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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

An optimization method for chaotic turbulent flow

Evidence indicates that quantities-of-interest in some turbulent flows can be controlled despite the overall chaotic dynamics. It is typically thought that this is via relatively deterministic, larger-scale components of the turbulence. However, finding such controls, if they exist, is challenging because chaos causes sensitivity gradients to explode and the search space to become intractably non-convex. This challenge is analyzed, and a penalty method is introduced to cope with it. In the new approach, the time domain is broken into segments approximately matching the chaos time scales, so that the solution within each segment is both physical and relatively deterministic. The initial condition of each segment is included in an adjoint-based gradient optimization, which temporarily introduces artificial Δq discontinuities in the overall solution. The optimization then proceeds in stages with increasing penalization of Δq. The method is developed and illustrated for a logistic map, the Lorenz Equation, and an advection augmented Kuramoto–Sivashinsky Equation. These examples show how the Δq temporarily increases the search scale prior to the strong Δq → 0 penalization that recovers a physical solution. It is then applied to turbulent Kolmogorov flow, for which it also far outperforms a standard adjoint-based gradient search. Finally, the utility of such an optimized chaotic solution is discussed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Fast dynamic aperture optimization with forward-reversal integration

A fast dynamic aperture (DA) optimization method for storage rings has been developed through the use of reversal integration. Even if dynamical systems have an exact reversal symmetry, a numerical forward integration differs from its reversal. For a chaotic trajectory, cumulative round-off errors are scaled, which results in an exponential growth on the difference. The exponential effect is a generic chaos indicator which represents the sensitivity of the chaotic motion to its initial condition. The chaos indicator of the charged particle motion can be obtained by comparing the forward integrations of particle trajectories with corresponding reversals, a.k.a. “backward integrations.” The indicator is observable even through short-term particle tracking simulations. Therefore, adopting it as an objective function could speed up optimization. Finally, the DA of the National Synchrotron Light Source II storage ring, and another test diffraction-limited light source ring, were optimized using this method for the purpose of demonstration.

43 PARTICLE ACCELERATORS↗
DOE OSTI2020

Machine Learning Analysis of Direct Dynamics Trajectory Outcomes for Thermal Deazetization of 2,3-Diazabicyclo[2.2.1]hept-2-ene

Experimentally, the thermal gas-phase deazetization of 2,3-diazabicyclo[2.2.1]hept-2-ene (1) results in the loss of N2 and the formation of bicyclo products 3 (exo) and 4 (endo) in a nonstatistical ratio, with preference for the exo product. Here, we report unrestricted M06-2X quasiclassical trajectories initialized from the concerted N2 ejection transition state that were able to replicate the experimental preference to form 3. We found that the 3:4 ratio results from the relative amounts of very fast (ballistic) exotype trajectories versus trajectories that lead to the 1,3-diradical intermediate 2. These quasiclassical trajectories provided a set of transition-state vibrational, velocity, momenta, and geometric features for the machine learning analysis. Additionally, a selection of popular supervised classification algorithms (e.g., random forest) provided poor prediction of trajectory outcomes based on only transition-state vibrational quanta and energy features. However, these machine learning models provided more accurate predictions using atomic velocities and atomic positions, attaining ~70% accuracy using initial conditions and between 85 and 95% accuracy at later reaction time steps. This increased accuracy allowed the feature importance analysis to reveal that, at the later-time analysis, the methylene bridge out-of-plane bending is correlated with trajectory outcomes for the formation of either the exo product or toward the diradical intermediate. Possible reasons for the struggle of machine learning algorithms to classify trajectories based on transition-state features is the heavily overlapping feature values, the finite but very large possible vibrational mode combinations, and the possibility of chaos as trajectories propagate. We examined this chaos by comparing a set of nearly identical trajectories that differed by only a very small scaling of the kinetic energies resulting from the transition-state reaction coordinate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Assessment of radial transport induced by Alfvénic resonances in tokamaks and stellarators

In a symmetric plasma confinement device, a perturbation such as an Alfvén mode produces a resonance island which flattens the local energy gradient due to induced rotation about the elliptic points of the resonance. The location of the resonance is mode frequency and particle energy dependent, and particles away from the resonance are not affected. Here, a projection onto the Poincaré subspace allows the evaluation of resonance widths and internal rotation rates. In a stellarator without symmetry because of the toroidal dependence of the equilibrium magnetic field, a mode instead produces chaos in all orbits passing where the amplitude is large and is, thus, much more effective in producing radial transport and loss. The mode growth rate and saturation are also affected by the local chaos.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Direct stellarator coil optimization for nested magnetic surfaces with precise quasi-symmetry

We present a robust optimization algorithm for the design of electromagnetic coils that generate vacuum magnetic fields with nested flux surfaces and precise quasi-symmetry. The method is based on a bilevel optimization problem, where the outer coil optimization is constrained by a set of inner least squares optimization problems whose solutions describe magnetic surfaces. The outer optimization objective targets coils that generate a field with nested magnetic surfaces and good quasi-symmetry. The inner optimization problems identify magnetic surfaces when they exist, and approximate surfaces in the presence of magnetic islands or chaos. We show that this formulation can be used to heal islands and chaos, thus producing coils that result in magnetic fields with precise quasi-symmetry. We show that the method can be initialized with coils from the traditional two-stage coil design process, as well as coils from a near-axis expansion optimization. We present a numerical example where island chains are healed and quasi-symmetry is optimized up to surfaces with aspect ratio 6. Another numerical example illustrates that the aspect ratio of nested flux surfaces with optimized quasi-symmetry can be decreased from 6 to approximately 4. In conclusion, the last example shows that our approach is robust and a cold-start using coils from a near-axis expansion optimization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Krylov winding and emergent coherence in operator growth dynamics

The operator wavefunction provides a fine-grained description of quantum chaos and of the irreversible growth of simple operators into increasingly complex ones. Remarkably, at finite temperature this wavefunction can acquire a phase that increases linearly with the operator’s size, a phenomenon called . Although size winding occurs naturally in a holographic setting, the emergence of a coherent phase in a scrambled operator remains mysterious from the standpoint of a thermalizing quantum many-body system. Here, in this article, we elucidate this phenomenon by introducing the related concept of , whereby the operator wavefunction acquires a phase which winds linearly with the Krylov index. We show that Krylov winding is a generic feature of quantum chaotic systems and is a direct consequence of the universal operator growth bound hypothesis. It gives rise to size winding under two additional conditions: (i) a low-rank mapping between the Krylov and size bases, which ensures phase alignment among operators of the same size, and (ii) the saturation of the "chaos-operator growth" bound 𝜆 𝐿 ≤ 2⁢𝛼 (with 𝜆 𝐿 the Lyapunov exponent and 𝛼 the growth rate), which ensures a linear phase dependence on size. For systems which do not saturate this bound, with ℎ = 𝜆 𝐿 /2⁢𝛼 < 1, the winding with Pauli size ℓ becomes superliner, behaving as ℓ 1/ℎ . We illustrate these results with two classes of microscopic models: the Sachdev-Ye-Kitaev (SYK) model and its variants, and a disordered 𝑘-local spin model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Online regularization of Poincaré map of storage rings with Shannon entropy

A measurable chaos indicator is used as the online optimization objective in tuning a complicated nonlinear system—the National Synchrotron Light Source-II storage ring. Through analyzing the Shannon entropy in measured Poincaré maps, not only can the commonly used nonlinear characterizations be extracted, but more importantly, the chaos can be quantified and then used for an online regularization of these maps. The method itself is general and applicable to other tunable nonlinear systems as well. Published by the American Physical Society 2025

36 MATERIALS SCIENCE↗
DOE OSTI2020

Early-Time Exponential Instabilities in Nonchaotic Quantum Systems

The majority of classical dynamical systems are chaotic and exhibit the butterfly effect: a minute change in initial conditions has exponentially large effects later on. But this phenomenon is difficult to reconcile with quantum mechanics. One of the main goals in the field of quantum chaos is to establish a correspondence between the dynamics of classical chaotic systems and their quantum counterparts. In isolated systems in the absence of decoherence, there is such a correspondence in dynamics, but it usually persists only over a short time window, after which quantum interference washes out classical chaos. In this work, we demonstrate that quantum mechanics can also play the opposite role and generate exponential instabilities in classically nonchaotic systems within this early-time window. Our calculations employ the out-of-time-ordered correlator (OTOC)—a diagnostic that reduces to the Lyapunov exponent in the classical limit but is well defined for general quantum systems. We show that certain classically nonchaotic models, such as polygonal billiards, demonstrate a Lyapunov-like exponential growth of the OTOC at early times with Planck’s-constant-dependent rates. This behavior is sharply contrasted with the slow early-time growth of the analog of the OTOC in the systems’ classical counterparts. These results suggest that classical-to-quantum correspondence in dynamics is violated in the OTOC even before quantum interference develops.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Integrable symplectic maps with a polygon tessellation

Identifying integrable dynamics remains a formidable challenge, and despite centuries of research, only a handful of examples are known to date. In this article, we explore a distinct form of area-preserving (symplectic) mappings derived from the stroboscopic Poincaré cross section of a kicked rotator—an oscillator subjected to an external force periodically switched on in short pulses. The significance of this class of problems extends to various applications in physics and mathematics, including particle accelerators, crystallography, and studies of chaos. Notably, Suris's theorem constrains the integrability within this category of mappings, outlining potential scenarios with analytic invariants of motion. In this paper, we challenge the assumption of the analyticity of the invariant by exploring piecewise linear transformations on a torus ( T 2 ) and associated systems on the plane ( R 2 ), incorporating arithmetic quasiperiodicity and discontinuities. Introducing a new automated technique, we discovered previously unknown scenarios featuring polygonal invariants that form perfect tessellations and, moreover, fibrations of the plane or torus. This work reveals a novel category of planar tilings characterized by discrete symmetries that emerge from the invertibility of transformations and are intrinsically linked to the presence of integrability. Our algorithm relies on the analysis of the Poincaré rotation number and its piecewise monotonic nature for integrable cases, contrasting with the noisy behavior in the case of chaos, thereby allowing for clear separation. Some of the newly discovered systems exhibit the peculiar behavior of “integrable diffusion,” characterized by infinite and quasirandom hopping between tiles while being confined to a set of invariant segments. Finally, through the implementation of a smoothening procedure, all mappings can be generalized to quasi-integrable scenarios with suppressed volume occupied by chaotic trajectories, thereby opening doors to potential practical applications. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

[Retracted] Research on Application Experience Design of Ice and Snow Sports Equipment Based on Bee Colony Model

Sports equipment is the key to the smooth development of ice and snow sports. With the rapid development of social economy and the improvement of people’s living standards, the demand for ice and snow sports equipment is increasing day by day. This article presents an improved method based on the chaos theory and the bee colony algorithm to quantify the application experience design of ice and snow sports equipment and reduce the influence of uncertain factors on the design results. First, the chaos theory can establish the dataset of application experience design and analyze the discreteness of the set. According to the bee colony algorithm, the dataset is divided into several groups, and each group obtains the best application experience design by using the design optimization strategy. Finally, the results are mixed to obtain the final experience design results. Through MATLAB simulation analysis and verification, the improved bee colony model can improve the accuracy of application experience design of ice and snow sports equipment in an uncertain environment, shorten the overall design time, and meet the requirements of application experience design of different ice and snow sports equipment. Therefore, the model proposed in this paper is suitable for the application experience design of ice and snow sports equipment.

Li, Yuanjing (ORCID:000000018276647X)↗
DOE OSTI2020

Fast Dynamic Aperture Optimization with Reversal Integration

A fast method for dynamic aperture (DA) optimization of storage rings has been developed through the use of reversal integration. Even if dynamical systems have an exact reversal symme- try, a numerical forward integration di ers from its reversal. For chaotic trajectories, cumulative round-o errors are scaled, which results in an exponential growth in the di erence. The exponential e ect, intrinsically associated with the Lyapunov exponent, is a generic indicator of chaos because it represents the sensitivity of chaotic motion to an initial condition. A chaos indicator of the charged particle motion is then obtained by comparing the forward integrations of particle trajectories with corresponding reversals, a.k.a. \backward integrations." The indicator was con rmed to be ob- servable through short-term particle tracking simulations. Therefore, adopting it as an objective function could speed up optimization. The DA of the National Synchrotron Light Source II storage ring, and another test di raction-limited light source ring, were optimized using this method for the purpose of demonstration.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Stochastic Framework for Optimal Control of Planetary Reentry Trajectories Under Multilevel Uncertainties

We present a novel stochastic optimal control framework that accounts for various types of uncertainties, with application to reentry trajectory planning. The formulation of the optimal trajectory control problem is presented in the context of an indirect method where a functional objective associated with the terminal vehicle speed is to be minimized. Uncertain input parameters in the optimal trajectory control model, including aerodynamic parameters and initial and terminal conditions, are modeled as aleatory random variables, while the statistical parameters of these aleatory distributions are themselves random variables. The parametric and model uncertainties are simultaneously propagated through an extended polynomial chaos expansion (EPCE) formalism. Several metrics are described to evaluate response statistics and presented as insightful tools for robust decision making. Specifically, the response probability density function (PDF) reflecting influence of both epistemic and aleatory uncertainties is obtained. By sampling over the random variables representing model error, an ensemble of response PDFs is generated and the associated failure probability is estimated as a random variable with its own polynomial chaos expansion. Besides, the sensitivity index functions of response PDF with respect to the statistical parameters are evaluated. Coupling parametric and model uncertainties within the EPCE framework leads to a robust and efficient paradigm for multilevel uncertainty propagation and PDF characterization in general optimal control problems.

Engineering↗
DOE OSTI2022

Uncertainty Quantification Framework for Predicting Material Response with Large Number of Parameters: Application to Creep Prediction in Ferritic-Martensitic Steels Using Combined Crystal Plasticity and Grain Boundary Models

This paper presents an uncertainty quantification (UQ) framework for the physics-based model prediction of material response with a large number of parameters. The application problem presented in this work is that of predicting creep in Grade 91 steel at 600°C. The material response is defined with a physically based microstructural model with constitutive equations emulating several observed phenomena in Grade 91 and embodied into an explicit geometry mesoscale finite element model for prior austenite grains and grain boundaries. Creep within the grains and in grain boundaries are represented by crystal plasticity for dislocation motion and a physics-based model for cavity growth and nucleation, respectively. The creep behavior of this material is influenced by several parameters, some of which have a wide range of variation based on experimental data. UQ combined with microstructural modeling can discover the core microstructural causes of experimental variability, leading to improved materials with lower variability in critical long-term material properties. In this study, we investigate the model's uncertainty to identify material properties that may be modified during production to increase creep life and analyze different components of the crystal plasticity model for improvements. For this purpose, a quantity of interest is defined as time to minimum creep rate, which correlates well to the creep failure of the material. A deep neural network model was trained and validated to be used as a surrogate for the finite element model. Then, a variance-based sensitivity analysis is performed on the surrogate model to find the Sobol indices of the input parameters in respect to the output quantity of interest. The Sobol indices are used to reduce the dimensionality of the model. Generalized polynomial chaos expansion is used on the reduced basis models to propagate the uncertainty from the input parameters to the quantity of interest using the deep neural network surrogate model. These results are benchmarked against uncertainty propagation using Monte Carlo simulations. In conclusion, the UQ performed through the reduced basis model captures almost all the uncertainty in the model with significantly fewer simulations, making it possible to perform the UQ directly via simulations with the finite element model rather than surrogate machine-learned models.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Isochronous and period-doubling diagrams for symplectic maps of the plane

Symplectic mappings of the plane serve as key models for exploring the fundamental nature of complex behavior in nonlinear systems. Central to this exploration is the effective visualization of stability regimes, which enables the interpretation of how systems evolve under varying conditions. While the area-preserving quadratic Hénon map has received significant theoretical attention, a comprehensive description of its mixed parameter-space dynamics remain lacking. This limitation arises from early attempts to reduce the full two-dimensional phase space to a one-dimensional projection, a simplification that resulted in the loss of important dynamical features. Consequently, there is a clear need for a more thorough understanding of the underlying qualitative aspects. This paper aims to address this gap by revisiting the foundational concepts of reversibility and associated symmetries, first explored in the early works of G.D. Birkhoff. We extend the original framework proposed by Hénon by adding a period-doubling diagram to his isochronous diagram, which allows to represents the system’s bifurcations and the groups of symmetric periodic orbits that emerge in typical bifurcations of the fixed point. A qualitative and quantitative explanation of the main features of the region of parameters with bounded motion is provided, along with the application of this technique to other symplectic mappings, including cases of multiple reversibility. Modern chaos indicators, such as the Reversibility Error Method (REM) and the Generalized Alignment Index (GALI), are employed to distinguish between various dynamical regimes in the mixed space of variables and parameters. These tools prove effective in differentiating regular and chaotic dynamics, as well as in identifying twistless orbits and their associated bifurcations. Additionally, we discuss the application of these methods to real-world problems, such as visualizing dynamic aperture in accelerator physics, where our findings have direct relevance.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

A functional global sensitivity measure and efficient reliability sensitivity analysis with respect to statistical parameters

Sensitivity analysis and reliability assessment are two important aspects of structural and system safety. Epistemic uncertainty with respect to probabilistic model of input parameters due to lack of knowledge is present in many scarce-data applications and complicates the characterization of uncertainty in model response. In this article, we present two importance measures to evaluate the impact of distribution parameters on the probability distribution function (PDF) of the output and the failure probability. The epistemic uncertainty associated with the distribution parameters is modeled as random variables. Additionally, a modified extended polynomial chaos expansion (MEPCE) approach is introduced in which aleatory and epistemic random variables are modeled and propagated simultaneously while allowing the separate assessment for any single epistemic variable. A MEPCE-based kernel density estimation (KDE) construction provides a composite map from each epistemic variable to the response PDF. The functional global sensitivity index of the PDF with respect to the distribution parameters is thus derived, as a function of output, which is both more informative and more efficient than standard scalar sensitivity measures. Reliability sensitivity indices can be readily evaluated by integrating the global sensitivity index function over the failure zone. Three illustrative examples are used to demonstrate the proposed methodology.

42 ENGINEERING↗
DOE OSTI2023

Multifidelity uncertainty quantification with models based on dissimilar parameters

Multifidelity uncertainty quantification (MF UQ) sampling approaches have been shown to significantly reduce the variance of statistical estimators while preserving the bias of the highest-fidelity model, provided that the low-fidelity models are well correlated. However, maintaining a high level of correlation can be challenging, especially when models depend on different input uncertain parameters, which drastically reduces the correlation. Existing MF UQ approaches do not adequately address this issue. In this work, we propose a new sampling strategy that exploits a shared space to improve the correlation among models with dissimilar parameterization. We achieve this by transforming the original coordinates onto an auxiliary manifold using the adaptive basis (AB) method (Tipireddy and Ghanem, 2014). The AB method has two main benefits: (1) it provides an effective tool to identify the low-dimensional manifold on which each model can be represented, and (2) it enables easy transformation of polynomial chaos representations from high- to low-dimensional spaces. This latter feature is used to identify a shared manifold among models without requiring additional evaluations. Here we present two algorithmic flavors of the new estimator to cover different analysis scenarios, including those with legacy and non-legacy high-fidelity (HF) data. We provide numerical results for analytical examples, a direct field acoustic test, and a finite element model of a nuclear fuel assembly. For all examples, we compare the proposed strategy against both single-fidelity and MF estimators based on the original model parameterization.

42 ENGINEERING↗
DOE OSTI2022

Stochastic boundary condition effects on supersonic leading edge blowing

The present manuscript studies the robustness of leading edge blowing for active control of the upstream bow shock and overall aerothermal characteristics of a supersonic airfoil subject to variability in the injection conditions. The injection boundary conditions were considered stochastic and their randomness was propagated to the flow topology and aerothermal quantities of interest by means of non-intrusive Polynomial Chaos Expansions. The evaluations needed to build these expansions were carried out via steady two-dimensional Reynolds-Averaged Navier Stokes simulations. Two different injection port sizes were considered, with the smallest promoting a Coanda effect that gives rise to non-symmetric flow topologies. The uncertain boundary conditions lead to significant variations in the flow topology, particularly at the injection exit and the bow shock position, with variations of up to 75% of the nominal value. Here this study identifies the key operating conditions to ensure the optimal application of leading-edge injection for active control of supersonic airfoils.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A modular methodology for time-domain stochastic seismic wave propagation

Presented here is a modular methodology for time-domain stochastic seismic wave propagation analysis. Presented methodology is designed to analyse uncertain seismic motions as an input, propagating through uncertain material. Traditional approach for uncertain wave propagation relies on models that include deep bedrock, local soil site, and their random process and random field information. Such models can become quite large and computationally intractable. The modular approach proposed herein features two step approach that allows separate consideration of the deep bedrock and local site along with corresponding random field information. In this work, the first step considers an auxiliary stochastic motions problem in the bedrock. Stochastic local site response can then be simulated in a reduced domain within certain depth from the surface. Application of uncertain seismic motions at depth, for local uncertain site response is done using stochastic effective forces developed through the Domain Reduction Method. By using Hermite polynomial chaos expansion to represent the non-Gaussian random field of material parameters and non-stationary random process of seismic motion, the proposed modular methodology is formulated using intrusive stochastic Galerkin approach, as seen in the Stochastic Elastic–Plastic Finite Element Method (SEPFEM). Developed modular methodology is illustrated using a 1-D stochastic seismic wave propagation analysis with three cases, and simulation results are also verified with results from conventional approach.

58 GEOSCIENCES↗