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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

The Polar System Analysis Package (Ver. 1 Specifications)

The Polar System Analysis Package (POLeSTAr) is a modern data fusion tool being designed to benchmark,evaluate and compare the polar physics and biogeochemistry of Earth System Models (ESMs). It is being written in Python to make use of libraries including Xarray, Matplotlib, SciPy, NumPy and PyTorch within algorithms developed specifically for polar system modeling. Initial POLeSTAr algorithms will be adapted from the MATLAB Ridgepack package that was designed to analyze the Model for Prediction Across Scales (MPAS) sea ice component of the Energy Exascale Earth System Model (E3SM) and sea ice model CICE within the Community Earth System Model (CESM).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Development and Application of a Risk Analysis Toolkit for Plant Resources Optimization

This report summarizes the R&D activities of the Risk Informed Asset Management (RIAM) project during fiscal year 2020 (FY20). This project focuses on the development of methods designed to optimize plant operations (e.g., maintenance/replacement schedule, optimal maintenance posture) provided system/component health/cost data. This project development lives in cooperation with the Plant Health Management (PHM) project which focuses on the development of methods that integrate component health data and propagate such information at the system level to evaluate most relevant sources of risk. This year’s activities for the RIAM project focused on the continuation of schedule optimization algorithms developed in FY19. While in FY19 we focused on both deterministic and stochastic capital budgeting methods, in FY20 we moved forward by implementing two versions of schedule optimization methods. The first one reformulates the capital budgeting problem in a distributionally robust form which allows the user to rely on data directly rather than proposing a distribution from the data itself. The second version reformulates the capital budgeting explicitly using risk measures as variables to maximize/minimize. Lastly, we focused on the development of methods designed to identify the optimal maintenance posture based on the Pareto Frontier analysis. Rather than performing a tradeoff analysis (i.e., identify the absolute best posture), the Pareto Frontier analysis performs a trade space exploration approach (i.e., identify value and costs of several postures and have the analyst perform the task of imposing desired value and cost constraints). This is performed by identifying maintenance postures that maximize value (e.g., system availability) and minimize operational costs, i.e., the Pareto frontier in a value-cost trade space.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Using Temporal Information from Human Mobility Data to Detect Anchor Points

Spatiotemporal mobility data are available in massive quantities, but large quantities of data typically include fewer variables or data fields. Often, the only available fields are User ID, Longitude, Latitude, Timestamp (ULLT). This raises an important question: how much can we infer about human mobility patterns using only these four fields? With ULLT data, we do not know individuals' socioeconomic status information or when they are visiting their anchor points (AP) or locations (such as homes, places of employment, or schools), and it is a modern challenge to use this data to infer these characteristics. When detecting anchor locations with limited input information, verification and validation (VV) are significant challenges. This paper addresses the problem of identifying individuals' anchor locations using only temporal information from spatiotemporal datasets with limited attributes. Our approach does not explicitly use latitude and longitude during analysis. Locationbased information is only employed in the preprocessing stage to identify periods of movement (trips) and stops (dwelling). Beyond this step, all analysis is based on temporal patterns. In theory, if stops and dwell times could be detected through alternative means, our method could function entirely without location-based input. We demonstrate this methodology on the 2017 National Household Travel Survey (NHTS) data, because it includes a carefully designed and collected time use survey with representative sampling and labeled ground truth. The high-quality survey data allows us to test the accuracy of our methods because NHTS contains intended place labels and agent/user characteristics. We have also applied our validated AP identification algorithm on very large-scale GPS based trajectory data for Patterns-of-Life (PoL) assessment and other applications, but due to space limit that could not be presented here.

McBride, Liz [ORNL] (ORCID:0000000286925869)↗
DOE OSTI2020

The Relationship Between Dose Rate and Decay Heat for Spent Nuclear Fuel Casks

Decay heat and dose rate are two important limits used for determining the allowable contents of spent fuel (SNF) in dry storage systems and transportation packages. While the decay heat limit is used to maintain fuel cladding integrity and ensure retrievability, dose rates are used to demonstrate compliance with regulatory requirements on radiation protection. Because both dose rate and decay heat result from decay of radioisotopes in SNF, this study is an attempt to examine the relationship between dose rate and decay heat for a given cask design. Dose rates were evaluated for 198 cask configurations, that include various SNF system designs (e.g., storage, transfer, transport), SNF characteristics (e.g., fuel types, burnup, cooling time), and loading maps (e.g., uniform loading, zone loading), while a constant decay heat was maintained. The decay heat was calculated using US Nuclear Regulatory Commission (NRC) Regulatory Guide (RG) 3.54, Revision 2, and verified using ORIGEN sequence within SCALE code system. The ORIGEN outputs were used as source terms in the dose analysis using 198 different configurations. A computer script was developed to calculate the cooling time necessary to achieve a given decay heat for a given enrichment, assembly average burnup, assembly mass, and in-core history using a rootfinder algorithm. Initially the computer script was developed to provide cooling time and burnup calculations directly to the analysis of dose rates and decay heats, so a comparison between Used Nuclear Fuel-Storage Transportation and Disposal Analysis Resource Data System (UNF-ST&DARDS) results and RG3.54 data was made; results are included in the appendix to this document. However, an iterative approach was used to compute cooling time, and its accuracy did not depend on the results of the RG3.54r2 algorithm, although the algorithm was still used. The results of the evaluation presented herein clearly demonstrate that a given decay heat does not correspond to a unique dose rate for a variety of cask and package designs. There is no clear pattern to develop a correlation between decay heat and the source terms. Depending on burnup, enrichment, cask type, and loading pattern, dose rates varied for the exact same decay heat—in some cases by 400% for a given cask. For cases in which decay heat was held constant through selection of the appropriate cooling time, dose rates would decrease with increasing burnup, and in other cases, dose rates would increase. The large variation in dose rates for a constant decay heat indicates that casks loaded based on decay heat—that is allowing any burnup, cooling time, and enrichment combinations that yield the qualified decay heat limit(s) —cannot ensure that an Independent Spent Fuel Storage Installation or a spent fuel transportation package will meet the regulatory limits set forth by the respective regulations, i.e., 10 CFR 72 or 10 CFR 71.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2023

Genetic algorithm optimization of a chemical kinetic mechanism for propane at engine relevant conditions

Propane has demonstrated significant potential for reductions in greenhouse gas and pollutant emissions in medium- and heavy-duty engine applications, but further improvements require accurate, compact, and scalable chemical kinetic mechanisms to design the next generation of propane fueled engines, particularly at the boosted operating conditions necessary to meet the power density demand of medium- and heavy-duty applications. In this work, six key chemical reactions were identified in a reduced mechanism with 70 species and 352 reactions through a sensitivity analysis performed at conditions typical of thermodynamic trajectories observed in a high compression ratio, long stroke engine operated on propane from throttled to boosted operating conditions. While the original mechanism was validated against rapid compression machine (RCM) data, it was found to overpredict experimental autoignition tendencies in 2-zone, 0-D SI engine simulations performed in Chemkin Pro. Subsequently, a genetic algorithm approach was used to optimize the six reaction rate parameters within established uncertainty bounds by performing RCM simulations and comparing to two independent sets of literature ignition delay times for propane, thus generating two new kinetic mechanisms. The first optimization achieved a mean absolute percent error (MPE) reduction in 2nd stage ignition delay of 61.4% in seven generations, while the second optimization utilized a newer experimental RCM dataset, and achieved MPE reduction of 56.7% in seven generations, and further marginal improvement to 57.8% reduction in 34 generations. Finally, the two mechanisms were then evaluated again in the 2-zone 0-D SI engine model in Chemkin Pro comparing typical mean and knocking cycle trajectories, and it was found that the second optimized mechanism provided better prediction of knock onset at the representative conditions evaluated in this work, particularly for higher load operating conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Cost Drivers for a Tokamak-Based Compact Pilot Plant

A comprehensive systems code that includes a range of physics and engineering considerations along with a simplified costing model has been utilized to evaluate the primary cost drivers for a compact tokamak pilot plant. The systems code has been benchmarked against several tokamak reactor designs and is utilized with sophisticated optimization algorithms to develop optimal solutions for a set of user-specified assumptions and design constraints. Here, in contrast to previous models that have focused on the cost of electricity as the key cost metric, this study uses the estimated capital cost of the facility. The analysis suggests that a pilot plant with the following features may offer potential for a cost-attractive pilot plant: A ~ 3, H 98y2 > 1.5, P net = 200 MW, 𝜏 𝑝⁢𝑢⁢𝑙⁢𝑠⁢𝑒 ~ 1 to 2 h utilizing rare-earth barium copper oxide (REBCO) magnet technology and a plug-bucked central solenoid/toroidal field (CS/TF) magnet support structure. While REBCO magnets offer some advantages relative to Nb 3 Sn magnets in all cases, the most gain is obtained when combined with the plug-bucked CS/TF bucking solution. Pulsed operation reduces capital cost requirements relative to steady-state operation, especially at low confinement. Cost sensitivity studies indicate that there are significant cost uncertainties associated with the achievable confinement quality, tritium breeding capability, attainable thermal efficiency, and achievable neutron wall loading, suggesting that these areas are the most critical areas in reducing the cost risk for a compact tokamak pilot plant. Further cost sensitivity studies indicate that the estimated cost is most sensitive to the underlying cost of the magnetic coils, providing further impetus to better establish cost-effective means for producing fusion magnets.

Compact pilot plant↗
DOE OSTI2021

pnnl/DPVPROT

Distributed photovoltaics protection software toolkit The code package includes several important functions for design and analysis of new grid protection schemes, for scenarios of distributed photovoltaic (DPV) generation approaching 100% of the peak feeder load, i.e., high-penetration DPV. Convert distribution feeder models, used by planning engineers, to electromagnetic transient (EMT) models that produce waveforms for advanced relay algorithms. Visualize the results of protection scheme operation. Tools to determine distance relay settings on distribution systems. Tools to predict the performance of time-domain, incremental distance relay algorithms

McDermott, Tom↗
DOE OSTI2023

Blockchain for Fault-Tolerant Grid Operations

Radial topology and vast geographic coverage make distribution systems prone to widespread power outages upon the failure of a single (or multiple) upstream component. Fault-handling algorithms depend heavily on correct estimations of the system’s state to effectively isolate the affected area and reduce the number of affected customers while maintaining operational safety. The work described here leverages the core features of distributed, consensus-based decision-making processes and the immutability of blockchain, and demonstrates their value in improving fault-tolerant grid operations. In this work, blockchain was used to create a trusted data-sharing platform that enables independent actors to reconstruct the system state; this enables distributed resources to make intelligent decisions with limited knowledge. Although the process requires data sharing, its algorithms have been designed to limit the amount of private information that is exchanged, which helps preserve business-sensitive data and maintain customer privacy. In addition, by reducing the information that must be shared, the communication requirements are also reduced; (however, an in-depth analysis of the communication requirements is beyond the scope of this project). The proposed use cases are intended to represent a foundational basis for third parties to develop functional solutions that can eventually be deployed in the field. To further provide guidance, the envisioned use cases have incorporated design requirements that consider the blockchain characteristics and a need to limit information from surrounding resources, which preserve the assumption and the possibility that such resources could belong to different entities. This report presents a detailed design of the three use cases with the tools needed to enable the analysis being tested. The implemented gross error detection method can detect mismatches when the error exceeds 3.8 times the sensor’s rated accuracy. Detection of the circuit breaker state successfully identified the correct states across all simulation tests. A distribution-system power-flow solution in the simulator OpenDSS generally possesses a convergency tolerance of 0.01% on the voltage magnitude. The evaluation of possible reconnection using voltage magnitude—preserving the data ownership—has a voltage magnitude difference smaller than 0.001% from the OpenDSS result. The results preserving data ownership have a difference within the expected power flow tolerance with full knowledge of the system, which surpasses expectations.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

ARQUIN: Architectures for Multinode Superconducting Quantum Computers

Many proposals to scale quantum technology rely on modular or distributed designs wherein individual quantum processors, called nodes, are linked together to form one large multinode quantum computer (MNQC). One scalable method to construct an MNQC is using superconducting quantum systems with optical interconnects. However, internode gates in these systems may be two to three orders of magnitude noisier and slower than local operations. Surmounting the limitations of internode gates will require improvements in entanglement generation, use of entanglement distillation, and optimized software and compilers. Still, it remains unclear what performance is possible with current hardware and what performance algorithms require. In this article, we employ a systems analysis approach to quantify overall MNQC performance in terms of hardware models of internode links, entanglement distillation, and local architecture. We show how to navigate tradeoffs in entanglement generation and distillation in the context of algorithm performance, lay out how compilers and software should balance between local and internode gates, and discuss when noisy quantum internode links have an advantage over purely classical links. Here, we find that a factor of 10–100× better link performance is required and introduce a research roadmap for the co-design of hardware and software towards the realization of early MNQCs. While we focus on superconducting devices with optical interconnects, our approach is general across MNQC implementations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Bridging Python to Silicon: The SODA Toolchain

Systems performing scientific computing, data analysis, and machine learning tasks have a growing demand for application-specific accelerators that can provide high computational performance while meeting strict size and power requirements. However, the algorithms and applications that need to be accelerated are evolving at a rate that is incompatible with manual design processes based on hardware description languages. Agile hardware design tools based on compiler techniques can help by quickly producing an application-specific integrated circuit (ASIC) accelerator starting from a high-level algorithmic description. Here, we present the software-defined accelerator (SODA) synthesizer, a modular and open-source hardware compiler that provides automated end-to-end synthesis from high-level software frameworks to ASIC implementation, relying on multilevel representations to progressively lower and optimize the input code. Our approach does not require the application developer to write any register-transfer level code, and it is able to reach up to 364 giga floating point operations per second (GFLOPS)/W efficiency (32-bit precision) on typical convolutional neural network operators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Distributed electric field sensing using fibre optics in borehole environments

In the past decade, rapid advances in distributed optical fibre sensing technologies have made it possible to record various geophysical data (e.g. strain, temperature and pressure) continuously in both time and space along the fibre, providing an unprecedented quantity and spatial density of data compared to traditional geophysical measurements as well as reducing data acquisition cost. To date, no distributed fibre-based electromagnetic field sensing system has been implemented although electromagnetic sensing could have a broad range of applications to geophysical imaging and monitoring in borehole environments. The goal of this paper is to provide a theoretical feasibility study regarding the design and use of an electromagnetic sensing optical fibre for geophysical applications. First, we present the sensitivity analysis of a ‘hypothetical’ optical fibre coated with polyvinylidene fluoride, a polymer that provides relatively high piezoelectric properties, yet unlike ceramics, is flexible. Next, using a two-dimensional electromagnetic modelling algorithm, we simulate the earth electric-field-to-fibre-strain transfer function and estimate the theoretical sensitivity of the optical fibre to electric fields. Given the state-of-the-art distributed acoustic sensing strain sensitivities in the picometres strain range, our numerical modelling analysis suggests that a perfectly coupled polyvinylidene fluoride–coated optical fibre can measure electric field values in the mV/m to V/m amplitude range. We then apply a cylindrically symmetric modelling algorithm to simulate numerical models demonstrating the applicability of such a fibre in an oilfield environment. Scenarios investigated employ an electric field source and suggest that the measurements can be used to distinguish the oil versus water ratio with a fibre mounted inside a producing steel cased oil well as well as distinguishing between brine and hydrocarbon filled reservoir zones with a fibre located outside of the casing.

58 GEOSCIENCES↗
DOE OSTI2021

Prognostics and Health Management in Nuclear Power Plants: An Updated Method-Centric Review With Special Focus on Data-Driven Methods

In a carbon-constrained world, future uses of nuclear power technologies can contribute to climate change mitigation as the installed electricity generating capacity and range of applications could be much greater and more diverse than with the current plants. To preserve the nuclear industry competitiveness in the global energy market, prognostics and health management (PHM) of plant assets is expected to be important for supporting and sustaining improvements in the economics associated with operating nuclear power plants (NPPs) while maintaining their high availability. Of interest are long-term operation of the legacy fleet to 80 years through subsequent license renewals and economic operation of new builds of either light water reactors or advanced reactor designs. Recent advances in data-driven analysis methods—largely represented by those in artificial intelligence and machine learning—have enhanced applications ranging from robust anomaly detection to automated control and autonomous operation of complex systems. The NPP equipment PHM is one area where the application of these algorithmic advances can significantly improve the ability to perform asset management. This paper provides an updated method-centric review of the full PHM suite in NPPs focusing on data-driven methods and advances since the last major survey article was published in 2015. The main approaches and the state of practice are described, including those for the tasks of data acquisition, condition monitoring, diagnostics, prognostics, and planning and decision-making. Research advances in non-nuclear power applications are also included to assess findings that may be applicable to the nuclear industry, along with the opportunities and challenges when adapting these developments to NPPs. Finally, this paper identifies key research needs in regard to data availability and quality, verification and validation, and uncertainty quantification.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Utilizing a Virtual Sodium-Cooled Fast Reactor Digital Twin to Aid in Diversion Pathway Analysis for International Safeguards Applications

We report digital twin technology has the potential to improve the effectiveness of international safeguards inspectors by providing a tool which can: first, perform an accurate diversion path analysis, identify their indicators, and required sensors to detect them; and second, monitor facilities in real-time using critical data streams that benefit from this safeguards-by-design approach. Safeguards inspectors are required to visit facilities and verify the nuclear material to ensure no diversion has taken place and detect misuse of the facility; however, this analysis and verification effort is time consuming, and with limited funding it is imperative that time spent at a nuclear facility is focused on key areas. A virtual digital twin of three prototypic sodium fast reactors was developed, where diversion and misuse scenarios were explored to determine how a digital twin could provide inspectors with an understanding of how proliferation may occur and where the most likely areas for proliferation would be. For each of the three reactors, an optimization algorithm was able to find core designs which would be difficult to detect via sensors alone; however, the use of a machine learning adapter provided by the digital twin was able to show general trends in where proliferation as likely to take place.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Intelligent Sampling for Surrogate Modeling, Hyperparameter Optimization, and Data Analysis

Sampling techniques are used in many fields, including design of experiments, image processing, and graphics. The techniques in each field are designed to meet the constraints specific to that field such as uniform coverage of the range of each dimension or random samples that are at least a certain distance apart from each other. When an application imposes new constraints, for example, by requiring samples in a non-rectangular domain or the addition of new samples to an existing set, a common solution is to modify the algorithm currently in use, often with less than satisfactory results. As an alternative, we propose the concept of intelligent sampling, where we devise algorithms specifically tailored to meet our sampling needs, either by creating new algorithms or by modifying suitable algorithms from other fields. Surprisingly, both qualitative and quantitative comparisons indicate that some relatively simple algorithms can be easily modified to meet the many sampling requirements of surrogate modeling, hyperparameter optimization, and data analysis; these algorithms outperform their more sophisticated counterparts currently in use, resulting in better use of time and computer resources.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Optimizing Cell-based Antimicrobials through Pooled Genomic Libraries

DNA synthesis and assembly technologies ushered in through synthetic biology have great promise for biomanufacturing, bioremediation, and the development of living therapeutics. Unfortunately, predicting sequence to function relationships, including for biosynthetic pathways expressed in a new host organism, is difficult and often requires many iterative cycles of design, construction, and testing. We are working to develop data-driven approaches to identify the genetic determinants of growth defects and productivity for the expression of a cell-based antimicrobial. We assayed the growth, pigment production, and antimicrobial activity of a collection of over 10,000 genetic mutants of the violacein biosynthetic pathway and sequenced the genetic variation of these mutants. Through this project, we have developed an innovative codebase to automate the determination of pigmentation and antimicrobial clearing diameter for tens of thousands of genetic mutants cultivated on agar dishes. Further, we have written DNA sequence analysis code to demultiplex & provide consensus sequences from high-throughput PacBio long-read circular consensus sequencing (CCS) datasets. From this foundation, we plan to map DNA sequence to function to predict an optimal genetic design to maximize antimicrobial activity while minimizing deleterious growth effects. The workflows and algorithms developed through this project can be broadly applied to other engineered functions in microbes, uncovering sequence to function relationships for complex phenotypes where function impacts fitness.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Determining the Adsorption Energetics of 2,3-Butanediol on RuO 2 (110): Coupling First-Principles Calculations With Global Optimizers

As climate change continues to pose a threat to the Earth due to the disrupted carbon cycles and fossil fuel resources remain finite, new sources of sustainable hydrocarbons must be explored. 2,3-butanediol is a potential source to produce butene because of its sustainability as a biomass-derived sugar. Butene is an attractive product because it can be used as a precursor to jet fuel, categorizing this work in the alcohol-to-jet pathway. While studies have explored the conversion of 2,3-butanediol to butene, little is understood about the fundamental reaction itself. We quantify the energetics for three pathways that were reported in the literature in the absence of a catalyst. One of these pathways forms a 1,3-butadiene intermediate, which is a highly exothermic process and thus is unlikely to occur since 2,3-butanediol likely gets thermodynamically trapped at this intermediate. We further determined the corresponding energetics of 2,3-butanediol adsorption on an ensemble of predetermined binding sites when it interacts with a defect-free stoichiometric RuO 2 (110) surface. Within this ensemble of adsorption sites, the most favorable site has 2,3-butanediol covering a Ru 5–coordinated cation. This approach is compared to that obtained using the global optimization algorithm as implemented in the Northwest Potential Energy Surface Search Engine. When using such a global optimization algorithm, we determined a more favorable ground-state structure that was missed during the manual adsorption site testing, with an adsorption energy of -2.61 eV as compared to -2.34 eV when using the ensemble-based approach. We hypothesize that the dehydration reaction requires a stronger chemical bond, which could necessitate the formation of oxygen vacancies. As such, this study has taken the first step toward the utilization of a global optimization algorithm for the rational design of Ru-based catalysts toward the formation of butene from sustainable resources.

09 BIOMASS FUELS↗
DOE OSTI2023

Integrated Land Suitability Assessment for Depots Siting in a Sustainable Biomass Supply Chain

A sustainable biomass supply chain would require not only an effective and fluid transportation system with a reduced carbon footprint and costs, but also good soil characteristics ensuring durable biomass feedstock presence. Unlike existing approaches that fail to account for ecological factors, this work integrates ecological as well as economic factors for developing sustainable supply chain development. For feedstock to be sustainably supplied, it necessitates adequate environmental conditions, which need to be captured in supply chain analysis. Using geospatial data and heuristics, we present an integrated framework that models biomass production suitability, capturing the economic aspect via transportation network analysis and the environmental aspect via ecological indicators. Production suitability is estimated using scores, considering both ecological factors and road transportation networks. These factors include land cover/crop rotation, slope, soil properties (productivity, soil texture, and erodibility factor) and water availability. This scoring determines the spatial distribution of depots with priority to fields scoring the highest. Two methods for depot selection are presented using graph theory and a clustering algorithm to benefit from contextualized insights from both and potentially gain a more comprehensive understanding of biomass supply chain designs. Graph theory, via the clustering coefficient, helps determine dense areas in the network and indicate the most appropriate location for a depot. Clustering algorithm, via K-means, helps form clusters and determine the depot location at the center of these clusters. An application of this innovative concept is performed on a case study in the US South Atlantic, in the Piedmont region, determining distance traveled and depot locations, with implications on supply chain design. The findings from this study show that a more decentralized depot-based supply chain design with 3depots, obtained using the graph theory method, can be more economical and environmentally friendly compared to a design obtained from the clustering algorithm method with 2 depots. In the former, the distance from fields to depots totals 801,031,476 miles, while in the latter, it adds up to 1,037,606,072 miles, which represents about 30% more distance covered for feedstock transportation.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2024

Machine-assisted discovery of integrable symplectic mappings

Integrable systems possess a hidden symmetry associated with the existence of conserved quantities known as integrals of motion. These systems play an important role in understanding general dynamics in accelerators and have potential for future designs. This work will cover two automated methods for finding integrable symplectic maps of the plane. The first algorithm is based on the observation that the evolution of an integrable system in phase space is confined to a lower-dimensional submanifold of a specific type. The second algorithm relies on an analysis of dynamical variables. Both methods rediscover some of the famous McMillan-Suris integrable mappings and ultra-discrete Painlev\'e equations. Over 100 new integrable families are presented and analyzed, some of which are isolated in the space of parameters, while others are families with one parameter (or the ratio of parameters) being either continuous or discrete. In addition, the newly discovered maps are related to a general 2D symplectic map through the use of discrete perturbation theory. A method is proposed for constructing smooth near-integrable dynamical systems based on mappings with polygon invariants.

43 PARTICLE ACCELERATORS↗