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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 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Kinetic theory of turbulence for parallel propagation revisited: Low-to-intermediate frequency regime

A previous paper [P. H. Yoon, “Kinetic theory of turbulence for parallel propagation revisited: Formal results,” Phys. Plasmas 22, 082309 (2015)] revisited the second-order nonlinear kinetic theory for turbulence propagating in directions parallel/anti-parallel to the ambient magnetic field, in which the original work according to Yoon and Fang [Phys. Plasmas 15, 122312 (2008)] was refined, following the paper by Gaelzer et al. [Phys. Plasmas 22, 032310 (2015)]. The main finding involved the dimensional correction pertaining to discrete-particle effects in Yoon and Fang's theory. However, the final result was presented in terms of formal linear and nonlinear susceptibility response functions. In the present paper, the formal equations are explicitly written down for the case of low-to-intermediate frequency regime by making use of approximate forms for the response functions. The resulting equations are sufficiently concrete so that they can readily be solved by numerical means or analyzed by theoretical means. The derived set of equations describe nonlinear interactions of quasi-parallel modes whose frequency range covers the Alfvén wave range to ion-cyclotron mode, but is sufficiently lower than the electron cyclotron mode. The application of the present formalism may range from the nonlinear evolution of whistler anisotropy instability in the high-beta regime, and the nonlinear interaction of electrons with whistler-range turbulence.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Onsets of hierarchy truncation and self–consistent Born approximation with quantum mechanics prescriptions invariance

The issue of efficient hierarchy truncation is related to many approximate theories. In this paper, we revisit this issue from both the numerical efficiency and quantum mechanics prescription invariance aspects. The latter requires that the truncation approximation made in Schrödinger picture, such as the quantum master equations and their self–consistent–Born–approximation improvements, should be transferable to their Heisenberg–picture correspondences, without further approximations. We address this issue with the dissipaton equation of motion (DEOM), which is a unique theory for the dynamics of not only reduced systems but also hybrid bath environments. We also highlight the DEOM theory is not only about how its dynamical variables evolve in time, but also the underlying dissipaton algebra. We demonstrate this unique feature of DEOM with model systems and report some intriguing nonlinear Fano interferences characteristics that are experimentally measurable.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Transient dynamics, damping, and mode coupling of nonlinear systems with internal resonances

The study of both linear and nonlinear structural vibrations routinely circles the concise yet complex problem of choosing a set of coordinates which yield simple equations of motion. In both experimental and mathematical methods, that choice is a difficult one because of measurement, computational, and interpretation difficulties. Often times, researchers choose to solve their problems in terms of linear, undamped mode shapes because they are easy to obtain; however, this is known to give rise to complicated phenomena such as mode coupling and internal resonance. This work considers the nature of mode coupling and internal resonance in systems containing non-proportional damping, linear detuning, and cubic nonlinearities through the method of multiple scales as well as instantaneous measures of effective damping. The energy decay observed in the structural modes is well approximated by the slow-flow equations in terms of the modal amplitudes, and it is shown how mode coupling enhances the damping observed in the system. Moreover, in the presence of a 3:1 internal resonance between two modes, the nonlinearities not only enhance the dissipation, but can allow for the exchange and transfer of energy between the resonant modes. However, this exchange depends on the resonant phase between the modes and is proportional to the energy in the lowest mode. The results of the analysis tie together interpretations used by both experimentalists and theoreticians to study such systems and provide a more concrete way to interpret these phenomena.

42 ENGINEERING↗
DOE OSTI2023

Impacts of Permeability Heterogeneity and Background Flow on Supercritical CO 2 Dissolution in the Deep Subsurface

Motivated by CO 2 capture and sequestration (CCS) design considerations, we consider the coupled effects of permeability heterogeneity and background flow on the dissolution of a supercritical CO 2 lens into an underlying deep, confined aquifer. We present the results of a large-scale Monte Carlo simulation study examining the interaction of background flow rate and three parameters describing multi-Gaussian log-permeability fields: mean, variance, and correlation length. Hundreds of high-resolution simulations were performed using the PFLOTRAN finite volume software to model CO 2 dissolution in a kilometer-scale aquifer over 1,000 years. Predictive dimensionless scaling relationships relating CO 2 dissolution rate to heterogeneity statistics, Rayleigh (Ra) and Péclet (Pe) numbers were developed for both gravitationally dominated free convection to background flow-dominated forced convection regimes. An empirical criterion, Pe = Ra 3/4 , was discovered for regime transition. All simulations converged quickly to a quasi-steady, approximately linear dissolution rate. However, this rate displayed profound variability between permeability field realizations sharing the same heterogeneity statistics, even under mild permeability heterogeneity. In general, increased heterogeneity was associated with a lower mean and higher variance of dissolution rate, undesirable from a CCS design perspective. The relationship between dissolution rate and background flow was found to be complex and nonlinear. Dimensionless scaling relationships were uncovered for a number of special cases. Results call into question the validity of the Boussinesq approximation in the context of modest-to-high background flow rates and the general applicability of numerical simulations without background flow.

42 ENGINEERING↗
DOE OSTI2018

A two-grid penalty method for American options

In this paper we consider the pricing of American options, governed by a partial differential complementarity problem. The differential problem is first approximated by a semi-linear PDE using two distinct penalty approaches which are well known in computational finance. We then initiate the two-grid algorithm by solving the nonlinear problem on a coarse grid and further the linearized in the interpolated coarse-grid solution problem on a fine grid. By means of the maximum principle the algorithm is shown to be of fourth order convergence rate in space. Numerical experiments verify the presented two-grid approach where we draw some interesting conclusions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Second harmonic generation for estimating state of charge of lithium-ion batteries

This study applied the nonlinear ultrasonic method, second harmonic generation, to precisely estimate the state of charge (SoC) in lithium-ion batteries. The second harmonic of the longitudinal wave is generated on a pouch cell battery at 5 MHz with a through-transmission setup. The relative nonlinear parameter β' is determined by analyzing the amplitudes at the fundamental and second harmonic frequencies. To enhance the nonlinear parameter's measurement accuracy, multiple excitation amplitudes are employed. Two separate charge/discharge tests (four-cycle and eight-cycle) are conducted on the battery at a rate of C/10. The nonlinear parameter is measured periodically during the charge/discharge process, and temperature compensation is applied to the measurement. The correlation curves between the nonlinear parameter and the actual SoC align well for the four-cycle and eight-cycle tests, and a robust linear relationship is observed for both correlation curves. A linear model and a second-order polynomial model are applied to fit the correlation using all data points from both tests. The two models are employed to validate the SoC prediction on a second battery by using a four-cycle test. Furthermore, the results indicate that both models can predict the SoC with an accuracy of approximately 3%, whereas the polynomial model demonstrates smaller errors in the regions near 0% and 100% SoC. Therefore, the nonlinear parameter β', measured through the second harmonic generation, can effectively predict lithium-ion battery SoC with an accuracy of less than 3%.

25 ENERGY STORAGE↗
DOE OSTI2017

On non-local energy transfer via zonal flow in the Dimits shift

The two-dimensional Terry–Horton equation is shown to exhibit the Dimits shift when suitably modified to capture both the nonlinear enhancement of zonal/drift-wave interactions and the existence of residual Rosenbluth–Hinton states. This phenomenon persists through numerous simplifications of the equation, including a quasilinear approximation as well as a four-mode truncation. It is shown that the use of an appropriate adiabatic electron response, for which the electrons are not affected by the flux-averaged potential, results in an $\boldsymbol{E}\times \boldsymbol{B}$ nonlinearity that can efficiently transfer energy non-locally to length scales of the order of the sound radius. The size of the shift for the nonlinear system is heuristically calculated and found to be in excellent agreement with numerical solutions. The existence of the Dimits shift for this system is then understood as an ability of the unstable primary modes to efficiently couple to stable modes at smaller scales, and the shift ends when these stable modes eventually destabilize as the density gradient is increased. This non-local mechanism of energy transfer is argued to be generically important even for more physically complete systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Nonlinear thermodynamic computing out of equilibrium

We present the design for a thermodynamic computer that can perform arbitrary nonlinear calculations in or out of equilibrium. Simple thermodynamic circuits, fluctuating degrees of freedom in contact with a thermal bath and confined by a quartic potential, display an activity that is a nonlinear function of their input. Such circuits can therefore be regarded as thermodynamic neurons, and can serve as the building blocks of networked structures that act as thermodynamic neural networks, universal function approximators whose operation is powered by thermal fluctuations. We simulate a digital model of a thermodynamic neural network, and show that its parameters can be adjusted by genetic algorithm to perform nonlinear calculations at specified observation times, regardless of whether the system has attained thermal equilibrium. This work expands the field of thermodynamic computing beyond the regime of thermal equilibrium, enabling fully nonlinear computations, analogous to those performed by classical neural networks, at specified observation times.

Whitelam, Stephen [Lawrence Berkeley National Labo↗
DOE OSTI2023

An Ensemble Score Filter for Tracking High-Dimensional Nonlinear Dynamical Systems

We propose an ensemble score filter (EnSF) for solving high-dimensional nonlinear filtering problems with superior accuracy. A major drawback of existing filtering methods, e.g., particle filters or ensemble Kalman filters, is the low accuracy in handling high-dimensional and highly nonlinear problems. EnSF attacks this challenge by exploiting the score-based diffusion model, defined in a pseudo-temporal domain, to characterizing the evolution of the filtering density. EnSF stores the information of the recursively updated filtering density function in the score function, in stead of storing the information in a set of finite Monte Carlo samples (used in particle filters and ensemble Kalman filters). Unlike existing diffusion models that train neural networks to approximate the score function, we develop a training-free score estimation that uses mini-batch-based Monte Carlo estimator to directly approximate the score function at any pseudo-spatial-temporal location, which provides sufficient accuracy in solving high-dimensional nonlinear problems as well as saves tremendous amount of time spent on training neural networks. Another essential aspect of EnSF is its analytical update step, gradually incorporating data information into the score function, which is crucial in mitigating the degeneracy issue faced when dealing with very high-dimensional nonlinear filtering problems. High-dimensional Lorenz systems are used to demonstrate the performance of our method. EnSF provides surprisingly impressive performance in reliably tracking extremely high-dimensional Lorenz systems (up to 1,000,000 dimension) with highly nonlinear observation processes, which is a well-known challenging problem for existing filtering methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

A simple method of measuring the effective SRS coefficient in single-mode optical fibres and its applicability limits

This paper describes techniques for measuring the SRS coefficient in a wide spectral range, including the region of small Stokes shifts. A simple, approximate method is proposed for evaluating the SRS coefficient near a gain peak. Spectral dependences of the SRS coefficient are presented for various telecom fibres. (nonlinear optical phenomena)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2016

Coarse-grained description of cosmic structure from Szekeres models

We show that the full dynamical freedom of the well known Szekeres models allows for the description of elaborated 3-dimensional networks of cold dark matter structures (over-densities and/or density voids) undergoing ''pancake'' collapse. By reducing Einstein's field equations to a set of evolution equations, which themselves reduce in the linear limit to evolution equations for linear perturbations, we determine the dynamics of such structures, with the spatial comoving location of each structure uniquely specified by standard early Universe initial conditions. By means of a representative example we examine in detail the density contrast, the Hubble flow and peculiar velocities of structures that evolved, from linear initial data at the last scattering surface, to fully non-linear 10–20 Mpc scale configurations today. To motivate further research, we provide a qualitative discussion on the connection of Szekeres models with linear perturbations and the pancake collapse of the Zeldovich approximation. This type of structure modelling provides a coarse grained—but fully relativistic non-linear and non-perturbative —description of evolving large scale cosmic structures before their virialisation, and as such it has an enormous potential for applications in cosmological research.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Linear response to long wavelength fluctuations using curvature simulations

We study the local response to long wavelength fluctuations in cosmological N -body simulations, focusing on the matter and halo power spectra, halo abundance and non-linear transformations of the density field. The long wavelength mode is implemented using an effective curved cosmology and a mapping of time and distances. The method provides an alternative, more direct, way to measure the isotropic halo biases. Limiting ourselves to the linear case, we find generally good agreement between the biases obtained from the curvature method and the traditional power spectrum method at the level of a few percent. We also study the response of halo counts to changes in the variance of the field and find that the slope of the relation between the responses to density and variance differs from the naïve derivation assuming a universal mass function by approximately 8–20%. This has implications for measurements of the amplitude of local non-Gaussianity using scale dependent bias. We also analyze the halo power spectrum and halo-dark matter cross-spectrum response to long wavelength fluctuations and derive second order halo bias from it, as well as the super-sample variance contribution to the galaxy power spectrum covariance matrix.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Lensing smoothing of BAO wiggles

We study non-perturbatively the effect of the deflection angle on the BAO wiggles of the matter power spectrum in real space. We show that from redshift z ∼2 this introduces a dispersion of roughly 1 Mpc at BAO scale, which corresponds approximately to a 1% effect. The lensing effect induced by the deflection angle, which is completely geometrical and survey independent, smears out the BAO wiggles. The effect on the power spectrum amplitude at BAO scale is about 0.1 % for z ∼2 and 0.2 % for z ∼4. We compare the smoothing effects induced by the lensing potential and non-linear structure formation, showing that the two effects become comparable at z ∼ 4, while the lensing effect dominates for sources at higher redshifts. We note that this effect is not accounted through BAO reconstruction techniques.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Analytic Chromaticity Formulas for the Muon g -2 experiment at fermilab

The Muon g-2 Experiment (E989) at Fermilab measured the muon anomalous magnetic moment aμ with unprecedented precision of 127 ppb using a storage ring. The experiment pushed the limits in terms of accuracy and systematic errors. Achieving the 78-ppb total systematic uncertainty required precise beam dynamics modeling and corrections for effects on the measured muon precession frequency. Here, we derived the first analytic aberration formulas up to the second order for the muon g-2 storage ring’s combined-function electrostatic quadrupoles (superimposed magnetic dipole and electric quadrupole fields) using an order-by-order perturbation method. From these, we obtained the exact chromaticity formulas for three ring models of different granularity and validated them against numerical calculations using COSY INFINITY, achieving analytic-numerical agreement to ⁠$\mathscr{O}(10^{-10})$. This work resolved discrepancies between previous approximate derivations and provided essential beam dynamics results for Runs 4-6 analyses. We also calculated nonlinear chromaticities up to ninth order. The experiment completed its final Run 6 in July 2023, collecting 21 times more data than the previous muon g-2 experiment at Brookhaven National Laboratory, with the final result announced in June 2025.

aberrations↗
DOE OSTI2016

Variational approach to studying solitary waves in the nonlinear Schrödinger equation with complex potentials

Here in this paper, we discuss the behavior of solitary wave solutions of the nonlinear Schrödinger equation (NLSE) as they interact with complex potentials, using a four-parameter variational approximation based on a dissipation functional formulation of the dynamics. We concentrate on spatially periodic potentials with the periods of the real and imaginary part being either the same or different. Our results for the time evolution of the collective coordinates of our variational ansatz are in good agreement with direct numerical simulation of the NLSE. We compare our method with a collective coordinate approach of Kominis and give examples where the two methods give qualitatively different answers. In our variational approach, we are able to give analytic results for the small oscillation frequency of the solitary wave oscillating parameters which agree with the numerical solution of the collective coordinate equations. We also verify that instabilities set in when the slope dp(t)/dv(t) becomes negative when plotted parametrically as a function of time, where p(t) is the momentum of the solitary wave and v(t) the velocity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Modeling pre-Exascale AMR Parallel I/O Workloads via Proxy Applications

The present work investigates the modeling of preexascale input/output (I/O) workloads of Adaptive Mesh Refinement (AMR) simulations through a simple proxy application. We collect data from the AMReX Castro framework running on the Summit supercomputer for a wide range of scales and mesh partitions for the hydrodynamic Sedov case as a baseline to provide sufficient coverage to the formulated proxy model. The non-linear analysis data production rates are quantified as a function of a set of input parameters such as output frequency, grid size, number of levels, and the Courant-Friedrichs-Lewy (CFL) condition number for each rank, mesh level and simulation time step. Linear regression is then applied to formulate a simple analytical model which allows to translate AMReX inputs into MACSio proxy I/O application parameters, resulting in a simple “kernel” approximation for data production at each time step. Results show that MACSio can simulate actual AMReX nonlinear “static” I/O workloads to a certain degree of confidence on the Summit supercomputer using the present methodology. The goal is to provide an initial level of understanding of AMR I/O workloads via lightweight proxy applications models to facilitate autotune data management strategies in anticipation of exascale systems.

Godoy, William↗
DOE OSTI2024

A Data-Driven Approach for High-Impedance Fault Localization in Distribution Systems [SWR-24-13]

This software provides a data-driven approach for efficiently identifying high impedance faults (HIFs) in distribution systems. To tackle the nonlinearity of the voltage current trajectory of HIFs, we first formulate linear least squares problems to approximate the trajectory with piecewise functions. Then we collect the function features of all segments as inputs and use the support vector machine approach to efficiently identify HIFs at different locations.

Zhou, Yuqi↗