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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Final Technical Report for NSF/DOE partnership grant 1004284/ER54905/SC0004660: 2011- 2013

Research has been performed on two topics: (1) Nonlinear time-dependent phenomena in the regime of electron magnetohydrodynamics (EMHD). (2) Plasma structures forming ”bubbles”. The latter are regions of localized density depletions or enhancements separated from the ambient plasma by sheaths or double layers. Three-dimensional magnetic null points can also be considered as ”magnetic bubbles”. Nonlinear EMHD fields are generated by pulsed magnetic loops. The magnetic field varies in time faster than an ion cyclotron period, hence interacts only with electrons. Space charge electric fields are created when magnetic forces try to separate electrons from ions. Electric and magnetic forces nearly balance to keep the plasma quasi neutral. This leads to rotational electron motions, i.e. Hall currents and associated magnetic perturbations. When the time scale falls between the ion and electron cyclotron period the magnetic perturbation is convected in the whistler mode. When the time-varying magnetic field exceeds the background magnetic field the whistler mode becomes highly nonlinear since its properties depend on the total magnetic field. When the time-varying magnetic field creates magnetic null points or null lines EMHD breaks down. Electrons can be accelerated in null lines which dissipated magnetic energy like in magnetic reconnection. Energized electrons with anisotropic distributions create secondary whistler instabilities. These effects have been observed in field topologies resembling spheromaks and field-reversed configurations (FRCs). The whistler mode propagation near magnetic nulls is not trivial when the field gradients and wavelength are comparable. Ray tracing is inappropriate when the WKB approximation breaks down. Experiments have been started to map wave propagation on curved field lines with null points. Initial results show that whistlers in highly nonuniform fields have highly oblique phase velocities but the energy flow remains dominantly along the field. Density bubbles are created by anode discharges, typically forming spherical ”fireballs” bounded by a double layer. In a magnetized plasma the shape becomes cylindrical, in nonuniform magnetic fields many asymmetric fireball shapes are possible. Due to electron energization the fireball plasma has higher density and temperature than the ambient plasma. The double layer can also be produced by a high transparency positively biased grid. Instabilities arise from the electron transit through the plasma bubble and the double layer. When a permanent magnet is biased positively the electrons perform ExB drifts in the equatorial plane between the poles. Electron drift modes are excited with a high spectral contents. Similarly, a negatively biased magnet produces a disk-shaped plasma bubble. The cold magnet emits secondary electrons due to the impact of energetic ions. Such magnetron discharges exhibit a variety of instabilities which affect the cross-field transport and sputtering applications. This report will summarize the main effects observed and provide references to more detailed publications.

, nonlinear time-dependent phenomena↗
DOE OSTI2024

Weighted Composition Operators for Learning Nonlinear Dynamics

Operator theoretic methods in dynamical system have been dominated by the use of Koopman operators and their continuous time counterparts, such as Koopman Generators and Liouville Operators. The advantage gained from their use primarily stems from the ability to extract subspaces and eigenfunctions within a space of observables that are invariant with respect to the Koopman operator over that space. When this occurs, a dynamic mode decomposition of the systems state provides a linear model for the dynamical system. Not all Koopman operators have eigenfunctions that may be exploited in this manner. However, the framework can still be leveraged for approximations using other operators. In this setting, we present a different operator for the study of dynamical systems, the weighted composition operator. These operators are compact for a wide range of dynamics and spaces, and through their interactions with occupation kernels and vector valued kernels, they admit an estimation of the underlying dynamics. Here, this manuscript presents a new algorithm for the data driven study of dynamical systems from data, and also provides two numerical experiments where convergence is achieved as a proof of concept.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Solitary waves in a peridynamic elastic solid

The propagation of large amplitude nonlinear waves in a peridynamic solid is ana- lyzed. With an elastic material model that hardens in compression, sufficiently large wave pulses propagate as solitary waves whose velocity can far exceed the linear wave speed. In spite of their large velocity and amplitude, these waves leave the material they pass through with no net change in velocity and stress. They are nondissipative and nondispersive, and they travel unchanged over large distances. An approximate solution for solitary waves is derived that reproduces the main features of these waves observed in computational simulations. We demonstrate, by numerical studies, that waves interact only weakly with each other when they collide. Finally, we found that wavetrains composed of many non-interacting solitary waves form and propagate under certain boundary and initial conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Matrix-Free High-Performance Saddle-Point Solvers for High-Order Problems in \(\boldsymbol{H}(\operatorname{\textbf{div}})\)

Here, this work describes the development of matrix-free GPU-accelerated solvers for high-order finite element problems in H(div). The solvers are applicable to grad-div and Darcy problems in saddle-point formulation, and have applications in radiation diffusion and porous media flow problems, among others. Using the interpolation–histopolation basis, efficient matrix-free preconditioners can be constructed for the (1, 1)-block and Schur complement of the block system. With these approximations, block-preconditioned MINRES converges in a number of iterations that is independent of the mesh size and polynomial degree. The approximate Schur complement takes the form of an M-matrix graph Laplacian and therefore can be well-preconditioned by highly scalable algebraic multigrid methods. High-performance GPU-accelerated algorithms for all components of the solution algorithm are developed, discussed, and benchmarked. Numerical results are presented on a number of challenging test cases, including the “crooked pipe” grad-div problem, the SPE10 reservoir modeling benchmark problem, and a nonlinear radiation diffusion test case.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Temporal reflection of an optical pulse from a short soliton: impact of Raman scattering

We study temporal reflection of an optical pulse from the refractive-index barrier created by a short pump soliton inside a nonlinear dispersive medium such as an optical fiber. One feature is that the soliton’s speed changes continuously as its spectrum redshifts because of intrapulse Raman scattering. We use the generalized nonlinear Schrödinger equation to find the shape and spectrum of the reflected pulse. Both are affected considerably by the soliton’s trajectory. The reflected pulse can become considerably narrower compared to the incident pulse under conditions that involve a type of temporal focusing. This phenomenon is explained through space–time duality by showing that the temporal situation is analogous to an optical beam incident obliquely on a parabolic mirror. We obtain an approximate analytic expression for the reflected pulse’s spectrum and use it to derive the temporal version of the transformation law for the

47 OTHER INSTRUMENTATION↗
DOE OSTI2014

Implementing Nonlinear Buoyancy and Excitation Forces in the WEC-Sim Wave Energy Converter Modeling Tool: Preprint

Wave energy converters (WECs) are commonly designed and analyzed using numerical models that combine multi-body dynamics with hydrodynamic models based on the Cummins Equation and linearized hydrodynamic coefficients. These modeling methods are attractive design tools because they are computationally inexpensive and do not require the use of high performance computing resources necessitated by high-fidelity methods, such as Navier Stokes computational fluid dynamics. Modeling hydrodynamics using linear coefficients assumes that the device undergoes small motions and that the wetted surface area of the devices is approximately constant. WEC devices, however, are typically designed to undergo large motions in order to maximize power extraction, calling into question the validity of assuming that linear hydrodynamic models accurately capture the relevant fluid-structure interactions. In this paper, we study how calculating buoyancy and Froude-Krylov forces from the instantaneous position of a WEC device (referred to as instantaneous buoyancy and Froude-Krylov forces from herein) changes WEC simulation results compared to simulations that use linear hydrodynamic coefficients. First, we describe the WEC-Sim tool used to perform simulations and how the ability to model instantaneous forces was incorporated into WEC-Sim. We then use a simplified one-body WEC device to validate the model and to demonstrate how accounting for these instantaneously calculated forces affects the accuracy of simulation results, such as device motions, hydrodynamic forces, and power generation.

13 HYDRO ENERGY↗
DOE OSTI2018

Difference-Frequency Generation of THz Radiation via Parametric Three-Wave Interaction in CdTe and ZnTe Crystals

Difference-frequency generation of terahertz (THz) radiation in a collinear single-crystal scheme with distributed feedback implemented by means of parametric interaction of counterpropagating optical waves in a periodically inhomogeneous medium exhibiting quadratic nonlinearity is investigated. Using ZnTe and CdTe crystals optically pumped at λ = 0.77 and 1.06 μm, respectively, as an example, the possibility of obtaining parametric generation of THz radiation with an optical-to-THz conversion efficiency exceeding 10{sup –3} (with an extremely narrow line of oscillation of less than 4 GHz for ZnTe and less than 9 GHz for CdTe at 1 THz) is demonstrated in the undepleted-pump-intensity approximation. The obtained results can be used for construction of narrow-band lasers in the THz frequency range with an output power (in the quasicw regime of oscillation) of about 10{sup 5} W/cm{sup 2}.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Vibrational coherences in charge-transfer dyes: A non-adiabatic picture

Essential-state models efficiently describe linear and nonlinear spectral properties of different families of charge-transfer chromophores. Here, the essential-state machinery is applied to the calculation of the early-stage dynamics after ultrafast (coherent) excitation of polar and quadrupolar chromophores. The fully non-adiabatic treatment of coupled electronic and vibrational motion allows for a reliable description of the dynamics of these intriguing systems. In particular, the proposed approach is reliable even when the adiabatic and harmonic approximations do not apply, such as for quadrupolar dyes that show a multistable, broken-symmetry excited state. Our approach quite naturally leads to a clear picture for a dynamical Jahn-Teller effect in these systems. The recovery of symmetry due to dynamical effects is however disrupted in polar solvents where a static symmetry lowering is observed. More generally, thermal disorder in polar solvents is responsible for dephasing phenomena, damping the coherent oscillations with particularly important effects in the case of polar dyes.

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

Resolving ECRH deposition broadening due to edge turbulence in DIII-D

Microwave heat pulse propagation experiments have demonstrated a correlation between millimeter-scale turbulence and deposition profile broadening of electron cyclotron (EC) waves on the DIII-D tokamak. In a set of discharges in DIII-D, a variation in edge density fluctuations on the mm-scale is associated with 40%–150% broader deposition profiles, expressed in terms of normalized minor radius, as compared with equilibrium ray tracing. The 1D power profile is determined from transport analysis of the electron temperature response to EC power modulation using perturbative analysis with a square wave power modulation at 20–70 Hz, producing a series of Fourier harmonics that are fit collectively to resolve transport. Fitting an integrated heat flux expressed in the Fourier basis of the modulation to diffusive, convective, and coupled transport terms in a linear model can resolve the broadened EC deposition width from the power perturbation to resolve a broadening in each case. The best fit degree of beam broadening observed scales approximately linearly with the Doppler backscattering measured fluctuation level in the steep gradient region. Quantifying the effect of edge fluctuation broadening on EC current drive power needs of future devices will require 3D full-wave codes that can be validated on the current generation of machines. These DIII-D experiments provide a quantitative measure of fluctuation effects and a dataset to benchmark full-wave simulations that can model and eventually predict nonlinear effects neglected by 1D equilibrium beam and ray tracing.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Quasinormal modes for non-minimally coupled scalar fields in regular black hole spacetimes: Grey-body factors, area spectrum and shadow radius

Black hole perturbation theory is a useful approach to study interactions between black holes and fundamental fields. A particular class of black hole solutions arising out of modification of Einstein’s general theory of relativity are regular black holes (RBHs) which can be constructed using a nonlinear electrodynamic Lagrangian. Because of their importance, we are interested in studying the behavior of three kinds of such RBHs under perturbations generated by an external field. Indeed, we investigate the quasinormal modes (QNMs) of a massive scalar field propagating near the RBHs which is non-minimally coupled to the Ricci scalar-tensor of background geometry. We will attempt to find the low-lying quasinormal frequencies of the perturbations by using WKB approximation. We shall also study the relationship between the QNMs and some characteristic properties of black holes such as grey-body factors, area quantization, and shadow radius.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Understanding the breakdown of classic two-phase theory and spray atomization at engine-relevant conditions

We present a generalized framework for multi-component liquid injections to understand and predict the breakdown of classic two-phase theory and spray atomization at engine-relevant conditions. The analysis focuses on the thermodynamic structure and the immiscibility state of representative gas-liquid interfaces. The most modern form of Helmholtz energy mixture state equation is utilized which exhibits a unique and physically-consistent behavior over the entire two-phase regime of fluid densities. It is combined with generalized models for non-linear Gradient Theory and for liquid injections to quantify multi-component two-phase interface structures in global thermal equilibrium. Then, the Helmholtz free energy is minimized which determines the interfacial species distribution as a consequence. This minimal free energy state is demonstrated to validate the underlying assumptions of classic two-phase theory and spray atomization. However, under certain engine-relevant conditions for which corroborating experimental data is presented, this requirement for interfacial thermal equilibrium becomes unsustainable. A rigorously derived probability density function quantifies the ability of the interface to develop internal spatial temperature gradients in the presence of significant temperature differences between injected liquid and ambient gas. Then, the interface can no longer be viewed as an isolated system at minimal free energy. Instead, the interfacial dynamics become intimately connected to those of the separated homogeneous phases. Hence, the interface transitions toward a state in local equilibrium whereupon it becomes a dense-fluid mixing layer. A new conceptual view of a transitional liquid injection process emerges from a transition time scale analysis. Close to the nozzle exit, the two-phase interface still remains largely intact and more classic two-phase processes prevail as a consequence. Further downstream, however, the transition to dense- fluid mixing generally occurs before the liquid length is reached. The significance of the presented modeling expressions is established by a direct comparison to a reduced model, which utilizes widely-applied approximations but fundamentally fails to capture the physical complexity discussed in this paper.

42 ENGINEERING↗
DOE OSTI2020

Forward sensitivity approach for estimating eddy viscosity closures in nonlinear model reduction

In this paper, we propose a variational approach to estimate eddy viscosity using forward sensitivity method (FSM) for closure modeling in nonlinear reduced order models. FSM is a data assimilation technique that blends model's predictions with noisy observations to correct initial state and/or model parameters. We apply this approach on a projection based reduced order model (ROM) of the one-dimensional viscous Burgers equation with a square wave defining a moving shock, and the two-dimensional vorticity transport equation formulating a decay of Kraichnan turbulence. We investigate the capability of the approach to approximate an optimal value for eddy viscosity with different measurement configurations. Specifically, we show that our approach can sufficiently assimilate information either through full field or sparse noisy measurements to estimate eddy viscosity closure to cure standard Galerkin reduced order model (GROM) predictions. Therefore, our approach provides a modular framework to correct forecasting error from a sparse observational network on a latent space. We highlight that the proposed GROM-FSM framework is promising for emerging digital twin applications, where real-time sensor measurements can be used to update and optimize surrogate model's parameters.

42 ENGINEERING↗
DOE OSTI2019

Interplay between Approximation Theory and Renormalization Group

The review presents general methods for treating complicated problems that cannot be solved exactly and whose solution encounters two major difficulties. First, there are no small parameters allowing for the safe use of perturbation theory in powers of these parameters, and even when small parameters exist, the related perturbative series are strongly divergent. Second, such perturbative series in powers of these parameters are rather short, so that the standard resummation techniques either yield bad approximations or are not applicable at all. The emphasis in the review is on the methods advanced and developed by the author. One of the general methods is Optimized Perturbation Theory now widely employed in various branches of physics, chemistry, and applied mathematics. The other powerful method is Self-Similar Approximation Theory allowing for quite simple and accurate summation of divergent series. These theories share many common features with the method of renormalization group, which is briefly sketched in order to stress the similarities in their ideas and their mutual interconnection.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Fully-Implicit Orthogonal Reconstructed Discontinuous Petrov-Galerkin Method for Multiphysics Problems

This document is focussed on the development of reconstructed discontinuous Galerkin (RDG P n P m ) method, based on orthogonal basis functions. Orthogonality of basis functions is essential for enabling robust and efficient fully-implicit Newton-Krylov based time discretization. The method is designed for generic partial differential equations, including transient hyperbolic, parabolic and/or elliptic operators, which are attributed to many multiphysics problems. Our driving application of interest is additive manufacturing, which requires simulations of fluid-solid-gas systems, with compressibility effects and phase change (melting/ solidification). Thus, we demonstrate the method capabilities for solving nonlinear heat conduction equation coupled with multi-material Navier-Stokes based compressible fluid (in low Mach number limit) systems. We focus our attention to the method accuracy (in both time and space), as well as solvability of linear algebra involved in linear steps of the Newton-based solver. We demonstrate the accuracy and efficacy of the method, emphasizing the advantages from the orthogonality of basis functions, which makes better conditioning of underlying (approximate) Jacobian matrices, and rapid convergence of Krylov methods. iii

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Unraveling Excitonic Effects for the First Hyperpolarizabilities of Chromophore Aggregates

Excitonic interactions often significantly affect the optoelectronic properties of molecular materials. However, their role in determining the nonlinear optical response of organic electro-optic materials remains poorly understood. In this paper, we explore the effects of excitonic interactions on the first hyperpolarizability for aggregates of donor–acceptor chromophores. We show that calculations of the first hyperpolarizabilty of chromophore aggregates based on a two-state model agree well with the more rigorous coupled perturbed Hartree–Fock method. We then use both time-dependent density functional theory calculations and the molecular exciton approximation to parametrize the two-state model. Use of the molecular exciton approximation to the two-state model (i) is appropriate for disordered aggregates (unlike band theory), (ii) is computationally efficient enough for calculating the first hyperpolarizability of materials that consist of thousands of interacting chromophores, and (iii) allows the unraveling of the effects of both excitonic interactions and electrostatic polarization of the chromophore electron density by its environment on the first hyperpolarizability of molecular materials. We find that use of the molecular exciton approximation to the two-state model does not introduce significant additional errors compared to those introduced by applying the two-state model alone. We determine that the absolute change to the first hyperpolarizability of chromophore aggregates due to excitonic interactions increases with the size of the aggregate. For all sizes of disordered aggregates of chromophores considered in this paper, the inclusion of excitonic interactions on average decreases the magnitude of the first hyperpolarizability by 12–14% compared to the case of non-interacting chromophores. Lastly, we present a method for analytically calculating the first hyperpolarizability of a one-dimensional periodic array of chromophores within the molecular exciton approximation to the two-state model. This technique can be used to include an approximate correction for excitonic effects when simulating the electro-optic response of disordered and ordered organic materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Ti:sapphire/KrF hybrid laser system generating trains of subterawatt subpicosecond UV pulses

The GARPUN-MTW Ti:sapphire/KrF hybrid laser system is used to investigate different multipass schemes for amplifying trains of ultrashort pulses (USPs) of subpicosecond duration. It is shown that, for an USP repetition period of 3 – 5 ns, which exceeds the gain-medium recovery time (∼2 ns), trains are amplified in the same way as single USPs. Due to this, a train can efficiently extract pump energy from the amplifier and sum energies of individual USPs. The energy of a four-USP train, extracted during four passes through the preamplifier and two passes through the final KrF amplifier (4 + 2 scheme), is saturated at a level of 1.6 J and corresponds to maximum USP peak powers of about 0.6 TW. The energy of amplified spontaneous emission (ASE), on the contrary, rapidly increases at a large total gain length L{sub eff} ≈ 6 m and is approximately equal to the USP energy. In the (4 + 1) and (2 + 2) schemes the USP energy decreases only slightly, to E{sub out} = 1.3 and 1.2 J, and the ASE fraction is reduced to about 10% and 3%, respectively. USP self-focusing leads to multiple laser beam filamentation and a 200-fold local increase in the radiation intensity in filaments, to ∼2 × 10{sup 11} W cm{sup -2}, a level at which the nonlinear loss in the output CaF{sub 2} windows of the KrF amplifier, caused by three-photon absorption, nonlinear scattering, and broadening of the radiation spectrum to a value exceeding the gain band of the KrF laser transition, becomes the main factor determining the saturation of the USP output energy. (lasers)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Direct statistical simulation of the Lorenz96 system in model reduction approaches

Direct statistical simulation (DSS) of nonlinear dynamical systems bypasses the traditional route of accumulating statistics by lengthy direct numerical simulations by solving the equations that govern the statistics themselves. DSS suffers, however, from the curse of dimensionality as the statistics (such as correlations) generally have higher dimensions than the underlying dynamical variables. Here we investigate two approaches to reduce the dimensionality of DSS, illustrating each method with numerical experiments with the Lorenz96 dynamical system. The forms of DSS chosen here involve approximate closures at second and third order in the equal-time cumulants. We demonstrate significant reduction in computational effort that can be achieved without sacrificing the accuracy of DSS. The methods developed here can be applied to turbulent fluid and magnetohydrodynamical systems. Published by the American Physical Society 2025

Li, Kuan↗