensities. For low energy surface, the attraction of surface atoms to water molecules is comparably weak, and the pre-existing clusters can depart from the surface and enter into the bulk vapor phase. The distribution of clusters within the bulk vapor phase becomes competitive as compared with that absorbed on surface. For moderate energy surfaces, heterogeneous nucleation predominates and the formation of clusters within bulk vapor phase is suppressed. The effect of high energy particles that embedded in low energy surface is also discussed under the same simulation system. The nucleation preferably initiates on the high energy particles, and the clusters that formed on the heterogeneous particles are trapped around their original positions instead of migrating around as that observed on smooth surfaces. This feature makes it possible for the heterogeneous particles to act as fixed nucleation sites, and simulation results also suggest that the number of nuclei increases monotonously with the number of high energy particles. The growth of nuclei on high energy particles can be divided into three sub-stages, beginning with the formation of a wet-spot, increase of contact angle with near-constant contact line, and finally growth with constant contact angle. The growth rate of nuclei also increases with the size of high energy particles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Low-lying excited states by constrained DFT

Exploiting the machinery of Constrained Density Functional Theory (CDFT), we propose a variational method for calculating low-lying excited states of molecular systems. We dub this method eXcited CDFT (XCDFT). Excited states are obtained by self-consistently constraining a user-defined population of electrons, N c , in the virtual space of a reference set of occupied orbitals. By imposing this population to be N c = 1.0, we computed the first excited state of 15 molecules from a test set. Our results show that XCDFT achieves an accuracy in the predicted excitation energy only slightly worse than linear-response time-dependent DFT (TDDFT), but without incurring into problems of variational collapse typical of the more commonly adopted ΔSCF method. In addition, we selected a few challenging processes to test the limits of applicability of XCDFT. We find that in contrast to TDDFT, XCDFT is capable of reproducing energy surfaces featuring conical intersections (azobenzene and H3) with correct topology and correct overall energetics also away from the intersection. Venturing to condensed-phase systems, XCDFT reproduces the TDDFT solvatochromic shift of benzaldehyde when it is embedded by a cluster of water molecules. Finally, we find XCDFT to be a competitive method among single-reference methods for computations of excited states in terms of time to solution, rate of convergence, and accuracy of the result.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Three-dimensional prominence-hosting magnetic configurations: Creating a helical magnetic flux rope

The magnetic configuration hosting prominences and their surrounding coronal structure is a key research topic in solar physics. Recent theoretical and observational studies strongly suggest that a helical magnetic flux rope is an essential ingredient to fulfill most of the theoretical and observational requirements for hosting prominences. To understand flux rope formation details and obtain magnetic configurations suitable for future prominence formation studies, we here report on three-dimensional isothermal magnetohydrodynamic simulations including finite gas pressure and gravity. Starting from a magnetohydrostatic corona with a linear force-free bipolar magnetic field, we follow its evolution when introducing vortex flows around the main polarities and converging flows toward the polarity inversion line near the bottom of the corona. The converging flows bring the feet of different loops together at the polarity inversion line, where magnetic reconnection and flux cancellation happen. Inflow and outflow signatures of the magnetic reconnection process are identified, and thereby the newly formed helical loops wind around preexisting ones so that a complete flux rope grows and ascends. When a macroscopic flux rope is formed, we switch off the driving flows and find that the system relaxes to a stable state containing a helical magnetic flux rope embedded in an overlying arcade structure. A major part of the formed flux rope is threaded by dipped field lines that can stably support prominence matter, while the total mass of the flux rope is in the order of 4-5× 10{sup 14} g.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

PLANET FORMATION IN CIRCUMBINARY CONFIGURATIONS: TURBULENCE INHIBITS PLANETESIMAL ACCRETION

The existence of planets born in environments highly perturbed by a stellar companion represents a major challenge to the paradigm of planet formation. In numerical simulations, the presence of a close binary companion stirs up the relative velocity between planetesimals, which is fundamental in determining the balance between accretion and erosion. However, the recent discovery of circumbinary planets by Kepler establishes that planet formation in binary systems is clearly viable. We perform N-body simulations of planetesimals embedded in a protoplanetary disk, where planetesimal phasing is frustrated by the presence of stochastic torques, modeling the expected perturbations of turbulence driven by the magnetorotational instability. We examine perturbation amplitudes relevant to dead zones in the midplane (conducive to planet formation in single stars), and find that planetesimal accretion can be inhibited even in the outer disk (4-10 AU) far from the central binary, a location previously thought to be a plausible starting point for the formation of circumbinary planets.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Metal 3D Printing of Low-NOX Fuel Injectors with Integrated Temperature Sensors (Final Technical Report)

This technical report presents the exploration of design and prototyping of an Oxy-fuel injector with integrated temperature sensing capabilities using Additive Manufacturing (AM) technology. The AM process has proven itself as a viable method to fabricate complex shapes for custom-designed metallic components rapidly. The lack of assembly requirements and the virtually unlimited geometrical complexity renders the AM process particularly attractive for fabricating complex energy system components. The unique layer-by-layer fabrication technique allows the embedding of sensors within complex components early in the design process. Sensors can be embedded (without post-production component modifications) in AM-fabricated components through two distinct processes: Stop and Go or Post-Integration. The Stop and Go fabrication process allows sensor placement within a cavity during fabrication; where the process is allowed to continue upon sensor placement. Post-integration process supports selective build of customized compartments for sensors within the part. The Stop and Go process requires an extremely accurate re-alignment of the powder-bed during the restart process. Additionally, metallization and shorting of sensors due to a considerably high temperature of the AM process creates significant fabrication challenges and limit the types of sensors that can be embedded. The Post-Integration of sensors is a practical alternative for components that can be effectively designed and fabricated with pre-built complex sensor compartments without the need for post-production component modifications. The proposed effort aimed at exploring the fabrication of an oxy-fuel injector designed for high-pressure Oxy-Combustion applications (Combustor for Directly Heated Supercritical Power Cycle) with integrated temperature measurement capabilities using the AM technique. Since the current design methodology of injectors is based on conventional fabrication techniques (e.g., multi-step machining and welding processes), a new paradigm of design methodology needs to be developed for their adaptation in the AM fabrication process. One of the most challenging issues addressed in powder bed fusion is the removal of powder from internal channels/cavities as the powder to be removed has been lightly sintered during the fabrication process. In this research, a major task has been assigned to developing and evaluating powder removal techniques that will ultimately be used when removing sintered powder from cavities/channels used for sensor placement. Achieving thorough powder removal will permit the incorporation of intricate cavities, integrated fasteners, or other novel features to incorporate sensors into parts directly post-fabrication – allowing for the novel, AM-based design practices to be developed and employ for sensor integration. The designed injector was initially tested at atmospheric conditions to review its successful operation. The tests were carried out for different firing inputs; with a minimum of 55 kW and a maximum of 275 kW. Later tests were carried out for pressurized conditions between 82 kW to 275 kW firing input. A pressure of 16.35bar was observed in the combustion chamber pressure during the pressurized test of 275 kW firing input; test duration was 15 seconds. Integrated thermocouples within the injector provided temperature data for test operations. The data revealed during the atmospheric condition the injector temperature is almost unaffected by the combustion. However, during the pressurized condition, the injector temperature rapidly up to 205°C within 15 seconds; at a 275 kW firing input.

42 ENGINEERING↗
DOE OSTI2019

Science & Technology Review May 2019

Lawrence Livermore’s “brain-on-a-chip” is designed to predict the effects of potentially harmful chemicals, viruses, and drugs on humans without relying on animal or human test subjects. In conjunction with an artificial blood–brain barrier, the device simulates the central nervous system by recording activity from brain cells grown onto a small platform embedded with microelectrode arrays. The brain-on-a-chip holds significant promise for national security and broader applications. For example, the device could be used to determine how soldiers are affected by exposure to chemical and biological weapons and the effectiveness of potential countermeasures and prophylactic pretreatments. The technology could also help predict the effects on the brain from promising drugs designed to treat neurological disorders. The brain-on-a-chip is the latest iteration of the Laboratory’s iCHIP (in vitro chip-based human investigational platform) project—a broad initiative at Livermore to advance human health with a focus on understanding, diagnosing, and potentially treating human neural problems and diseases.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Systematic Evaluation of Backdoor Data Poisoning Attacks on Image Classifiers

Backdoor data poisoning attacks have recently been demonstrated in computer vision research as a potential safety risk for machine learning (ML) systems. Traditional data poisoning attacks manipulate training data to induce unreliability of an ML model, whereas backdoor data poisoning attacks maintain system performance unless the MLmodel is presented with an input containing an embedded“trigger” that provides a predetermined response advantageous to the adversary. Our work builds upon prior back-door data-poisoning research for ML image classifiers and systematically assesses different experimental conditions including types of trigger patterns, persistence of trigger patterns during retraining, poisoning strategies, architectures (ResNet-50, NasNet, NasNet-Mobile), datasets (Flowers, CIFAR-10), and potential defensive regularization techniques (Contrastive Loss, Logit Squeezing, Manifold Mixup,Soft-Nearest-Neighbors Loss). Experiments yield four key findings. First, the success rate of backdoor poisoning at-tacks varies widely, depending on several factors, including model architecture, trigger pattern and regularization technique. Second, we find that poisoned models are hard to detect through performance inspection alone. Third, regularization typically reduces backdoor success rate, although it can have no effect or even slightly increase it, depending on the form of regularization. Finally, backdoors inserted through data poisoning can be rendered ineffective after just a few epochs of additional training on a small set of clean data without affecting the model’s performance.

Truong, Loc T.↗
DOE OSTI2014

Electron correlation in solids via density embedding theory

Density matrix embedding theory [G. Knizia and G. K.-L. Chan, Phys. Rev. Lett. 109, 186404 (2012)] and density embedding theory [I. W. Bulik, G. E. Scuseria, and J. Dukelsky, Phys. Rev. B 89, 035140 (2014)] have recently been introduced for model lattice Hamiltonians and molecular systems. In the present work, the formalism is extended to the ab initio description of infinite systems. An appropriate definition of the impurity Hamiltonian for such systems is presented and demonstrated in cases of 1, 2, and 3 dimensions, using coupled cluster theory as the impurity solver. Additionally, we discuss the challenges related to disentanglement of fragment and bath states. The current approach yields results comparable to coupled cluster calculations of infinite systems even when using a single unit cell as the fragment. The theory is formulated in the basis of Wannier functions but it does not require separate localization of unoccupied bands. The embedding scheme presented here is a promising way of employing highly accurate electronic structure methods for extended systems at a fraction of their original computational cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

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↗