Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “parameterized dynamical systems”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Object-Based Evaluation of Tropical Precipitation Systems in DYAMOND Simulations over the Maritime Continent

The present study uses an object-based evaluation metric to examine the precipitation bias over the Maritime Continent in the global cloud-resolving models. We specifically focus on the difference between the models that directly resolve convection and those using convection parameterization. The 40-day hindcast experiments of the DYnamics of the Atmospheric general circulation Modeled On Non-hydrostatic Domain (DYAMOND) intercomparison project are evaluated against the high-resolution satellite rainfall products. The hindcast of the Central Weather Bureau Global Forecast System (CWBGFS) under the DYAMOND protocol is also included. The results indicate that most models simulate insufficient numbers of large precipitation system [object-based precipitation system (OPS), > 370 km in scale], indicating weaker convection organization. The observation indicates that the maximum precipitation within the OPS intensifies with increasing object size. All of the models capture this positive relationship, but most of them overestimate the sensitivity. Most of the models overestimate both the frequency and intensity of small OPS (< 160 km), except for the models with convection parameterization [i.e., CWBGFS, European Centre for Medium-Range Weather Forecasts Integrated Forecasting System (IFS)-9 km]. Although most of the models can reproduce the observed peak time of diurnal precipitation over the land area in the Maritime Continent, the simulated fractional contribution of different sizes of OPS to the total precipitation varies from model to model, and their peak times do not follow the observed ones with delayed peak times as the size of OPS increases from small, mid-size, to large categories. Most of the models reasonably capture the mean diurnal cycle peak time, but only the models with convection parameterization and Model for Prediction Across Scales (MPAS) can represent the diurnal evolution of fractional contribution from different OPSs. The implications of the current results to the upscale processes of the tropical convection systems in the global models are also discussed.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Quantum optimal control for pure-state preparation using one initial state

This paper presents a framework for solving the pure-state preparation problem using numerical optimal control. As an example, we consider the case where a number of qubits are dispersively coupled to a readout cavity. Herein, we model open system quantum dynamics using the Markovian Lindblad master equation driven by external control pulses. The main result of this paper develops a basis of density matrices (a parameterization) where each basis element is a density matrix by itself. Utilizing a specific objective function, we show how an ensemble of the basis elements can be used as a single initial state throughout the optimization process—independent of the system dimension. We apply the general framework to the specific application of ground-state reset of one and two qubits coupled to a readout cavity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Integrating Characteristic Arctic Vegetation in a Land Surface Model Improves Representation of Carbon Dynamics Across a Tundra Landscape

Arctic warming is altering vegetation and carbon dynamics with global implications, yet Earth System Model (ESM) predictions in the Arctic remain highly uncertain, in part due to historically limited data for model parameterization and validation. As such, ESMs typically represent Arctic ecosystems in an oversimplified manner. Recently, nine plant functional types (PFTs) designed to realistically represent tundra vegetation were integrated into the Energy Exascale Earth System Model (E3SM) Land Model (ELM) and parameterized using plot-scale observations from a single site. Additional evaluation was needed to determine their transferability across the Arctic. Here, in this study, we evaluated whether refined representation of tundra vegetation improved model accuracy by conducting spatially explicit 100 × 100 m resolution ELM simulations on Alaska's Seward Peninsula. Simulations with the default two-PFT configuration and with the nine Arctic-specific PFTs were benchmarked against observations of net ecosystem exchange, gross primary production, and aboveground biomass from multiple data streams including an eddy covariance flux tower, flux chambers, and aircraft and unoccupied aerial system hyperspectral remote sensing. Evaluation revealed that Arctic-specific PFT simulations produced more realistic landscape-level carbon exchanges, and better captured observed heterogeneity in biomass and productivity, explaining 60%–70% of spatial variance (R 2 = 0.6–0.7) compared to just 12%–18% (R 2 = 0.12–0.18) with the default configuration. However, the refined model failed to reproduce observed aboveground biomass for highly productive alder-willow communities, requiring further evaluation of carbon allocation parameterizations for tall shrubs that are increasingly expanding across tundra landscapes. Our results demonstrate that enhanced representation of vegetation heterogeneity boosts predictive understanding of tundra carbon dynamics, facilitating regional to pan-Arctic model and remote-sensing scaling.

Murphy, Bailey A. [Oak Ridge National Laboratory (↗
DOE OSTI2026

Higher-order LaSDI: Reduced order modeling with multiple time derivatives

Solving complex partial differential equations (PDEs) is essential across scientific disciplines but often requires numerical models that can be prohibitively expensive in time-sensitive applications. Reduced-order models (ROMs) address this challenge by exploiting low-dimensional structure to create fast approximations. The Latent Space Dynamics Identification (LaSDI) framework has demonstrated success in learning ROMs for parameterized PDE families, but remains limited to first-order systems. Here, in this paper, we propose Higher-Order LaSDI (HLaSDI), which extends the LaSDI framework to PDEs with arbitrary order of time derivatives. This generalization significantly expands the applicability of LaSDI-based methods to systems previously outside their scope, including hyperbolic PDEs. We demonstrate HLaSDI’s accuracy and efficiency on several linear and nonlinear benchmark problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Cluster-dynamics-based parameterization for sulfuric acid–dimethylamine nucleation: comparison and selection through box and three-dimensional modeling

Clustering of gaseous sulfuric acid (SA) enhanced by dimethylamine (DMA) is a major mechanism for new particle formation (NPF) in polluted atmospheres. However, uncertainty remains regarding the SA–DMA nucleation parameterization that reasonably represents cluster dynamics and is applicable across various atmospheric conditions. This uncertainty hinders accurate three-dimensional (3-D) modeling of NPF and the subsequent assessment of its environmental and climatic impacts. Here we extensively compare different cluster-dynamics-based parameterizations for SA–DMA nucleation and identify the most reliable one through a combination of box model simulations, 3-D modeling, and in situ observations. Results show that the parameterization derived from Atmospheric Cluster Dynamic Code (ACDC) simulations, incorporating the latest theoretical insights (DLPNO-CCSD(T)/aug-cc-pVTZ//ωB97X-D/6-311++G(3df,3pd) level of theory) and adequate representation of cluster dynamics, exhibits dependable performance in 3-D NPF simulation for both winter and summer conditions in Beijing and shows promise for application in diverse atmospheric conditions. Another ACDC-derived parameterization, replacing the level of theory with RI-CC2/aug-cc-pV(T+d)Z//M06-2X/6–311++G(3df,3pd), also performs well in NPF modeling at relatively low temperatures around 280 K but exhibits limitations at higher temperatures due to inappropriate representation of SA–DMA cluster thermodynamics. Additionally, a previously reported parameterization incorporating simplifications is applicable for simulating NPF in polluted atmospheres but tends to overestimate particle formation rates under conditions of elevated temperature (>∼300 K) and low-condensation sink (<∼3×10 -3 s −1 ). Our findings highlight the applicability of the new ACDC-derived parameterization, which couples the latest SA–DMA nucleation theory and holistic cluster dynamics, in 3-D NPF modeling. The ACDC-derived parameterization framework provides a valuable reference for developing parameterizations for other nucleation systems.

Shen, Jiewen↗
DOE OSTI2022

Evaluating power grid model hydropower feasibility with a river operations model

Production cost models (PCMs) simulate dispatch of generators across a large power grid and are used widely by planners to study the reliability of electricity supply. As energy systems transition away from the thermoelectric technologies that have traditionally balanced electricity supply and demand, hydropower and its representation in PCMs is of increasing importance. A limitation of PCMs applied to continental power grids with diverse generation portfolios is that hydropower generation is simulated without full consideration of complex river dynamics, leading to possible misrepresentation of grid flexibility and performance. In addition, data used in PCMs may reflect outdated operating policies. In this paper we propose a hydropower generation feasibility test for PCMs. The approach uses a detailed hydropower model to determine whether the hourly hydropower schedule from a PCM with simplified monthly parameterization can be attained after accounting for realistic river dynamics and operating policies, such as spill requirements and general water movement and balance through a cascade reservoir system. We perform this hydropower generation test for the ‘Big 10’ hydropower system on the Columbia River (part of the Western Interconnect of the United States), revealing 9% overestimation of available hydropower generation in a PCM solution in an average hydrologic year. Our evaluation provides insight on the cost and opportunities for better representing hydropower in PCMs.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Recent Advances in Small Angle X-ray Scattering for Superlattice Study

Small-angle x-ray scattering is used for the structure determination of superlattice for its superior resolution, nondestructive nature, and high penetration power of x rays. With the advent of high brilliance x-ray sources and innovative computing algorithms, there have been notable advances in small angle x-ray scattering analysis of superlattices. High brilliance x-ray beams have made data analyses less model-dependent. Additionally, novel data acquisition systems are faster and more competitive than ever before, enabling a more accurate mapping of the superlattices' reciprocal space. Fast and high-throughput computing systems and algorithms also make possible advanced analysis methods, including iterative phasing algorithms, non-parameterized fitting of scattering data with molecular dynamics simulations, and the use of machine learning algorithms. As a result, solving nanoscale structures with high resolutions has become an attainable task. In this review, we highlight new developments in the field and introduce their applications for the analysis of nanoscale ordered structures, including nanoparticle supercrystals, nanoscale lithography patterns, and supramolecular self-assemblies. Particularly, we highlight the reciprocal space mapping techniques and the use of iterative phase retrieval algorithms. We also cover coherent-beam-based small angle x-ray scattering techniques such as ptychography and ptycho-tomography in view of the traditional small angle x-ray scattering perspective.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Parameterization of generic positive sequence models to represent behavior of inverter based resources in low short circuit scenarios

The connection of large inverter based resources (IBR) in transmission systems is often located geographically and electrically far away from load centers. This, coupled with the displacement of synchronous machine plants, results in a reduction of the network short circuit strength at the point of connection. Under these conditions, state-of-the-art positive sequence simulation platforms and models can have difficulties maintaining numerical stability and/or providing an accurate representation of IBR plant dynamic behavior. As a result, computationally heavy time domain electromagnetic transient (EMT) simulations may be required to evaluate these systems. In this paper, a recently developed improved generic positive sequence model is parameterized to provide a representation of IBR behavior in low short circuit networks. Further, comparisons against generic and detailed EMT models demonstrate the suitability of the improved positive sequence model to study practical stability issues experienced with presently in-service plants. Such a model can provide some of the accuracy of an EMT representation with a much lower computational burden. The performance of the positive sequence model is validated against the behavior shown by both open white box and closed black box EMT domain models from around the world.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

The Simple Cloud-Resolving E3SM Atmosphere Model Running on the Frontier Exascale System

We present an efficient and performance portable implementation of the Simple Cloud Resolving E3SM Atmosphere Model (SCREAM). SCREAM is a full featured atmospheric global circulation model with a nonhydrostatic dynamical core and state-of-the-art parameterizations for microphysics, moist turbulence and radiation. It has been written from scratch in C++ with the Kokkos library used to abstract the on-node execution model for both CPUs and GPUs. SCREAM is one of only a few global atmosphere models to be ported to GPUs. As far as we know, SCREAM is the first such model to run on both AMD GPUs and NVIDIA GPUs, as well as the first to run on nearly an entire Exascale system (Frontier). On Frontier, we obtained a record setting performance of 1.26 simulated years per day for a realistic cloud resolving simulation.

Taylor, Mark↗
DOE OSTI2023

A dynamic kinetic model captures cell-free metabolism for improved butanol production

Cell-free systems are useful tools for prototyping metabolic pathways and optimizing the production of various bioproducts. Mechanistically-based kinetic models are uniquely suited to analyze dynamic experimental data collected from cell-free systems and provide vital qualitative insight. However, to date, dynamic kinetic models have not been applied with rigorous biological constraints or trained on adequate experimental data to the degree that they would give high confidence in predictions and broadly demonstrate the potential for widespread use of such kinetic models. In this work, we construct a large-scale dynamic model of cell-free metabolism with the goal of understanding and optimizing butanol production in a cell-free system. Using a combination of parameterization methods, the resultant model captures experimental metabolite measurements across two experimental conditions for nine metabolites at timepoints between 0 and 24 hours. Here, we present analysis of the model predictions, provide recommendations for butanol optimization, and identify the aldehyde/alcohol dehydrogenase as the primary bottleneck in butanol production. Sensitivity analysis further reveals the extent to which various parameters are constrained, and our approach for probing valid parameter ranges can be applied to other modeling efforts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

The Strong Impact of Weak Horizontal Convergence on Continental Shallow Convection

Idealized large-eddy simulation (LES) is a basic tool for studying three-dimensional turbulence in the planetary boundary layer. LES is capable of providing benchmark solutions for parameterization development efforts. However, real small-scale atmospheric flows develop in heterogeneous and transient environments with locally varying vertical motions inherent to open multiscale interactive dynamical systems. These variations are often too subtle to detect them by state-of-the-art remote and in situ measurements, and are typically excluded from idealized simulations. The present study addresses the impact of weak [i.e., O(10-6) s-1] short-lived low-level large-scale convergence/divergence perturbations on continental shallow convection. The results show a strong response of shallow nonprecipitating convection to the applied weak large-scale dynamical forcing. Evolutions of CAPE, mean liquid water path, and cloud-top heights are significantly affected by the imposed convergence/divergence. In contrast, evolving cloud-base properties, such as the area coverage and mass flux, are only weakly affected. To contrast those impacts with microphysical sensitivity, the baseline simulations are perturbed assuming different observationally based cloud droplet number concentrations and thus different rainfall. For the tested range of microphysical perturbations, the imposed convergence/divergence provides significantly larger impact than changes in the cloud microphysics. Simulation results presented here provide a stringent test for convection parameterizations, especially important for large-scale models progressing toward resolving some nonhydrostatic effects.

Meteorology & Atmospheric Sciences↗
DOE OSTI2024

Causally‐Informed Deep Learning to Improve Climate Models and Projections

Abstract Climate models are essential to understand and project climate change, yet long‐standing biases and uncertainties in their projections remain. This is largely associated with the representation of subgrid‐scale processes, particularly clouds and convection. Deep learning can learn these subgrid‐scale processes from computationally expensive storm‐resolving models while retaining many features at a fraction of computational cost. Yet, climate simulations with embedded neural network parameterizations are still challenging and highly depend on the deep learning solution. This is likely associated with spurious non‐physical correlations learned by the neural networks due to the complexity of the physical dynamical system. Here, we show that the combination of causality with deep learning helps removing spurious correlations and optimizing the neural network algorithm. To resolve this, we apply a causal discovery method to unveil causal drivers in the set of input predictors of atmospheric subgrid‐scale processes of a superparameterized climate model in which deep convection is explicitly resolved. The resulting causally‐informed neural networks are coupled to the climate model, hence, replacing the superparameterization and radiation scheme. We show that the climate simulations with causally‐informed neural network parameterizations retain many convection‐related properties and accurately generate the climate of the original high‐resolution climate model, while retaining similar generalization capabilities to unseen climates compared to the non‐causal approach. The combination of causal discovery and deep learning is a new and promising approach that leads to stable and more trustworthy climate simulations and paves the way toward more physically‐based causal deep learning approaches also in other scientific disciplines.

Meteorology & Atmospheric Sciences↗
DOE OSTI2020

Dynamic projection of anthropogenic emissions in China: methodology and 2015–2050 emission pathways under a range of socio-economic, climate policy, and pollution control scenarios

Abstract. Future trends in air pollution and greenhouse gas (GHG)emissions for China are of great concern to the community. A set of globalscenarios regarding future socio-economic and climate developments, combiningshared socio-economic pathways (SSPs) with climate forcing outcomes asdescribed by the Representative Concentration Pathways (RCPs), was createdby the Intergovernmental Panel on Climate Change (IPCC). Chinese researchers have also developed various emission scenarios by considering detailed local environmental and climate policies. However, a comprehensive scenario set connecting SSP–RCP scenarios with local policies and representing dynamic emission changes under local policies is still missing. In this work, to fill this gap, we developed a dynamic projection model, the Dynamic Projection model for Emissions in China (DPEC), to explore China'sfuture anthropogenic emission pathways. The DPEC is designed tointegrate the energy system model, emission inventory model, dynamicprojection model, and parameterized scheme of Chinese policies. The modelcontains two main modules, an energy-model-driven activity rate projectionmodule and a sector-based emission projection module. The activity rateprojection module provides the standardized and unified future energyscenarios after reorganizing and refining the outputs from the energy systemmodel. Here we use a new China-focused version of the Global ChangeAssessment Model (GCAM-China) to project future energy demand and supply inChina under different SSP–RCP scenarios at the provincial level. Theemission projection module links a bottom-up emission inventory model, theMulti-resolution Emission Inventory for China (MEIC), to GCAM-China andaccurately tracks the evolution of future combustion and production technologiesand control measures under different environmental policies. We developedtechnology-based turnover models for several key emitting sectors (e.g.coal-fired power plants, key industries, and on-road transportationsectors), which can simulate the dynamic changes in the unit/vehicle fleetturnover process by tracking the lifespan of each unit/vehicle on an annualbasis. With the integrated modelling framework, we connected five SSP scenarios(SSP1–5), five RCP scenarios (RCP8.5, 7.0, 6.0, 4.5, and 2.6), and threepollution control scenarios (business as usual, BAU; enhanced controlpolicy, ECP; and best health effect, BHE) to produce six combined emissionscenarios. With those scenarios, we presented a wide range of China's futureemissions to 2050 under different development and policy pathways. We foundthat, with a combination of strong low-carbon policy and air pollutioncontrol policy (i.e. SSP1-26-BHE scenario), emissions of major airpollutants (i.e. SO 2 , NO x , PM 2.5 , and non-methane volatile organic compounds – NMVOCs) in China willbe reduced by 34%–66% in 2030 and 58%–87% in 2050 compared to 2015. End-of-pipe control measures are more effective for reducing air pollutant emissions before 2030, while low-carbon policy will play a more important rolein continuous emission reduction until 2050. In contrast, China's emissionswill remain at a high level until 2050 under a reference scenario without activeactions (i.e. SSP3-70-BAU). Compared to similar scenarios set from theCMIP6 (Coupled Model Intercomparison Project Phase 6), our estimates ofemission ranges are much lower than the estimates from the harmonized CMIP6 emissions dataset in2020–2030, but their emission ranges become similar in the year 2050.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Data-driven discovery of dynamics from time-resolved coherent scattering

Coherent X-ray scattering (CXS) techniques are capable of interrogating dynamics of nano- to mesoscale materials systems at time scales spanning several orders of magnitude. However, obtaining accurate theoretical descriptions of complex dynamics is often limited by one or more factors—the ability to visualize dynamics in real space, computational cost of high-fidelity simulations, and effectiveness of approximate or phenomenological models. In this work, we develop a data-driven framework to uncover mechanistic models of dynamics directly from time-resolved CXS measurements without solving the phase reconstruction problem for the entire time series of diffraction patterns. Our approach uses neural differential equations to parameterize unknown real-space dynamics and implements a computational scattering forward model to relate real-space predictions to reciprocal-space observations. This method is shown to recover the dynamics of several computational model systems under various simulated conditions of measurement resolution and noise. Moreover, the trained model enables estimation of long-term dynamics well beyond the maximum observation time, which can be used to inform and refine experimental parameters in practice. Finally, we demonstrate an experimental proof-of-concept by applying our framework to recover the probe trajectory from a ptychographic scan. Our proposed framework bridges the wide existing gap between approximate models and complex data.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Physics-Informed Gaussian Process Regression for States Estimation and Forecasting in Power Grids

Real-time state estimation and forecasting are critical for the efficient operation of power grids. In this paper, a physics-informed Gaussian process regression (PhI-GPR) method is presented and used for forecasting and estimating the phase angle, angular speed, and wind mechanical power of a three-generator power grid system using sparse measurements. In standard data-driven Gaussian process regression (GPR), parameterized models for the prior statistics are fit by maximizing the marginal likelihood of observed data. In the PhI-GPR method, we propose to compute the prior statistics offline by solving stochastic differential equations (SDEs) governing the power grid dynamics. The short-term forecast of a power grid system dominated by wind generation is complicated by the stochastic nature of the wind and the resulting uncertainty in wind mechanical power. Here, we assume that the power grid dynamics are governed by swing equations, with the wind mechanical power fluctuating randomly in time. We solve these equations for the mean and covariances of the power grid states using the Monte Carlo simulation method. We demonstrate that the proposed PhI-GPR method can accurately forecast and estimate observed and unobserved states. For the considered problem, PhI-GPR has computational advantages over the ensemble Kalman filter (EnKF) method: In PhI-GPR, ensembles are computed offline and independently of the data acquisition process, whereas for EnFK, ensembles are computed online with data acquisition, rendering real-time forecast more challenging. We also demonstrate that the PhI-GPR forecast is more accurate than the EnKF forecast when the random mechanical wind power is non-Markovian. In contrast, the two methods produce similar forecasts for the Markovian mechanical wind power. For observed states, we show that PhI-GPR provides a forecast comparable to the standard data-driven GPR; both forecasts are significantly more accurate than the autoregressive integrated moving average (ARIMA) forecast. We also show that the ARIMA forecast is more sensitive to observation frequency and measurement errors than the PhI-GPR forecast.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Validation and parameterization of a novel physics-constrained neural dynamics model applied to turbulent fluid flow

We report, in fluid physics, data-driven models to enhance or accelerate time to solution are becoming increasingly popular for many application domains, such as alternatives to turbulence closures, system surrogates, or for new physics discovery. In the context of reduced order models of high-dimensional time-dependent fluid systems, machine learning methods grant the benefit of automated learning from data, but the burden of a model lies on its reduced-order representation of both the fluid state and physical dynamics. In this work, we build a physics-constrained, data-driven reduced order model for Navier–Stokes equations to approximate spatiotemporal fluid dynamics in the canonical case of isotropic turbulence in a triply periodic box. The model design choices mimic numerical and physical constraints by, for example, implicitly enforcing the incompressibility constraint and utilizing continuous neural ordinary differential equations for tracking the evolution of the governing differential equation. We demonstrate this technique on a three-dimensional, moderate Reynolds number turbulent fluid flow. In assessing the statistical quality and characteristics of the machine-learned model through rigorous diagnostic tests, we find that our model is capable of reconstructing the dynamics of the flow over large integral timescales, favoring accuracy at the larger length scales. More significantly, comprehensive diagnostics suggest that physically interpretable model parameters, corresponding to the representations of the fluid state and dynamics, have attributable and quantifiable impact on the quality of the model predictions and computational complexity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

SympGNNs: Symplectic Graph Neural Networks for identifying high-dimensional Hamiltonian systems and node classification

Existing neural network models to learn Hamiltonian systems, such as SympNets, although accurate in low-dimensions, struggle to learn the correct dynamics for high-dimensional many-body systems. Herein, we introduce Symplectic Graph Neural Networks (SympGNNs) that can effectively handle system identification in high-dimensional Hamiltonian systems, as well as node classification. SympGNNs combine symplectic maps with permutation equivariance, a property of graph neural networks. Specifically, we propose two variants of SympGNNs: (i) G-SympGNN and (ii) LA-SympGNN, arising from different parameterizations of the kinetic and potential energy. We demonstrate the capabilities of SympGNN on two physical examples: a 40-particle coupled Harmonic oscillator, and a 2000-particle molecular dynamics simulation in a two-dimensional Lennard-Jones potential. Furthermore, we demonstrate the performance of SympGNN in the node classification task, achieving accuracy comparable to the state-of-the-art. Finally, we also empirically show that SympGNN can overcome the oversmoothing and heterophily problems, two key challenges in the field of graph neural networks.

Deep learning↗
DOE OSTI2025

Dynamics of McMillan mappings II. axially symmetric map

Here, in this article, we investigate the transverse dynamics of a single particle in a model integrable accelerator lattice, based on a McMillan axially-symmetric electron lens. Although the McMillan e-lens has been considered as a device potentially capable of mitigating collective space charge forces, some of its fundamental properties have not been described yet. The main goal of our work is to close this gap and understand the limitations and potentials of this device. It is worth mentioning that the McMillan axially symmetric map provides the first-order approximations of dynamics for a general linear lattice plus an arbitrary thin lens with motion separable in polar coordinates. Therefore, advancements in its understanding should give us a better picture of more generic and not necessarily integrable round beams. In the first part of the article, we classify all possible regimes with stable trajectories and find the canonical action-angle variables. This provides an evaluation of the dynamical aperture, Poincaré rotation numbers as functions of amplitudes, and thus determines the spread in nonlinear tunes. Also, we provide a parameterization of invariant curves, allowing for the immediate determination of the map image forward and backward in time. The second part investigates the particle dynamics as a function of system parameters. We show that there are three fundamentally different configurations of the accelerator optics causing different regimes of nonlinear oscillations. Each regime is considered in great detail, including the limiting cases of large and small amplitudes. In addition, we analyze the dynamics in Cartesian coordinates and provide a description of observable variables and corresponding spectra.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗