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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS2009

Precise Stabilization of the Optical Frequency of WGMRs

Crystalline whispering gallery mode resonators (CWGMRs) made of crystals with axial symmetry have ordinary and extraordinary families of optical modes. These modes have substantially different thermo-refractive constants. This results in a very sharp dependence of differential detuning of optical frequency on effective temperature. This frequency difference compared with clock gives an error signal for precise compensation of the random fluctuations of optical frequency. Certain crystals, like MgF2, have turnover points where the thermo-refractive effect is completely nullified. An advantage for applications using WGMRs for frequency stabilization is in the possibility of manufacturing resonators out of practically any optically transparent crystal. It is known that there are crystals with negative and zero thermal expansion at some specific temperatures. Doping changes properties of the crystals and it is possible to create an optically transparent crystal with zero thermal expansion at room temperature. With this innovation s stabilization technique, the resultant WGMR will have absolute frequency stability The expansion of the resonator s body can be completely compensated for by nonlinear elements. This results in compensation of linear thermal expansion (see figure). In three-mode, the MgF2 resonator, if tuned at the turnover thermal point, can compensate for all types of random thermal-related frequency drift. Simplified dual-mode method is also available. This creates miniature optical resonators with good short- and long-term stability for passive secondary frequency ethalon and an active resonator for active secondary frequency standard (a narrowband laser with long-term stability).

Savchenkov, Anatoliy↗
DOE OSTI2022

Spin-piston problem for a ferromagnetic thin film: Shock waves and solitons

In this report the unsteady, nonlinear magnetization dynamics induced by spin injection in an easy-plane ferromagnetic channel subject to an external magnetic field are studied analytically. Leveraging a dispersive hydrodynamic description, the Landau-Lifshitz equation is recast in terms of hydrodynamic-like variables for the magnetization's perpendicular component (spin density) and azimuthal phase gradient (fluid velocity). Spin injection acts as a moving piston that generates nonlinear, dynamical spin textures in the ferromagnetic channel with downstream quiescent spin density set by the external field. In contrast to the classical problem of a piston accelerating a compressible gas, here, variable spin injection and field lead to a rich variety of nonlinear wave phenomena from oscillatory spin shocks to solitons and rarefaction (expansion) waves. A full classification of solutions is provided using nonlinear wave modulation theory by identifying two key aspects of the fluid-like dynamics: subsonic/supersonic conditions and convex/nonconvex hydrodynamic flux. Familiar waveforms from the classical piston problem such as rarefaction waves and shocks manifest in their spin-based counterparts as smooth and highly oscillatory transitions, respectively, between two distinct magnetic states. The spin shock is an example of a dispersive shock wave, which arises in many physical systems. New features without a gas dynamics counterpart include composite wave complexes with “contact” spin shocks and rarefactions. Magnetic supersonic conditions lead to two pronounced piston edge behaviors including a stationary soliton and an oscillatory wave train. These coherent wave structures have physical implications for the generation of high frequency spin waves from pulsed injection and persistent, stable stationary and/or propagating solitons in the presence of magnetic damping. The analytical results are favorably compared with numerical simulations.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Soliton Generation in Negative Thermal Expansion Materials

Strain solitons have been observed statically in several 2D materials and dynamically in substrate materials using ultrafast laser pulses. The latter case relies on lattice relaxation in response to ultrafast heating in a light-absorbing transducer material, a process which is sensitive to the thermal expansion coefficient. Here we consider an unusual case where the sign of the thermal expansion coefficient is negative, a scenario which is experimentally feasible in light of rapid and recent advances in the discovery of negative thermal expansion materials. We present numerical solutions to a nonlinear differential equation which has been repeatedly demonstrated to quantitatively model experimental data and discuss the salient results using realistic parameters for material linear and nonlinear elasticity. The solitons that emerge from the initial value problem with negative and positive thermal expansion are qualitatively different in several ways. The new case of negative thermal expansion gives rise to a nearly-periodic soliton train with chirped profile and free of an isolated shock front. We suggest this unanticipated result may be realized experimentally and assess the potential for certain applications of this generic effect.

36 MATERIALS SCIENCE↗
NASA NTRS1975

Stability analysis of nonlinear autonomous systems - General theory and application to flutter

The analysis makes use of a singular perturbation method, the multiple time scaling. Concepts of stable and unstable limit cycles are introduced. The solution is obtained in the form of an asymptotic expansion. Numerical results are presented for the nonlinear flutter of panels and airfoils in supersonic flow. The approach used is an extension of a method for analyzing nonlinear panel flutter reported by Morino (1969).

Smith, L. L.↗
NASA NTRS1996

A dual-input nonlinear system analysis of autonomic modulation of heart rate

Linear analyses of fluctuations in heart rate and other hemodynamic variables have been used to elucidate cardiovascular regulatory mechanisms. The role of nonlinear contributions to fluctuations in hemodynamic variables has not been fully explored. This paper presents a nonlinear system analysis of the effect of fluctuations in instantaneous lung volume (ILV) and arterial blood pressure (ABP) on heart rate (HR) fluctuations. To successfully employ a nonlinear analysis based on the Laguerre expansion technique (LET), we introduce an efficient procedure for broadening the spectral content of the ILV and ABP inputs to the model by adding white noise. Results from computer simulations demonstrate the effectiveness of broadening the spectral band of input signals to obtain consistent and stable kernel estimates with the use of the LET. Without broadening the band of the ILV and ABP inputs, the LET did not provide stable kernel estimates. Moreover, we extend the LET to the case of multiple inputs in order to accommodate the analysis of the combined effect of ILV and ABP effect on heart rate. Analyzes of data based on the second-order Volterra-Wiener model reveal an important contribution of the second-order kernels to the description of the effect of lung volume and arterial blood pressure on heart rate. Furthermore, physiological effects of the autonomic blocking agents propranolol and atropine on changes in the first- and second-order kernels are also discussed.

NASA Discipline Regulatory Physiology↗
DOE OSTI2021

Vacuum magnetic fields with exact quasisymmetry near a flux surface. Part 1. Solutions near an axisymmetric surface

While several results have pointed to the existence of exactly quasisymmetric fields on a surface (Garren & Boozer, Phys. Fluids B, vol. 3, 1991, pp. 2805–2821; 2822–2834; Plunk & Helander, J. Plasma Phys. , vol. 84, 2018, 905840205), we have obtained the first such solutions using a vacuum surface expansion formalism. We obtain a single nonlinear parabolic partial differential equation for a function $\eta$ such the field strength satisfies $B = B(\eta )$ . Closed-form solutions are obtained in cylindrical, slab and isodynamic geometries. Numerical solutions of the full nonlinear equations in general axisymmetric toroidal geometry are obtained, resulting in a class of quasihelical local vacuum equilibria near an axisymmetric surface. The analytic models provide additional insight into general features of the nonlinear solutions, such as localization of the surface perturbations on the inboard side. The local solutions thus obtained can be continued globally only for special initial surfaces.

Physics↗
DOE OSTI2021

Growth of accretion driven scalar hair around Kerr black holes

We report that Scalar fields around compact objects are of interest for scalar-tensor theories of gravity and dark matter models consisting of a massive scalar, e.g., axions. We study the behavior of a scalar field around a Kerr black hole with nontrivial asymptotic boundary conditions - both nonzero density and nonzero angular momentum. Starting from an initial radially homogeneous configuration, a scalar cloud is accreted, which asymptotes to known stationary configurations over time. We study the cloud growth for different parameters including black hole spin, scalar field mass, and the scalar field density and angular momentum far from the black hole. We characterize the transient growth of the mass and angular momentum in the cloud, and the spatial profile of the scalar around the black hole, and relate the results of fully nonlinear simulations to an analytic perturbative expansion. We also highlight the potential for these accreted clouds to create monochromatic gravitational wave signals - similar to the signals from superradiant clouds, although significantly weaker in amplitude.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1993

A generalized Zel'dovich approximation to gravitational instability

The orbits of particles undergoing gravitational instability are parameterized by generalizing the Zel'dovich approximation to a series expansion of arbitrary accuracy in the nonlinear regime. The coefficients of this series are determined from an action principle, or, more generally, from moments of the equation of motion. It is shown that the series is more rapidly convergent than previous nonlinear approximations. The method therefore provides a practical means of determining particle orbits, even for highly nonlinear perturbations. As an alternative, we also outline how the nonlinear dynamics may be computed as a field theory in which the evolution of the density and the velocity is determined in fixed comoving Eulerian coordinates.

Giavalisco, M.↗
NASA NTRSDate not supplied

Dynamical Sensitivity in Response to a Wide Range of Abrupt CO 2 Forcings

An improved understanding of dynamical variability is important for projecting future changes in extratropical weather and the interaction between the extratropical troposphere and the tropics, stratosphere, cryosphere and ocean. Despite their simplicity, the abrupt 2x- and 4xCO 2 forcing simulations from the Coupled Model Intercomparison Project (CMIP) Phase 6 DECK experiments enable a mechanistic look into the forcing and feedback response characteristics of models that can be unambiguously attributed to an increase in carbon dioxide concentrations. Thus, while typically used to evaluate the climate sensitivity in models, with a primary focus on global surface temperature change, here we focus on several measures of extratropical variability, including projected changes in the storm tracks and in stratospheric polar vortex variability. Results are primarily based on simulations produced using low- and high-top versions of the NASA Goddard Institute for Space Studies Model (ModelE) but results are also presented from the larger CMIP6 multi-model ensemble. In addition to the 2x- and 4xCO 2 simulations, we also explore the linearity of the response of extratropical dynamical variability in ModelE to varying levels of CO 2 spanning the range 1/8-8xCO 2 . In particular, we show that the expansion of the jet streams varies nonlinearly with increasing CO 2 , especially in the Northern Hemisphere, and that this can be interpreted in terms of variations in ocean heat transport. The impact of composition feedbacks on changes in variability is also discussed.

dynamical variability↗
DOE OSTI2023

Applying Quantum Computing to Simulate Power System Dynamics

Power system dynamics are generally modeled by high dimensional nonlinear differential-algebraic equations due to a large number of generators, loads, and transmission lines. Thus, its computational complexity grows exponentially with the system size. This paper demonstrates the potential use of quantum computing algorithms to model the power system dynamics. Leveraging a symbolic programming framework, we equivalently convert the power system dynamics’ differential algebraic equations (DAEs) into ordinary differential equations (ODEs), where the data of the state vector can be encoded into quantum computers via amplitude encoding. The system's nonlinearity is captured by Taylor polynomial expansion, the quantum state tensor, and Hamiltonian simulation, whereas state variables can be updated by a quantum linear equation solver. Our results show that quantum computing can simulate the dynamics of the power system with high accuracy, whereas its complexity is polynomial in the logarithm of the system dimension. Our work also illustrates the use of scientific machine learning tools for implementing scientific computing concepts, e.g., Taylor expansion, DAEs/ODEs transform, and quantum computing solver, in the field of power engineering.

Tran, Huynh↗
NASA NTRS1973

Program for the solution of multipoint boundary value problems of quasilinear differential equations

Linear equations are solved by a method of superposition of solutions of a sequence of initial value problems. For nonlinear equations and/or boundary conditions, the solution is iterative and in each iteration a problem like the linear case is solved. A simple Taylor series expansion is used for the linearization of both nonlinear equations and nonlinear boundary conditions. The perturbation method of solution is used in preference to quasilinearization because of programming ease, and smaller storage requirements; and experiments indicate that the desired convergence properties exist although no proof or convergence is given.

Source record↗
NASA NTRS1992

Nonlinear spatial equilibration of an externally excited instability wave in a free shear layer

A two-dimensional disturbance evolving from a strictly linear, finite-growth-rate instability wave, with nonlinear effects first becoming important in the critical layer is considered. The analysis is carried out for a general weakly nonparallel mean flow using matched asymptotic expansions. The flow in the critical layer is governed by a nonlinear vorticity equation which includes a spatial-evolution term. As in Goldstein and Hultgren (1988), the critical layer ages into a quasi-equilibrium one and the initial exponential growth of the instability wave is converted into a weak algebraic growth during the roll-up process. This leads to a next stage of evolution where the instability-wave growth is simultaneously affected by mean-flow divergence and nonlinear critical-layer effects and is eventually converted to decay. Expansions for the various streamwise regions of the flow are combined into a single composite formula accounting for both shear-layer spreading and nonlinear critical-layer effects and good agreement with the experimental results of Thomas and Chu (1989) and Freymuth (1966) is demonstrated.

Hultgren, Lennart S.↗
NASA NTRS1992

Kinetic treatment of nonlinear magnetized plasma motions - General geometry and parallel waves

The expansion of kinetic equations in the limit of a strong magnetic field is presented. This gives a natural description of the motions of magnetized plasmas, which are slow compared to the particle gyroperiods and gyroradii. Although the approach is 3D, this very general result is used only to focus on the parallel propagation of nonlinear Alfven waves. The derivative nonlinear Schroedinger-like equation is obtained. Two new terms occur compared to earlier treatments, a nonlinear term proportional to the heat flux along the magnetic field line and a higher-order dispersive term. It is shown that kinetic description avoids the singularities occurring in magnetohydrodynamic or multifluid approaches, which correspond to the degenerate case of sound speeds equal to the Alfven speed, and that parallel heat fluxes cannot be neglected, not even in the case of low parallel plasma beta. A truly stationary soliton solution is derived.

Khabibrakhmanov, I. KH.↗
NASA NTRS1989

Two-dimensional magnetohydrodynamic model of emerging magnetic flux in the solar atmosphere

The nonlinear undular mode of the magnetic buoyancy instability in an isolated horizontal magnetic flux embedded in a two-temperature layered atmosphere (solar corona-chromosphere/photosphere) is investigated using a two-dimensional magnetohydrodynamic code. The results show that the flux sheet with beta of about 1 is initially located at the bottom of the photosphere, and that the gas slides down the expanding loop as the instability develops, with the evacuated loop rising as a result of enhanced magnetic buoyancy. The expansion of the magnetic loop in the nonlinear regime displays self-similar behavior. The rise velocity of the magnetic loop in the high chromosphere (10-15 km/s) and the velocity of downflow noted along the loop (30-50 km/s) are consistent with observed values for arch filament systems.

Shibata, K.↗
DOE OSTI2021

Nonlinear proper orthogonal decomposition for convection-dominated flows

Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when integrated with a time series predictive model. In this Letter, we put forth a nonlinear proper orthogonal decomposition (POD) framework, which is an end-to-end Galerkin-free model combining autoencoders with long short-term memory networks for dynamics. By eliminating the projection error due to the truncation of Galerkin models, a key enabler of the proposed nonintrusive approach is the kinematic construction of a nonlinear mapping between the full-rank expansion of the POD coefficients and the latent space where the dynamics evolve. We test our framework for model reduction of a convection-dominated system, which is generally challenging for reduced order models. Our approach not only improves the accuracy, but also significantly reduces the computational cost of training and testing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Accurate parameterization of the kinetic energy functional for calculations using exact-exchange

In this report, electronic structure calculations based on Kohn-Sham density functional theory (KSDFT) that incorporate exact exchange or hybrid functionals are associated with large computational expense, a consequence of the inherent cubic scaling bottleneck and large associated prefactor, which limits the length and time scales that can be accessed. Though orbital-free density functional theory (OFDFT) calculations scale linearly with system size and are associated with significantly smaller prefactor, they are limited by the absence of accurate density-dependent kinetic energy functionals. Therefore, the development of accurate density-dependent kinetic energy functionals is important for OFDFT calculations of large realistic systems. To this end, we propose a method to train kinetic energy functional models at the exact-exchange level of theory by using a dictionary of physically relevant terms that have been proposed in the literature in conjunction with linear or nonlinear regression methods to obtain the fitting coefficients. For our dictionary, we use gradient expansion of the kinetic energy, nonlocal models proposed in the literature and their nonlinear combinations, such as a model that incorporates spatial correlations between higher order derivatives of electron density at two points. The predictive capabilities of these models are assessed by using a variety of model one-dimensional systems that exhibit diverse bonding characteristics, such as a chain of eight hydrogens, LiF, LiH, C 4 H 2 , C 4 N 2 and C 3 O 2 . We show that by using data from model one-dimensional KSDFT calculations performed using the exact-exchange functional for only a few neutral structures, it is possible to generate models with high accuracy for charged systems as well as electron and kinetic energy densities during self-consistent field iterations. In addition, we show that it possible to learn both the orbital dependent terms, i.e., the kinetic energy and the exact-exchange energy, and models that incorporate additional nonlinearities in spatial correlations, such as a quadratic model, are needed to capture subtle features of the kinetic energy density that are present in exact-exchange-based KSDFT calculations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1993

Nonlinear response of graphite-epoxy wide columns subject to eccentric load

It is shown that including the effects of bend-twist coupling and material nonlinearity on the large displacement flexural response of graphite-epoxy wide columns is necessary to adequately model their response. Results from static tests on 0(30)T and (30/0/-30 sub 5)s laminated specimens under eccentric axial compression are compared to a nonlinear analysis. The analysis is based on a Kantrovich expansion of the displacements in the width coordinate and a finite element representation in the axial coordinate. An incremental, updated Lagrangian formulation and element corotational coordinates are employed. Nonlinear elastic material behavior was measured in a separate set of material characterization tests, and these data are used to compute tangent stillnesses in the updated configuration.

Griffin, O. H., Jr.↗