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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 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Medium and Heavy Duty Vehicle Powertrain Electrification and Fleet Demonstration

The Contract Award Grant # EE0007513 dated 2 June, 2016 is for the design, development and demonstration of medium duty package delivery vehicles that will result in a 100% increase in fuel economy as measured in miles per gallon. The project was proposed in 3 phases over two budget periods. The Phases were: 1. Modeling and Simulation – This phase was completed and formed the basis of the specifications for the design and build of the physical systems. The modeling and simulation was conducted by AVL and used real world package delivery routes that AVL mapped. The motors, battery pack, range extender and balance of plant support systems were modeled and iterated until a system with the desired fuel economy improvement was realized. Early design of the major subsystems using the actual vehicle space constraints was also completed. This phase was successfully completed in May of 2017. 2. 1st Build and FE Confirmation - This phase was completed and resulted in the final design, release, procurement and build of all major vehicle systems for commissioning into the first vehicle. The work was a partnered effort between McLaren and AVL. McLaren built the eAxle system while AVL built the range extender and integrated the range extender, battery and balance of plant sub-systems into the first vehicle with a control system to make it operate. Prior to the end of this phase a real world HIL system test gave evidence that the fuel economy improvement would be achieved in the real world. This phase was exited with a 7 month delay due mostly to procurement and supply base issues and ended in May, 2018. 3. Final Build and Demonstration - This phase included the final build and commissioning of the four program vehicles and the operation of a demonstration on a set of routes near San Diego California. During this phase, a multitude of issues arose in different systems in the vehicle. These issue resolution exercises were quite complex and caused repeated delays but were all successfully completed. It should also be noted that an early commercialization analysis resulted in the conclusion that the complexity of the system would not make it cost effective, leading to the start of a follow-on design that used newly available component technologies to specify a more cost effective system. This design will be repurposed and put into demonstration on a separately (non-DOE) funded program. It was decided and agreed with DOE that this phase should be considered completed. The knowledge and know-how gained on this program has been incorporated into and transferred to the new program. This phase and the entire program was considered closed on June 1, 2021.

33 ADVANCED PROPULSION SYSTEMS↗
NASA NTRS1984

An integrated GIS/remote sensing data base in North Cache soil conservation district, Utah: A pilot project for the Utah Department of Agriculture's RIMS (Resource Inventory and Monitoring System)

A basic geographic information system (GIS) for the North Cache Soil Conservation District (SCD) was sought for selected resource problems. Since the resource management issues in the North Cache SCD are very complex, it is not feasible in the initial phase to generate all the physical, socioeconomic, and political baseline data needed for resolving all management issues. A selection of critical varables becomes essential. Thus, there are foud specific objectives: (1) assess resource management needs and determine which resource factors ae most fundamental for building a beginning data base; (2) evaluate the variety of data gathering and analysis techniques for the resource factors selected; (3) incorporate the resulting data into a useful and efficient digital data base; and (4) demonstrate the application of the data base to selected real world resoource management issues.

Wheeler, D. J.↗
DOE OSTI2023

hpMCA: A Python-based Graphical Program for Energy Dispersive X-Ray Diffraction Data Collection and Analysis

Energy-dispersive X-ray diffraction (EDXD) at synchrotron beamlines is commonly used for the study of material properties under high pressure and/or high temperature. Experimenters typically rely on the availability of robust data collection and analysis at a beamline, but this has become increasingly difficult, especially with the introduction of multi-element detectors that generate complex, multi-dimensional data sets. These data sets have energy resolution, and they can also be resolved in relation to sample position, diffraction angle, or different external stimuli. We report a new Python-based graphical program, hpMCA, for EDXD data collection and analysis that streamlines the experimental process for the beamline users. The program features a user-friendly interface, capability for online viewing and analyzing data from multi-element energy-dispersive detectors, and includes features useful for working with samples under high pressure and/or high temperature, such as crystal phase identification, real-time unit cell lattice refinement, and pressure determination based on an equation of state.

data analysis software↗
DOE OSTI2022

Feature Extraction for Pipeline Defects Inspection Based Upon Distributed Acoustic Fiber Optic Sensing Data

Fiber-optic distributed acoustic sensing (DAS) is becoming an increasingly important tool for real-time monitoring of energy and civil infrastructure structural health such as pipelines. We present a systematic theoretical study of the potential for DAS to be directly coupled with guided ultrasonic waves typically used in conventional acoustic non-destructive evaluation (NDE) methods for real-time pipeline health monitoring. We are referring to this innovative new NDE technique as ultrasonic guided wave and optical fiber sensor fusion. In the practical application of DAS coupled with guided ultrasonic waves, the structural design of (1) the specific guided waves excited, (2) the physical installation of the acoustic transducers and the fiber optic sensors, and (3) the functional performance specifications (gauge length, sensitivity, Etc.) of fiber optic DAS have an important influence on overall capabilities of the monitoring system. Meanwhile, physics-based analysis of acoustic waves is still a challenge due to the complex nature of the Lamb wave when it propagates, scatters, and disperses in the presence of structural defects. In this work, we simulate carbon steel pipes relevant for oil and gas pipeline applications with diameters of approximately 6-12” and wall thickness of 0.5” as the objects to be monitored. By establishing and implementing these capabilities, we seek to pursue an in-depth study on structural parameter optimization of DAS network, measurement range, and signal processing with an ultimate goal of increasing the sensitivity and efficacy of DAS to defect identification for various modes of corrosion expected in practice. To study the characteristics of scattered acoustic waves and performance of DAS for defect identification, we simulated the response of DAS for multiple pipe structures, defect types, and DAS sensor network configuration using finite element software Ansys, then the properties of signal response are extracted to construct defect-sensitive features. The raw data simulated, and the associated features extracted can ultimately be utilized as annotated training data to benchmark various designs for DAS applications, guided acoustic excitation sources, and learning model parameters to enhance early detection of potentially problematic defects.

Pipeline Defects Inspection, Fiber-optic sensors, ↗
DOE OSTI2025

Accelerating Advanced Light Source Science Through Multi-Facility HPC Workflows

Synchrotron light sources support a wide array of techniques to investigate materials, often producing complex, high-volume data that challenge traditional workflows. At the Advanced Light Source (ALS), we developed infrastructure to move microtomography data over ESnet to ALCF and NERSC, where CPU- and GPU-based algorithms generate 3D reconstructed volumes of experimental samples. We employ two data movement and reconstruction models: real-time processing as data streams directly to NERSC compute nodes, and automated file transfer to NERSC and ALCF file systems. The streaming pipeline provides users with feedback in under ten seconds, while the file-based workflow produces high-quality reconstructions suitable for deeper analysis in 20-30 minutes. This infrastructure enables users to utilize HPC resources without direct access to backend systems. We plan to extend this architecture to more endstations, supporting our beamline scientists and users.

Abramov, David↗
DOE OSTI2026

Mauka Energy FEVER Tool Dataset

Mauka Energy’s dataset, developed under the Forestry Electric Vehicle Energy Routing (FEVER) project and funded by the U.S. Department of Energy’s Small Business Innovation Research program, is a high-resolution geospatial resource designed to support energy modeling for electric log trucks in complex forestry environments. The dataset integrates detailed spatial and road network data to enable accurate simulation of vehicle performance across varied terrain. At its core, the dataset incorporates lidar-derived elevation models, road alignments, and surface classifications from Oregon State University’s McDonald-Dunn Research Forest. These data capture fine-scale variations in slope, curvature, and surface conditions across forest road systems, allowing for vehicle-level analysis of energy consumption and recovery. The dataset also includes data collected on the surrounding public and private road networks in Benton County, Oregon, used in real-world haul routes. These connecting segments provide critical context for modeling transitions between forest operations and regional transportation infrastructure, incorporating attributes such as grade profiles, elevation change, and speed constraints. This combined dataset underpins the development of Mauka Energy’s rolldown tool, which quantifies energy use and regenerative braking potential on downhill and variable-grade segments. By leveraging high-resolution terrain and road data, the FEVER project enables more accurate assessment of electric vehicle feasibility and performance in forestry applications.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2023

Supporting Risk-informed Decision-making During Reactor Accidents

Uncertainty in severe accident evolution and outcome is driven by event bifurcations that represent distinctive challenges to defensive layers and tend to promote the emergence of discrete classes of core damage and accident risk. This discrete set of "attractor" states arise from the complex networks of competing physical phenomena and conditional event cascades occurring as the overall system degrades – a process that yields increasing degrees of freedom and accident progression pathways. Characterization of these event spaces has proven elusive to more traditional data interrogation methods, but proves tractable by application of more advanced data collection and machine learning approaches. Through application of these approaches we demonstrate a conceptual framework that enables real-time/robust, risk-informed decision-making support to improve accident mitigation and encourage “graceful exits” during low probability, extreme events limiting accident consequences. In this analysis, we simulated over 8,000 short-term station blackout (STSBO) accidents with the state-of-the-art integral severe accident code, MELCOR, and demonstrate the potential for ML approaches to predict simulation outcomes. We chose to pair ML tools with interpretable and mechanistic event trees for the considered STSBO accident space to predict the likelihood of future event paths along the tree. In addition to the current state of the system, we use information from recent trajectories of temperature, pressure, and other physical features, combining both the current state and past trajectories to forecast future event paths. Finally, we simulate the random injection of variable amounts of water to quantify the efficacy of available actions at reducing risks along the many branches in the event tree. We identify scenarios and windows of opportunity to mitigate risk as well as scenarios in which such actions are unlikely to alter the accident end-state.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1991

Optical constants of solid methane and ethane from 10,000 to 450/cm

Near- and mid-IR spectra of thin films of crystalling phase I and phase II C2H6 are presented using a combined least squares and Kramers-Kronig analysis. Complex refractive indices derived from these data are also presented. To obtain material in phase I, samples are annealed at 33 K for about 30 min; phase II is obtained by recooling below the transition temperature of 20.4 K. The derived optical parameters are shown. The infrared spectrum of phase I CH4 exhibits broad structureless absorptions at about 1300 and 2600/cm. On cooling the sample below 20.4 K (phase II), the absorptions are sharpened, and each band develops fine structure. The present results and those of Roux et al. (1979) are compared. The agreement with the real parts is found to be excellent; given the difference in resolution, the agreement with the imaginary parts is also good.

Pearl, J.↗
NASA NTRS1992

DEPEND: A simulation-based environment for system level dependability analysis

The design and evaluation of highly reliable computer systems is a complex issue. Designers mostly develop such systems based on prior knowledge and experience and occasionally from analytical evaluations of simplified designs. A simulation-based environment called DEPEND which is especially geared for the design and evaluation of fault-tolerant architectures is presented. DEPEND is unique in that it exploits the properties of object-oriented programming to provide a flexible framework with which a user can rapidly model and evaluate various fault-tolerant systems. The key features of the DEPEND environment are described, and its capabilities are illustrated with a detailed analysis of a real design. In particular, DEPEND is used to simulate the Unix based Tandem Integrity fault-tolerance and evaluate how well it handles near-coincident errors caused by correlated and latent faults. Issues such as memory scrubbing, re-integration policies, and workload dependent repair times which affect how the system handles near-coincident errors are also evaluated. Issues such as the method used by DEPEND to simulate error latency and the time acceleration technique that provides enormous simulation speed up are also discussed. Unlike any other simulation-based dependability studies, the use of these approaches and the accuracy of the simulation model are validated by comparing the results of the simulations, with measurements obtained from fault injection experiments conducted on a production Tandem Integrity machine.

Goswami, Kumar↗
NASA NTRSDate not supplied

Runtime Analysis with R2U2: A Tool Exhibition Report

We present R2U2 (Realizable, Responsive, Unobtrusive Unit), a hardware- supported tool and framework for the continuous monitoring of safetycritical and embedded cyber-physical systems.With the widespread advent of autonomous systems such as Unmanned Aerial Systems (UAS), satellites, rovers, and cars, real-time, on-board decision making requires unobtrusive monitoring of properties for safety, performance, security, and system health. R2U2 models combine past-time and future-time Metric Temporal Logic, “mission time” Linear Temporal Logic, probabilistic reasoning with Bayesian Networks, and modelbased prognostics. The R2U2 monitoring engine can be instantiated as a hardware solution, running on an FPGA, or as a software component. The FPGA realization enables R2U2 to monitor complex cyber-physical systems without any overhead or instrumentation of the flight software. In this tool exhibition report, we present R2U2 and demonstrate applications on system runtime monitoring, diagnostics, software health management, and security monitoring for a UAS. Our tool demonstration uses a hardware-based processor-in-the-loop “iron-bird” configuration.

Johann Martin Schumann↗
NASA NTRS1996

Development of High Speed Imaging and Analysis Techniques Compressible Dynamics Stall

Dynamic stall has limited the flight envelope of helicopters for many years. The problem has been studied in the laboratory as well as in flight, but most research, even in the laboratory, has been restricted to surface measurement techniques such as pressure transducers or skin friction gauges, except at low speed. From this research, it became apparent that flow visualization tests performed at Mach numbers representing actual flight conditions were needed if the complex physics associated with dynamic stall was to be properly understood. However, visualization of the flow field during compressible conditions required carefully aligned and meticulously reconstructed holographic interferometry. As part of a long-range effort focused on exposing of the physics of compressible dynamic stall, a research wind tunnel was developed at NASA Ames Research Center which permits visual access to the full flow field surrounding an oscillating airfoil during compressible dynamic stall. Initially, a stroboscopic schlieren technique was used for visualization of the stall process, but the primary research tool has been point diffraction interferometry(PDI), a technique carefully optimized for use in th is project. A review of the process of development of PDI will be presented in the full paper. One of the most valuable aspects of PDI is the fact that interferograms are produced in real time on a continuous basis. The use of a rapidly-pulsed laser makes this practical; a discussion of this approach will be presented in the full paper. This rapid pulsing(up to 40,000 pulses/sec) produces interferograms of the rapidly developing dynamic stall field in sufficient resolution(both in space and time) that the fluid physics of the compressible dynamic stall flowfield can be quantitatively determined, including the gradients of pressure in space and time. This permits analysis of the influence of the effect of pitch rate, Mach number, Reynolds number, amplitude of oscillation, and other parameters on the dynamic stall process. When interferograms can be captured in real time, the potential for real-time mapping of a developing unsteady flow such as dynamic stall becomes a possibility. This has been achieved in the present case through the use of a high-speed drum camera combined with electronic circuitry which has resulted in a series of interferograms obtained during a single cycle of dynamic stall; images obtained at the rate of 20 KHz will be presented as a part of the formal presentation. Interferometry has been available for a long time; however, most of its use has been limited to visualization. The present research has focused on use of interferograms for quantitative mapping of the flow over oscillating airfoils. Instantaneous pressure distributions can now be obtained semi-automatically, making practical the analysis of the thousands of interferograms that are produced in this research. A review of the techniques that have been developed as part of this research effort will be presented in the final paper.

Chandrasekhara, M. S.↗
NASA NTRS1991

Rainbow net analysis of VAXcluster system availability

A system modeling technique, Rainbow Nets, is used to evaluate the availability and mean-time-to-interrupt of the VAXcluster. These results are compared to the exact analytic results showing that reasonable accuracy is achieved through simulation. The complexity of the Rainbow Net does not increase as the number of processors increases, but remains constant, unlike a Markov model which expands exponentially. The constancy is achieved by using tokens with identity attributes (items) that can have additional attributes associated with them (features) which can exist in multiple states. The time to perform the simulation increases, but this is a polynomial increase rather than exponential. There is no restriction on distributions used for transition firing times, allowing real situations to be modeled more accurately by choosing the distribution which best fits the system performance and eliminating the need for simplifying assumptions.

Johnson, Allen M., Jr.↗
NASA NTRS1984

Perturbation analysis of the limit cycle of the free van der Pol equation

A power series expansion in the damping parameter, epsilon, of the limit cycle of the free van der Pol equation is constructed and analyzed. Coefficients in the expansion are computed in exact rational arithmetic using the symbolic manipulation system MACSYMA and using a FORTRAN program. The series is analyzed using Padeapproximants. The convergence of the series for the maximum amplitude of the limit cycle is limited by two pair of complex conjugate singularities in the complex epsilon-plane. A new expansion parameter is introduced which maps these singularities to infinity and leads to a new expansion for the amplitude which converges for all real values of epsilon. Amplitudes computed from this transformed series agree very well with reported numerical and asymptotic results. For the limit cycle itself, convergence of the series expansion is limited by three pair of complex conjugate branch point singularities. Two pair remain fixed throughout the cycle, and correspond to the singularities found in the maximum amplitude series, while the third pair moves in the epsilon-plane as a function of t from one of the fixed pairs to the other. The limit cycle series is transformed using a new expansion parameter, which leads to a new series that converges for larger values of epsilon.

Dadfar, M. B.↗
NASA NTRS1992

Visualization of second order tensor fields and matrix data

We present a study of the visualization of 3-D second order tensor fields and matrix data. The general problem of visualizing unsymmetric real or complex Hermitian second order tensor fields can be reduced to the simultaneous visualization of a real and symmetric second order tensor field and a real vector field. As opposed to the discrete iconic techniques commonly used in multivariate data visualization, the emphasis is on exploiting the mathematical properties of tensor fields in order to facilitate their visualization and to produce a continuous representation of the data. We focus on interactively sensing and exploring real and symmetric second order tensor data by generalizing the vector notion of streamline to the tensor concept of hyperstreamline. We stress the importance of a structural analysis of the data field analogous to the techniques of vector field topology extraction in order to obtain a unique and objective representation of second order tensor fields.

Delmarcelle, Thierry↗
NASA NTRS2003

On the Hilbert-Huang Transform Data Processing System Development

One of the main heritage tools used in scientific and engineering data spectrum analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). The Fourier view of nonlinear mechanics that had existed for a long time, and the associated FFT (fairly recent development), carry strong a-priori assumptions about the source data, such as linearity and of being stationary. Natural phenomena measurements are essentially nonlinear and nonstationary. A very recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT) proposes a novel approach to the solution for the nonlinear class of spectrum analysis problems. Using the Empirical Mode Decomposition (EMD) followed by the Hilbert Transform of the empirical decomposition data (HT), the HHT allows spectrum analysis of nonlinear and nonstationary data by using an engineering a-posteriori data processing, based on the EMD algorithm. This results in a non-constrained decomposition of a source real value data vector into a finite set of Intrinsic Mode Functions (IMF) that can be further analyzed for spectrum interpretation by the classical Hilbert Transform. This paper describes phase one of the development of a new engineering tool, the HHT Data Processing System (HHTDPS). The HHTDPS allows applying the "T to a data vector in a fashion similar to the heritage FFT. It is a generic, low cost, high performance personal computer (PC) based system that implements the HHT computational algorithms in a user friendly, file driven environment. This paper also presents a quantitative analysis for a complex waveform data sample, a summary of technology commercialization efforts and the lessons learned from this new technology development.

Kizhner, Semion↗
NASA NTRS2023

Forward for the new edition of: “What Every Engineer Should Know About Risk Engineering and Management"

In aerospace and engineering in general, the major metrics are capability, cost, and safety/risk. With the increasingly rapid emergence and utilization of new technologies and systems of increasing complexity, ensuring safety becomes more difficult. The technology and practice/applications of safety/risk technologies require updating in concert with capability and systems technology changes. Hence the new, updated edition of this risk engineering book. Major changes in technology and applications, now and going forward, increasingly involve artificial intelligence (AI)/autonomy and complex systems, which are rapidly developing and moving targets when it comes to risk/safety analysis. These introduce both new risks and safety issues, and they alter more usual ones. The current reality is that often the best AI is when it is “Black Boxed”, developed “independently”, without detailed human understanding of how and by what processes decisions and results are produced. There are ongoing efforts to make the AI processes more understandable by humans, with results to be determined. Also, trusted and true autonomy is free of human intervention, which would require machines to ideate to solve in real time issues that arise due to unknown unknowns and even known unknowns. Machines using generative adversarial network (GANs) and other approaches are beginning to ideate. Overall, the capabilities and practice of AI/autonomy utilization is a work in progress with the rate of progress substantial and the impacts upon system risk/safety major.

Dennis M. Bushnell↗
DOE OSTI2024

FORCE Update 2024

The Framework for Optimization of Resources and Economics (FORCE) tool suite is the U.S. Department of Energy’s Nuclear Integrated Energy Systems (IES) Program flagship tool suite for technoeconomic IES analysis of IES. This tool suite is useful for analysis designed to evaluate and improve the technoeconomics of energy production systems, particularly for systems including nuclear technology. In this report, we document the development activity for the FORCE tool suite to extend its capabilities as performed during fiscal year 2024. In addition to reliability and accessibility, capability is one of the three standards guiding the development of the FORCE tool suite and the software codes that are its constituent parts. Extending the capabilities of the FORCE tool suite allows analysis both within the IES program as well as industry, university, and laboratory partners to perform analysis with more accuracy, insight, and impactful narrative. Four areas of capability development were the focus of activity this year: economic parameter uncertainty quantification, multiresolution analysis, components-to-optimization workflow automation, and statespace construction workflows for real-time optimal control. In economic parameter uncertainty quantification, the ability of HERON to capture risk due to scenarios (weather and energy demand uncertainty) was expanded to also include uncertainties in financial parameters such as capital cost or operation and maintenance costs. By including these sources of uncertainty, which are sometimes very large compared with scenario uncertainty, HERON is better able to capture the risk posed by investment in various IES technology. Because of this, analysts can also consider the reduction in risks that can be realized by choice of some technologies. In multiresolution analysis, development activity extended on work completed previously. In fiscal year 2023, methods for decomposing time series signals, such as demand, solar and wind availability, and price profiles, were analyzed and down-selected to those most effective at splitting signals into different resolutions. These resolutions allow considering the influence of different energy demand and supply behaviors across different time scales. For example, energy demand might be divided into seasonal, weekly, and hourly profiles. In fiscal year 2024, this preliminary work was extended and implemented within the Risk Analysis Virtual Environment (RAVEN) risk and uncertainty analysis platform, which is used throughout the FORCE framework. This development of the “multi-resolution time series analysis” (MR-TSA) module in RAVEN allows training synthetic history generators on complex time series. These synthetic history generators can then be used in HERON for generating scenarios that represent possible market and weather scenarios that can be analyzed on different time scales. We envision completing this work in the future, implementing multiresolution dispatch optimization strategies that can make the most beneficial use of these stratified time histories. In components-to-optimization workflow development, workflows for translating user inputs of components into algorithms for algebraic optimization were selected and implemented. Similar algorithms within the Holistic Energy Resource Optimization Network (HERON) were separated from the main code base of HERON and gathered with the components-to-optimization workflows in the new Dispatch Optimization Variable Engine (DOVE) software library. This modularization allows FORCE users to analyze dispatch optimization and energy system duty cycles independently of HERON, which previously was a burdensome task. Additionally, these dispatch optimization algorithms, set up in an independent library, can now be used across all software applications within FORCE, especially including the real-time optimal control software Optimization of Real-time Capacity Allocation (ORCA). Allowing FORCE software to share dispatch optimization algorithms within a single library allows for improved software maintenance and reliability. In statespace characterization workflow development, alternative workflows for optimizing dispatch with additional technical accuracy was the focus, particularly to improve the real-time optimization decision making in ORCA. Using algorithms and workflows initially developed for the Feasible Actuator Range Modifier (FARM), workflows for determining the statespace representation of IES were identified and demonstrated. The resulting dispatch optimization required a more robust optimization algorithm than that originally used in HERON (and moved to DOVE), which required adding an alternate workflow to DOVE that can more accurately match the behavior of physical systems using a partial differential equation representation. In conclusion, capability developments in the FORCE tool suite in fiscal year 2024 have improved the ability of the FORCE tool suite to perform

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
NASA NTRS1983

Perturbation analysis of the limit cycle of the free van der Pol equation

A power series expansion in the damping parameter, epsilon, of the limit cycle of the free van der Pol equation is constructed and analyzed. Coefficients in the expansion are computed in exact rational arithmetic using the symbolic manipulation system MACSYMA and using a FORTRAN program. The series is analyzed using Pade approximants. The convergence of the series for the maximum amplitude of the limit cycle is limited by two pair of complex conjugate singularities in the complex epsilon-plane. A new expansion parameter is introduced which maps these singularities to infinity and leads to a new expansion for the amplitude which converges for all real values of epsilon. Amplitudes computed from this transformed series agree very well with reported numerical and asymptotic results. For the limit cycle itself, convergence of the series expansion is limited by three pair of complex conjugate branch point singularities. Two pair remain fixed throughout the cycle, and correspond to the singularities found in the maximum amplitude series, while the third pair moves in the epsilon-plane as a function of t from one of the fixed pairs to the other. The limit cycle series is transformed using a new expansion parameter, which leads to a new series that converges for larger values of epsilon.

Dadfar, M. B.↗