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Results for “nonlinear expansion”

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 433 records · Page 24

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NASA NTRS1981

Determination of two-stroke engine exhaust noise by the method of characteristics

A computational technique was developed for the method of characteristics solution of a one-dimensional flow in a duct as applied to the wave action in an engine exhaust system. By using the method, it was possible to compute the unsteady flow in both straight pipe and tuned expansion chamber exhaust systems as matched to the flow from the cylinder of a small two-stroke engine. The radiated exhaust noise was then determined by assuming monopole radiation from the tailpipe outlet. Very good agreement with experiment on an operation engine was achieved in the calculation of both the third octave radiated noise and the associated pressure cycles at several locations in the different exhaust systems. Of particular interest is the significance of nonlinear behavior which results in wave steepening and shock wave formation. The method computes the precise paths on the x-t plane of a finite number of C(sub +), C(sub -) and P characteristics, thereby obtaining high accuracy in determining the tailpipe outlet velocity and the radiated noise.

Jones, A. D.↗

NASA NTRS1990

Some aeroacoustic and aerodynamic applications of the theory of nonequilibrium thermodynamics

An exact equation is derived for the dissipation function of a homogeneous, isotropic, Newtonian fluid, with terms associated with irreversible compression or expansion, wave radiation, and the square of the vorticity. This and other forms of the dissipation function are used to identify simple flows, such as incompressible channel flow, the potential vortex with rotational core, and incompressible, irrotational flow as minimally dissipative distributions. A comparison of the hydrodynamic and thermodynamic stability characteristics of a parallel shear flow suggests that an association exists between flow stability and the variation of net dissipation with disturbance amplitude, and that nonlinear effects, such as bounded disturbance amplitude, may be examined from a thermodynamic basis.

Horne, W. Clifton↗

DOE OSTI2022

Determination of the nonlinear thermo-optic coefficient of silicon nitride and oxide using an effective index method

There is little literature characterizing the temperature-dependent thermo-optic coefficient (TOC) for low pressure chemical vapor deposition (LPCVD) silicon nitride or plasma enhanced chemical vapor deposition (PECVD) silicon dioxide at temperatures above 300 K. In this study, we characterize these material TOC’s from approximately 300-460 K, yielding values of (2.51 ± 0.08) · 10 −5 K −1 for silicon nitride and (5.67 ± 0.53) · 10 −6 K −1 for silicon oxide at room temperature (300 K). We use a simplified experimental setup and apply an analytical technique to account for thermal expansion during the extraction process. We also show that the waveguide geometry and method used to determine the resonant wavelength have a substantial impact on the precision of our results, a fact which can be used to improve the precision of numerous ring resonator index sensing experiments.

36 MATERIALS SCIENCE↗

NASA NTRS1993

Three-dimensional magnetohydrodynamics of the emerging magnetic flux in the solar atmosphere

The nonlinear evolution of an emerging magnetic flux tube or sheet in the solar atmosphere is studied through 3D MHD simulations. In the initial state, a horizontal magnetic flux sheet or tube is assumed to be embedded at the bottom of MHD two isothermal gas layers, which approximate the solar photosphere/chromosphere and the corona. The magnetic flux sheet or tube is unstable against the undular mode of the magnetic buoyancy instability. The magnetic loop rises due to the linear and then later nonlinear instabilities caused by the buoyancy enhanced by precipitating the gas along magnetic field lines. We find by 3D simulation that during the ascendance of loops the bundle of flux tubes or even the flux sheet develops into dense gas filaments pinched between magnetic loops. The interchange modes help produce a fine fiber flux structure perpendicular to the magnetic field direction in the linear stage, while the undular modes determine the overall buoyant loop structure. The expansion of such a bundle of magnetic loops follows the self-similar behavior observed in 2D cases studied earlier. Our study finds the threshold flux for arch filament system (AFS) formation to be about 0.3 x 10 exp 20 Mx.

Matsumoto, R.↗

NASA NTRS1986

What have we learned about galaxies through large computations?

Numerical models permit modelling processes within galaxies that are seemingly beyond the reach of physical contact or close-up viewing from different angles. N-body equations permit simple computations of the interactions of individual stars within galaxies, but the motions of these objects feature nonlinear characteristics because of the forces exerted by the complex as a whole which are not amenable to examination with Newtonian laws of force. The models have, however, revealed that thin disk galactic are not stable forms, that barlike structures rotating end-over-end are more stable structures, and that galactic contraction occurs during collisions between galaxies. Internal effects have been successfully predicted for galaxies which are part of clusters, growth rate disturbances due to the expansion of the Universe have been quantified as 2-3 percent and dynamical friction has been shown to damage galaxies which are sliding into background material.

Miller, R. H.↗

NASA NTRS1994

Quantum propagation in single mode fiber

This paper presents a theory for quantum light propagation in a single-mode fiber which includes the effects of the Kerr nonlinearity, group-velocity dispersion, and linear loss. The theory reproduces the results of classical self-phase modulation, quantum four-wave mixing, and classical solution physics, within their respective regions of validity. It demonstrates the crucial role played by the Kerr-effect material time constant, in limiting the quantum phase shifts caused by the broadband zero-point fluctuations that accompany any quantized input field. Operator moment equations - approximated, numerically, via a terminated cumulant expansion - are used to obtain results for homodyne-measurement noise spectra when dispersion is negligible. More complicated forms of these equations can be used to incorporate dispersion into the noise calculations.

Joneckis, Lance G.↗

DOE OSTI2020

Robust PCA-Deep Belief Network Surrogate Model for Distribution System Topology Identification with DERs

With the expansion of distribution networks and increased penetration of distributed energy resources (DERs), it is becoming increasingly important to obtain accurate distribution network topology in real-time. In this paper, a robust principal component analysis coupled deep belief network (PCA-DBN) surrogate model is proposed for distribution system topology identification. It integrates the benefits of robust feature extraction from PCA to deal with data quality issues and filter out noise, and the strength of DBN in capturing the nonlinear relationship between voltage amplitudes and the binary states of switchable connections. This also significantly reduces the DBN training complexity without loss of accuracy. It is shown that the widely used standard deviation of voltage drop and the voltage covariance matrix features yield less accuracy as compared to that of the voltage amplitudes in presence of high penetration of DERs and ZIP loads. Comparison results with other alternatives, such as the random forest (RF), multi-output regression (MOR) and the traditional DBN methods demonstrate that the proposed method can achieve a much higher topology identification accuracy while maintaining robustness to missing data and measurement noise under various penetration levels of DERs.

deep belief network↗

NASA NTRS1983

Equivalent source modeling of the core magnetic field using magsat data

Experiments are carried out on fitting the main field using different numbers of equivalent sources arranged in equal area at fixed radii at and inside the core-mantle boundary. In fixing the radius for a given series of runs, the convergence problems that result from the extreme nonlinearity of the problem when dipole positions are allowed to vary are avoided. Results are presented from a comparison between this approach and the standard spherical harmonic approach for modeling the main field in terms of accuracy and computational efficiency. The modeling of the main field with an equivalent dipole representation is found to be comparable to the standard spherical harmonic approach in accuracy. The 32 deg dipole density (42 dipoles) corresponds approximately to an eleventh degree/order spherical harmonic expansion (143 parameters), whereas the 21 dipole density (92 dipoles) corresponds to approximately a seventeenth degree and order expansion (323 parameters). It is pointed out that fixing the dipole positions results in rapid convergence of the dipole solutions for single-epoch models.

Mayhew, M. A.↗

NASA NTRS1981

A four-dimensional primitive equation model for coupled coastal-deep ocean studies

A prototype four dimensional continental shelf/deep ocean model is described. In its present form, the model incorporates the effects of finite amplitude topography, advective nonlinearities, and variable stratification and rotation. The model can be forced either directly by imposed atmospheric windstress and surface pressure distributions, and energetic mean currents imposed by the exterior oceanic circulation; or indirectly by initial distributions of shoreward propagation mesoscale waves and eddies. To avoid concerns over the appropriate specification of 'open' boundary conditions on the cross-shelf and seaward model boundaries, a periodic channel geometry (oriented along-coast) is used. The model employs a traditional finite difference expansion in the cross-shelf direction, and a Fourier (periodic) representation in the long-shelf coordinate.

Haidvogel, D. B.↗

NASA NTRS1983

The COREL and W12SC3 computer programs for supersonic wing design and analysis

Two computer codes useful in the supersonic aerodynamic design of wings, including the supersonic maneuver case are described. The nonlinear full potential equation COREL code performs an analysis of a spanwise section of the wing in the crossflow plane by assuming conical flow over the section. A subsequent approximate correction to the solution can be made in order to account for nonconical effects. In COREL, the flow-field is assumed to be irrotional (Mach numbers normal to shock waves less than about 1.3) and the full potential equation is solved to obtain detailed results for the leading edge expansion, supercritical crossflow, and any crossflow shockwaves. W12SC3 is a linear theory panel method which combines and extends elements of several of Woodward's codes, with emphasis on fighter applications. After a brief review of the aerodynamic theory used by each method, the use of the codes is illustrated with several examples, detailed input instructions and a sample case.

Mason, W. H.↗

NASA NTRS2002

Empirical mode decomposition apparatus, method and article of manufacture for analyzing biological signals and performing curve fitting

A computer implemented physical signal analysis method includes four basic steps and the associated presentation techniques of the results. The first step is a computer implemented Empirical Mode Decomposition that extracts a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform which produces a Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum. The third step filters the physical signal by combining a subset of the IMFs. In the fourth step, a curve may be fitted to the filtered signal which may not have been possible with the original, unfiltered signal.

Huang, Norden E.↗

NASA NTRS2004

Empirical mode decomposition apparatus, method and article of manufacture for analyzing biological signals and performing curve fitting

Huang, Norden E.↗

NASA NTRS1990

Development of Renormalization Group Analysis of Turbulence

The renormalization group (RG) procedure for nonlinear, dissipative systems is now quite standard, and its applications to the problem of hydrodynamic turbulence are becoming well known. In summary, the RG method isolates self similar behavior and provides a systematic procedure to describe scale invariant dynamics in terms of large scale variables only. The parameterization of the small scales in a self consistent manner has important implications for sub-grid modeling. This paper develops the homogeneous, isotropic turbulence and addresses the meaning and consequence of epsilon-expansion. The theory is then extended to include a weak mean flow and application of the RG method to a sequence of models is shown to converge to the Navier-Stokes equations.

L M Smith↗

DOE OSTI2020

Multi-Stage and Multi-Timescale Robust Co-Optimization Planning for Reliable and Sustainable Power Systems. Final Report

In this project, Clarkson University, in collaboration with Southern Methodist University and University of Pittsburgh, conducted the research to model, design, and implement a sophisticated generation and transmission co-optimization planning decision tool, called Multi-stage and Multi-timescale robust Co-Optimization Planning (MMCOP). The MMCOP decision tool intends to facilitate generation and transmission co-optimization planning of emerging power systems, while mitigating risks and uncertainties in both short-term operation dynamics and long-term policy and technology changes. Long-term power system planning aims at optimizing asset utilization by investing in a proper mix of various generation technologies and transmission lines to supply the future load growth. In particular, the Clean Power Plan (CPP), which is designed to combat climate change and reduce carbon emissions by setting a national limit on carbon pollution from power plants, may dramatically change the landscape of the power industry by further promoting clean energy and phasing out emissions-intensive generation technologies. In addition, novel non-wire alternatives (e.g., demand response (DR), distributed generation (DG), energy efficiency (EE), and smart grid technologies) and the computational complexity for large-scale systems significantly complicate the system planning procedure even further. However, existing conventional planning approaches neglect short-term variability and uncertainty of renewable energy, hourly chronological operation details, and physical nonlinear characteristics of the alternating current transmission network. As a result, existing conventional planning approaches may not work properly, and power systems reliability could be in jeopardy. In observing the limitations of existing conventional planning approaches and addressing new challenges of emerging power systems, the main scope of this project to develop co-optimization planning models within a multi-stage and multi-timescale framework. In particular, random contingencies, key uncertainty factors, and AC power flows are included to derive expansion plans while considering both long-term reliability and short-term flexibility.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1999

Computer implemented empirical mode decomposition method, apparatus and article of manufacture

A computer implemented physical signal analysis method is invented. This method includes two essential steps and the associated presentation techniques of the results. All the steps exist only in a computer: there are no analytic expressions resulting from the method. The first step is a computer implemented Empirical Mode Decomposition to extract a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform. The final result is the Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum.

Huang, Norden E.↗

DOE OSTI2025

Generalized framework for likelihood-based field-level inference of growth rate from velocity and density fields

Measuring the growth rate of large-scale structures ( f ) as a function of redshift has the potential to break degeneracies between modified gravity and dark energy models, when combined with expansion-rate probes. Direct estimates of peculiar velocities of galaxies have attracted interest as a means of estimating fσ 8 . In particular, field-level methods can be used to fit the field nuisance parameter along with cosmological parameters simultaneously. This article aims to provide the community with a unified framework for the theoretical modeling of the likelihood-based field-level inference by performing fast field covariance calculations for velocity and density fields. Our purpose is to lay the foundations for a nonlinear extension of the likelihood-based method at the field level. We have developed a generalized framework, implemented in the dedicated software flip to perform a likelihood-based inference of fσ 8 . We derived a new field covariance model, which includes wide-angle corrections. We also included the models previously described in the literature inside our framework. We compared their performance against ours, and we validated our model by comparing it with the two-point statistics of a recent N-body simulation. The tests we performed have allowed us to validate our software and determine the appropriate wavenumber range to integrate our covariance model and its validity in terms of separation. Our framework allows for a wider wavenumber coverage to be used in our calculations than in previous works, which is particularly interesting for nonlinear model extensions. Finally, our generalized framework allows us to efficiently perform a survey geometry-dependent Fisher forecast of the fσ 8 parameter. We show that the Fisher forecast method we developed gives an error bar that is 30% closer to a full likelihood-based estimation than a standard volume Fisher forecast.

Ravoux, Corentin↗

DOE OSTI2023

Quantum algorithm for the linear Vlasov equation with collisions

The Vlasov equation is a nonlinear partial differential equation that provides a first-principles description of the dynamics of plasmas. Its linear limit is routinely used in plasma physics to investigate plasma oscillations and stability. In this paper, we present a quantum algorithm that simulates the linearized Vlasov equation with and without collisions, in the one-dimensional electrostatic limit. Rather than solving this equation in its native spatial and velocity phase space, we adopt an efficient representation in the dual space yielded by a Fourier-Hermite expansion. For a given simulation time, the Fourier-Hermite representation is exponentially more compact, thus yielding a classical algorithm that can match the performance of a previously proposed quantum algorithm for this problem. Further, this representation results in a system of linear ordinary differential equations (ODEs) which can be solved with well-developed quantum algorithms: a Hamiltonian simulation in the collisionless case, and quantum ODE solvers in the collisional case. In particular, we demonstrate that a quadratic speedup in system size is attainable.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

GFiRe—Gauge Field integrator for Reheating

We present a new numerical algorithm and code, GFiRe, for solving the nonlinear evolution of Abelian gauge fields coupled to complex scalar fields in homogeneous and isotropic spacetimes. We adopt a hybrid approach to solving the system: the spatial derivatives are discretized using standard Lattice Gauge Field Theory techniques, whereas the time evolution of the fields and scale factor is implemented with explicit, composite, symplectic integrators. An important property of our compound algorithm is that the discretized Gauss constraint is respected exactly, regardless of the order of the symplectic integrator. This remains true even when the background expansion is computed “self-consistently”; that is, when the expansion history is computed using spatial averaged components of the energy momentum tensor in the simulation volume. Hence, our code can also be used in cases where the fields dominate the energy density of the universe, for example, during reheating after inflation. We test the algorithm in scenarios of reheating where the inflaton is a complex scalar field with a potential ∝(2|Φ| 2 - v 2 ) 2 and is coupled to an Abelian gauge field. Tracing the evolution of the system through complex dynamics (including resonant excitation of fields, backreaction, formation of solitons, and changes in the equation of state) in a self-consistently expanding universe, we find the energy conservation violation (<10 -4 ) to be very stable and the Gauss constraint violation (<10 -6 ) to be dominated by differencing noise.

79 ASTRONOMY AND ASTROPHYSICS↗