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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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DOE OSTI2024

Approximate Entropy Analysis for Nonlinear Beam Dynamics

In this paper, we applied an approximate entropy (ApEn) analysis to nonlinear beam dynamics. Due to the presence of strong nonlinear magnets, the degree of chaos in beam motion gradually increases proportionally with its amplitude. Such chaos can be quantitatively characterized with ApEn of beam turn-by-turn readings. ApEn analysis is a technique used to quantify the amount of regularity and the unpredictability of fluctuations with respect to time-series data. The ApEn, when applied as a chaos indicator, can then be used for nonlinear lattice optimization and analysis. The National Synchrotron Light Source II (NSLS-II) electron storage ring lattice was used as an example of a real-world application of our technique.

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

Programmatic Advantages of Linear Equivalent Seismic Models

Underground explosions nonlinearly deform the surrounding earth material and can interact with the free surface to produce spall. However, at typical seismological observation distances the seismic wavefield can be accurately modeled using linear approximations. Although nonlinear algorithms can accurately simulate very near field ground motions, they are computationally expensive and potentially unnecessary for far field wave simulations. Conversely, linearized seismic wave propagation codes are orders of magnitude faster computationally and can accurately simulate the wavefield out to typical observational distances. Thus, devising a means of approximating a nonlinear source in terms of a linear equivalent source would be advantageous both for scenario modeling and for interpretation of seismic source models that are based on linear, far-field approximations. This allows fast linear seismic modeling that still incorporates many features of the nonlinear source mechanics built into the simulation results so that one can have many of the advantages of both types of simulations without the computational cost of the nonlinear computation. In this report we first show the computational advantage of using linear equivalent models, and then discuss how the near-source (within the nonlinear wavefield regime) environment affects linear source equivalents and how well we can fit seismic wavefields derived from nonlinear sources.

58 GEOSCIENCES↗
DOE OSTI2022

Approximating a linear multiplicative objective in watershed management optimization

Implementing management practices in a cost-efficient manner is critical for regional efforts to reduce the amount of pollutants entering the Chesapeake Bay. We study the problem of selecting a subset of practices that minimizes pollutant load—subject to budgetary and environmental constraints—as simulated in a widely used regulatory watershed model. Mimicking the computation of pollutant load in the regulatory model, we formulate this problem as a continuous optimization model with a linear multiplicative objective function and linear constraints. To lay the groundwork for incorporating additional stakeholder requirements in the future, especially those that would require integer variables, we present and study a continuous linear optimization model that approximates the nonlinear model. The linear model, which requires an exponential number of variables, arises naturally as an alternative model for the same underlying physical process. We examine the theoretical behavior of these optimization models and investigate restrictions of the linear model to handle its large number of variables. Through extensive computational tests on real and randomly generated instances, we demonstrate that the linear model and its restrictions provide optimal solutions close to those of the nonlinear model in practice, despite poor approximation properties in the worst case. We conclude that the linear model—together with our approach to handling its large number of variables—provides a viable framework from which to extend the optimization model to better meet the needs of the Chesapeake Bay watershed management stakeholders.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Development of a Control Co-Design Modeling Tool for Marine Hydrokinetic Turbines: Preprint

This report describes the ongoing and planned development of the software package CT-Opt (Current/Tidal Optimization), a control co-design modeling tool for marine hydrokinetic turbines. The commercialization of these turbines has faced significant challenges due to the complex, multidisciplinary nature of their design and the extreme environmental conditions of their operation. This project aims to create a modeling tool that will enable the efficient design of robust, cost-competitive hydrokinetic turbine systems. Rather than using traditional optimization methods, CT-Opt combines multiple models across a range of fidelities to enable coupled optimization of the system design and system controller via a control co-design approach. With this method, the parameters that affect system performance are considered more comprehensively at every stage of the design process. The lowest-fidelity, frequency-domain model called by CT-Opt is RAFT (Response Amplitudes of Floating Turbines), which was originally developed by the National Renewable Energy Laboratory (NREL) to model response amplitudes of floating offshore wind turbines. The highest-fidelity, time-domain model is OpenFAST, which was developed by NREL for land-based and offshore wind turbines. As part of the CT-Opt project, new functionalities will be added to RAFT and OpenFAST to enable the accurate simulation of fixed and floating marine hydrokinetic turbines. In addition to expanding the capabilities of RAFT and OpenFAST, new midfidelity models will be developed. These models will be based on RAFT and OpenFAST and will consist of linearized, state-space models derived from the fully coupled, nonlinear OpenFAST equations and derivative function surrogate models that approximate the nonlinear system behavior. Each model will be coupled with controllers to allow control co-design methods to be applied both within models and across fidelity levels, enabling efficient system optimization.

control co-design↗
DOE OSTI2021

Drift waves enstrophy, zonal flow, and nonlinear evolution of the modulational instability

The interaction of the drift wave (DW) turbulence and zonal flow (ZF) is investigated with the modified Hasegawa–Mima equation taking into account the backreaction of ZF velocity on DW turbulence. It is shown that the y-averaged enstrophy of DW turbulence and the velocity of ZF are intrinsically related. By utilizing this feature, a nonlinear stage of DW modulational instability is considered within the framework of the wave kinetic equation. It is shown that in this approximation, the nonlinear stage of the modulational instability results in the collapsing solutions, accompanied by the “wave breaking” phenomenon. Numerical simulations based on the Hasegawa–Mima equation show that for a weak DW turbulence, Φ ̃ = ( e φ ̃ / T e ) ( L n / ρ s ) ⪝ 1 , the collapsing-like features on both ZF and y-averaged enstrophy of DW turbulence decay in time and then re-emerge again at different locations. For the case of a strong DW turbulence, Φ ̃ > 1 , where nonlinear interactions of DW harmonics dominate, stable spatial structures of ZF and y-averaged enstrophy of DW turbulence emerge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Multilevel well modeling in aggregation-based nonlinear multigrid for multiphase flow in porous media

A full approximation scheme (FAS) nonlinear multigrid solver for two-phase flow and transport problems driven by wells with multiple perforations is developed here. It is an extension to our previous work on FAS solvers for diffusion and transport problems. The solver is applicable to discrete problems defined on unstructured grids as the coarsening algorithm is aggregation-based and algebraic. To construct coarse basis that can better capture the radial flow near wells, coarse grids in which perforated well cells are not near the coarse-element interface are desired. This is achieved by an aggregation algorithm proposed in this paper that makes use of the location of well cells in the cell-connectivity graph. Numerical examples in which the FAS solver is compared against Newton's method on benchmark problems are given. In particular, for a refined version of the SAIGUP model, the FAS solver is at least 35% faster than Newton's method for time steps with a CFL number greater than 10.

58 GEOSCIENCES↗
DOE OSTI2025

McCormick envelopes in mixed-integer PDE-constrained optimization

McCormick envelopes are a standard tool for deriving convex relaxations of optimization problems that involve polynomial terms. Such McCormick relaxations provide lower bounds, for example, in branch-and-bound procedures for mixed-integer nonlinear programs but have not gained much attention in PDE-constrained optimization so far. This lack of attention may be due to the distributed nature of such problems, which on the one hand leads to infinitely many linear constraints (generally state constraints that may be difficult to handle) in addition to the state equation for a pointwise formulation of the McCormick envelopes and renders bound-tightening procedures that successively improve the resulting convex relaxations computationally intractable. We analyze McCormick envelopes for a model problem class that is governed by a semilinear PDE involving a bilinearity and integrality constraints. We approximate the nonlinearity and in turn the McCormick envelopes by averaging the involved terms over the cells of a partition of the computational domain on which the PDE is defined. This yields convex relaxations that underestimate the original problem up to an a priori error estimate that depends on the mesh size of the discretization. These approximate McCormick relaxations can be improved by means of an optimization-based bound-tightening procedure. We show that their minimizers converge to minimizers to a limit problem with a pointwise formulation of the McCormick envelopes when driving the mesh size to zero. We provide a computational example, for which we certify all of our imposed assumptions. The results point to both the potential of the methodology and the gaps in the research that need to be closed. Our methodology provides a framework first for obtaining pointwise underestimators for nonconvexities and second for approximating them with finitely many linear inequalities in an infinite-dimensional setting.

Approximations and Expansions↗
DOE OSTI2025

Analytical and EZmock covariance validation for the DESI 2024 results

The estimation of uncertainties in cosmological parameters is an important challenge in Large-Scale-Structure (LSS) analyses. For standard analyses such as Baryon Acoustic Oscillations (BAO) and Full-Shape two approaches are usually considered. First: analytical estimates of the covariance matrix use Gaussian approximations and (nonlinear) clustering measurements to estimate the matrix, which allows a relatively fast and computationally cheap way to generate matrices that adapt to an arbitrary clustering measurement. On the other hand, sample covariances are an empirical estimate of the matrix based on an ensemble of clustering measurements from fast and approximate simulations. While more computationally expensive due to the large amount of simulations and volume required, these allow us to take into account systematics that are impossible to model analytically. In this work we compare these two approaches in order to enable DESI's key analyses. We find that the configuration space analytical estimate performs satisfactorily in BAO analyses and its flexibility in terms of input clustering makes it the fiducial choice for DESI's 2024 BAO analysis. On the contrary, the analytical computation of the covariance matrix in Fourier space does not reproduce the expected measurements in terms of Full-Shape analyses, which motivates the use of a corrected mock covariance for DESI's 2024 Full Shape analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

GenMod: A generative modeling approach for spectral representation of PDEs with random inputs

Here, we propose a method for quantifying uncertainty in high-dimensional PDE systems with random parameters, where the number of solution evaluations is small. Parametric PDE solutions are often approximated using a spectral decomposition based on polynomial chaos expansions. For the class of systems we consider (i.e., high dimensional with limited solution evaluations) the coefficients are given by an underdetermined linear system in a regression formulation. This implies additional assumptions, such as sparsity of the coefficient vector, are needed to approximate the solution. Here, we present an approach where we assume the coefficients are close to the range of a generative model that maps from a low to a high dimensional space of coefficients. Our approach is inspired be recent work examining how generative models can be used for compressed sensing in systems with random Gaussian measurement matrices. Using results from PDE theory on coefficient decay rates, we construct an explicit generative model that predicts the polynomial chaos coefficient magnitudes. The algorithm we developed to find the coefficients, which we call GenMod, is composed of two main steps. First, we predict the coefficient signs using Orthogonal Matching Pursuit. Then, we assume the coefficients are within a sparse deviation from the range of a sign-adjusted generative model. This allows us to find the coefficients by solving a nonconvex optimization problem, over the input space of the generative model and the space of sparse vectors. We obtain theoretical recovery results for a Lipschitz continuous generative model and for a more specific generative model, based on coefficient decay rate bounds. We examine three high-dimensional problems and show that, for all three examples, the generative model approach outperforms sparsity promoting methods at small sample sizes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Non-intrusive nonlinear model reduction via machine learning approximations to low-dimensional operators

Abstract Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing such a reduced-order model typically requires significant modifications to the underlying simulation code. To address this, we propose a method that enables traditionally intrusive reduced-order models to be accurately approximated in a non-intrusive manner. Specifically, the approach approximates the low-dimensional operators associated with projection-based reduced-order models (ROMs) using modern machine-learning regression techniques. The only requirement of the simulation code is the ability to export the velocity given the state and parameters; this functionality is used to train the approximated low-dimensional operators. In addition to enabling nonintrusivity, we demonstrate that the approach also leads to very low computational complexity, achieving up to $$10^3{\times }$$ 10 3 × in run time. We demonstrate the effectiveness of the proposed technique on two types of PDEs. The domain of applications include both parabolic and hyperbolic PDEs, regardless of the dimension of full-order models (FOMs).

42 ENGINEERING↗
DOE OSTI2019

Self-focusing of cosh-Gaussian laser beam and its effect on the excitation of ion-acoustic wave and stimulated Brillouin backscattering in collisionless plasma

An analytical and numerical study has been carried out for self-focusing of an intense cosh-Gaussian laser beam in collisionless plasma and its impact on the excitation of ion-acoustic wave and stimulated Brillouin backscattering process. The analytical model has been developed under Wentzel–Kramers–Brillouin and paraxial ray approximations. The nonlinearities of ponderomotive force on electron and the relativistic oscillation of the electron mass have been used in this study. The nonlinear differential equations have been set up for the beam width parameters of the main beam, ion-acoustic wave, backscattered wave and back reflectivity of stimulated Brillouin scattering (SBS). These equations have been solved numerically for different values of decentred parameter (b), relative plasma density (ω{sub p0}/ω{sub 0}) and incident laser intensity (a). The results have been compared with only relativistic nonlinearity and Gaussian profile of laser beam. The focusing of laser beam, ion-acoustic wave and scattered wave are found to be strong under relativistic-ponderomotive regime compared to only relativistic regime. Further, it is observed that focusing/intensity of main laser beam, ion acoustic wave and SBS back reflectivity increases with increasing the values of b and ω{sub p0}/ω{sub 0}. Itis also found that back reflectivity of SBS process gets suppressed with the increase in the value of a. This study may be useful in laser induced fusion scheme where back scattering of SBS plays very important role.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Optimal Design of Sustainable Ammonia-Based Food–Energy–Water Systems with Nitrogen Management

As the basis for virtually any form of nitrogen fertilizers, ammonia plays a vital role in agriculture; in addition, there has been an increased interest in its use as a carbon-free energy carrier. However, ammonia is also associated with two major environmental concerns: CO 2 emissions from the conventional production process and nitrogen pollution from the excessive use of ammonia-based fertilizers. To mitigate these environmental impacts, we develop an optimization framework for the design of a sustainable ammonia-based agricultural system that synergistically integrates the production of ammonia from renewable resources and effective measures for nitrogen management. The proposed model captures the effect of intermittency by incorporating both design and detailed operational decisions. Here, by applying a multiscale time representation that reduces the problem size and a tailored surrogate model that accurately approximates model nonlinearity, we are able to achieve optimal solutions within reasonable computation times. A computational case study is conducted using real-world data from a local farm in Morris, Minnesota, and the results indicate the trade-off between cost and nitrogen loss. Importantly, we show that practicing effective nitrogen management can significantly reduce the nitrogen loss with only a small increase in net present cost.

10 SYNTHETIC FUELS↗
DOE OSTI2021

Analytic and numerical vibronic spectra from quasi-classical trajectory ensembles

The truncated Wigner approximation to quantum dynamics in phase space is explored in the context of computing vibronic line shapes for monomer linear optical spectra. We consider multiple model potential forms including a shifted harmonic oscillator with both equal and unequal frequencies on the ground and excited state potentials as well as a shifted Morse potential model. For the equal-frequency shifted harmonic oscillator model, we derive an analytic expression for the exact vibronic line shape that emphasizes the importance of using a quantum mechanical distribution of phase space initial conditions. For the unequal-frequency shifted harmonic oscillator model, we are no longer able to obtain an exact expression for the vibronic line shape in terms of independent deterministic classical trajectories. We show how one can rigorously account for corrections to the truncated Wigner approximation through nonlinear responses of the line shape function to momentum fluctuations along a classical trajectory and demonstrate the qualitative improvement in the resulting spectrum when the leading-order quantum correction is included. Finally, we numerically simulate absorption spectra of a highly anharmonic shifted Morse potential model. We find that, while finite quantization and the dissociation limit are captured with reasonable accuracy, there is a qualitative breakdown of the quasi-classical trajectory ensemble’s ability to describe the vibronic line shape when the relative shift in Morse potentials becomes large. The work presented here provides clarity on the origin of unphysical negative features known to contaminate absorption spectra computed with quasi-classical trajectory ensembles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

CI-MOR Final Report: Analysis and Validation of Critical Infrastructure Models using Model Order Reduction

This report summarizes the research and capabilities developed as part of the project “Analysis and Validation of Critical Infrastructure Models using Model Order Reduction” (CI-MOR) LDRD project. CI-MOR research enables the solution of large, complex optimization models that naturally arise in national security challenges involving critical infrastructures. Specifically, CI-MOR researchers developed methods to (1) rigorously approximate complex, nonlinear optimization formulations, (2) identify alternative near-optimal solutions, (3) accelerate optimization workflows used for complex applications, and (4) rigorously integrate domain knowledge in stochastic-process models. This report provides an overview of the research done in CI-MOR, and we describe application exemplars used to illustrate CI-MOR capabilities. Furthermore, we describe the software developed by CI-MOR that researchers can leverage to analyze new applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

SUHMO: an adaptive mesh refinement SUbglacial Hydrology MOdel v1.0

Abstract. Water flowing under ice sheets and glaciers can have a strong influence on ice dynamics, particularly through pressure changes, suggesting that a comprehensive ice sheet model should include the effect of basal hydrology. Modeling subglacial hydrology remains a challenge, however, mainly due to the range of spatial and temporal scales involved – from subglacial channels to vast subglacial lakes. Additionally, networks of subglacial drainage channels dynamically evolve over time. To address some of these challenges, we have developed an adaptive mesh refinement (AMR) model based on the Chombo software framework. We extend the model proposed by Sommers et al. (2018) with a small but significant change to accommodate the transition from unresolved to resolved flow features. We handle the strong nonlinearities present in the equations by resorting to an efficient nonlinear full approximation scheme multigrid (FAS-MG) algorithm. We outline the details of the algorithm and present convergence analysis results demonstrating its good performance. Additionally, we present results validating our approach, using test cases from the Subglacial Hydrology Model Intercomparison Project (SHMIP) (de Fleurian et al., 2018). We finish by presenting a more complex, 100 km-by-100 km synthetic test case with peaks and valleys that we use to investigate the effective pressure distribution as the number of AMR levels increases. These preliminary results suggest that a minimum spatial resolution is needed to properly capture channel features, but additional work is required to precisely quantify this and its impact on accurately modeling the coupled ice sheet–hydrology system. The efficiency of our approach, relying on localized refinement, is also demonstrated. Future work will include coupling the SUbglacial Hydrology MOdel (SUHMO) with the BISICLES AMR ice sheet model (Cornford et al., 2013), both built on the same numerical framework.

58 GEOSCIENCES↗
DOE OSTI2024

Nonlinear susceptibilities for weakly turbulent magnetized plasma: Electrostatic approximation

The plasma weak turbulence theory is a perturbative nonlinear theory, which has been proven to be quite valid in a number of applications. However, the standard weak turbulence theory found in the literature is fully developed for highly idealized unmagnetized plasmas. As many plasmas found in nature and laboratory are immersed in a background static magnetic field, it is necessary to extend the existing discussions to include the effects of ambient magnetic field. Such a task is quite formidable, however, which has prevented fundamental and significant progresses in the subject matter. The central difficulty lies in the formulation of the complete nonlinear response functions for magnetized plasmas. The present paper derives the nonlinear susceptibilities for weakly turbulent magnetized plasmas up to the third order nonlinearity, but in doing so, a substantial reduction in mathematical complexity is achieved by the use of Bessel function addition theorem (or sum rule). The present paper also constructs the weak turbulence wave kinetic equation in a formal sense. For the sake of simplicity, however, the present paper assumes the electrostatic interaction among plasma particles. Fully electromagnetic generalization is a subject of a subsequent paper.

Physics↗
DOE OSTI2025

Virtual element approximations of the time-fractional nonlinear convection-diffusion equation on polygonal meshes

We extend the Virtual Element Method to a two-dimensional unsteady nonlinear convection-diffusion equation characterized by a fractional-order derivative with respect to the time variable. Our methodology is based on three fundamental technical components: a fractional version of the Grunwald-Letnikov approximation, discrete maximal regularity, and the regularity theory associated with non-linearity. We prove the method's well-posedness, i.e., the approximate solution's existence and uniqueness to the time-fractional convection-diffusion equation with a Lipschitz nonlinear source term. The fully discrete scheme inherently maintains stability and consistency by leveraging the discrete maximal regularity and the energy projection operator. The convergence in the L 2 -norm and H 1 -norm to various mesh configurations is validated by numerical results, underlining the practical effectiveness of the proposed method.

97 MATHEMATICS AND COMPUTING↗