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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

The Adjoint Petrov–Galerkin method for non-linear model reduction

Here, we formulate a new projection-based reduced-order modeling technique for non-linear dynamical systems. The proposed technique, which we refer to as the Adjoint Petrov–Galerkin (APG) method, is derived by decomposing the generalized coordinates of a dynamical system into a resolved coarse-scale set and an unresolved fine-scale set. A Markovian finite memory assumption within the Mori–Zwanzig formalism is then used to develop a reduced-order representation of the coarse scales. This procedure leads to a closed reduced-order model that displays commonalities with the adjoint stabilization method used in finite elements. The formulation is shown to be equivalent to a Petrov–Galerkin method with a non-linear, time-varying test basis, thus sharing some similarities with the Least-Squares Petrov–Galerkin method. Theoretical analysis examining a priori error bounds and computational cost is presented. Numerical experiments on the compressible Navier–Stokes equations demonstrate that the proposed method can lead to improvements in numerical accuracy, robustness, and computational efficiency over the Galerkin method on problems of practical interest. Improvements in numerical accuracy and computational efficiency over the Least-Squares Petrov–Galerkin method are observed in most cases.

42 ENGINEERING↗
DOE OSTI2022

Electrical Conductivity of Clayey Rocks and Soils: A Non-Linear Model

It is well-accepted that Archie's law is only applicable to “clean” rocks and soils but fails in “dirty” ones where clay minerals possess an additional component of surface conductivity. Although several models, for example, Waxman-Smits model, were presented to account for this phenomenon, surface conductivity is always inappropriately treated as constant, which actually only holds at high salinities. The essential non-linear characteristic differing over fluid salinities has not been physically or mathematically explained well in those models. Here, we scrutinize the conduction mechanism of clayey rocks and soils and ascribe this non-linear feature to (a) variation of the electrical double layer and (b) the intrinsic clay-and-water conduction pattern. With effective medium theory, we develop an easy-to-use non-linear model that both reflects electrochemical theories and explains the measurement data well. Our model can be used to produce more accurate results for laboratory- and field-scale petrophysical parameter evaluations than the previous models.

58 GEOSCIENCES↗
DOE OSTI2018

Load-Flow in Multiphase Distribution Networks: Existence, Uniqueness, Non-Singularity, and Linear Models

This paper considers unbalanced multiphase distribution systems with generic topology and different load models, and extends the Z-bus iterative load-flow algorithm based on a fixed-point interpretation of the AC load-flow equations. Explicit conditions for existence and uniqueness of load-flow solutions are presented. These conditions also guarantee convergence of the load-flow algorithm to the unique solution. The proposed methodology is applicable to generic systems featuring (i) wye connections; (ii) ungrounded delta connections; (iii) a combination of wye-connected and delta-connected sources/loads; and, (iv) a combination of line-to-line and line-to-grounded-neutral devices at the secondary of distribution transformers. Further, a sufficient condition for the non-singularity of the load-flow Jacobian is proposed. Lastly, linear load-flow models are derived, and their approximation accuracy is analyzed. Theoretical results are corroborated through experiments on IEEE test feeders.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2015

Quasi-linear modeling of lower hybrid current drive in ITER and DEMO

First pass absorption of the Lower Hybrid waves in thermonuclear devices like ITER and DEMO is modeled by coupling the ray tracing equations with the quasi-linear evolution of the electron distribution function in 2D velocity space. As usually assumed, the Lower Hybrid Current Drive is not effective in a plasma of a tokamak fusion reactor, owing to the accessibility condition which, depending on the density, restricts the parallel wavenumber to values greater than n{sub ∥crit} and, at the same time, to the high electron temperature that would enhance the wave absorption and then restricts the RF power deposition to the very periphery of the plasma column (near the separatrix). In this work, by extensively using the “ray{sup star}” code, a parametric study of the propagation and absorption of the LH wave as function of the coupled wave spectrum (as its width, and peak value), has been performed very accurately. Such a careful investigation aims at controlling the power deposition layer possibly in the external half radius of the plasma, thus providing a valuable aid to the solution of how to control the plasma current profile in a toroidal magnetic configuration, and how to help the suppression of MHD mode that can develop in the outer part of the plasma. This analysis is useful not only for exploring the possibility of profile control of a pulsed operation reactor as well as the tearing mode stabilization, but also in order to reconsider the feasibility of steady state regime for DEMO.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Running vacuum cosmological models: linear scalar perturbations

In cosmology, phenomenologically motivated expressions for running vacuum are commonly parameterized as linear functions typically denoted by Λ( H {sup 2}) or Λ( R ). Such models assume an equation of state for the vacuum given by P-bar {sub Λ} = - ρ-bar {sub Λ}, relating its background pressure P-bar {sub Λ} with its mean energy density ρ-bar {sub Λ} ≡ Λ/8π G . This equation of state suggests that the vacuum dynamics is due to an interaction with the matter content of the universe. Most of the approaches studying the observational impact of these models only consider the interaction between the vacuum and the transient dominant matter component of the universe. We extend such models by assuming that the running vacuum is the sum of independent contributions, namely ρ-bar {sub Λ} = Σ {sub i} ρ-bar {sub Λ} {sub i} . Each Λ i vacuum component is associated and interacting with one of the i matter components in both the background and perturbation levels. We derive the evolution equations for the linear scalar vacuum and matter perturbations in those two scenarios, and identify the running vacuum imprints on the cosmic microwave background anisotropies as well as on the matter power spectrum. In the Λ( H {sup 2}) scenario the vacuum is coupled with every matter component, whereas the Λ( R ) description only leads to a coupling between vacuum and non-relativistic matter, producing different effects on the matter power spectrum.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Non-linear Model Predictive Control of Wave Energy Converters with Realistic Power Take-off Configurations and Loss Model

Model Predictive Control (MPC) has been recognized as a well-developed control strategy for optimizing the performance of wave energy converters (WECs). The standard problem involves maximizing the absorbed power from oncoming waves while respecting motion constraints of the device and force constraints of the power take-off (PTO). The generated electrical power is then calculated by assuming an ideal PTO with no power conversion losses or limitations to power flow. In this article, we remove the assumption of an ideal PTO and present four different control options that reflect unique combinations of PTO control and power flow constraints. We also recast the MPC problem to maximize the generated power instead of the absorbed power by accounting for the losses in the power train. Using a WEC with a hydraulic PTO, we develop a loss model suitable for controls optimization. Lastly, we illustrate the process of setting up the non-linear MPC problem and compare the performance of competing control strategies using a common benchmark based on annual energy captured at a reference site.

16 TIDAL AND WAVE POWER↗
DOE OSTI2017

Universal Method of Modeling Linear Stationary Physical Fields

The aim of this paper is to develop a method, described earlier, of solving quantum-mechanical problems into a universal numerical method of modeling fields of various physical nature. This method is based on reducing the initial equation of mathematical physics describing a given physical field to a simpler inhomogeneous equation with a known fundamental solution. This equation is then transformed into an inhomogeneous integral equation with a kernel expressed in terms of the known fundamental solution. The obtained integral equation with boundary conditions is solved numerically. To confirm the efficiency of the proposed numerical method, a two-dimensional and a three-dimensional boundary value problem with known solutions have been solved. Another important illustration of the efficiency of the proposed method is the solution of quantum-mechanical problems for one-dimensional and two-dimensional quantum oscillators. It is shown that the considered method allows one to find the energy eigenvalues and the eigenfunctions with acceptable accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Protocol to detect dilution cycles in chemostat experiments and estimate growth rate slopes with linear modeling with R software chemostat_regression

Chemostat growth chambers measure optical density over time and require manual calculation of growth rates. Here, we present chemostat_regression, R software that enables users to automatically identify chemostat cycles and estimate growth rate using a linear regression approach. We describe steps for creating requisite software environment(s), formatting input data, executing the software via command line/RStudio/R-Shiny, interpreting results, assessing the validity of results, and modifying input parameters.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Exploring Causal Physical Mechanisms via Non-Gaussian Linear Models and Deep Kernel Learning: Applications for Ferroelectric Domain Structures

Rapid emergence of multimodal imaging in scanning probe, electron, and optical microscopies has brought forth the challenge of understanding the information contained in these complex data sets, targeting the intrinsic correlations between different channels, and further exploring the underpinning causal physical mechanisms. Here, we develop such an analysis framework for Piezoresponse Force Microscopy. We argue that under certain conditions, we can bootstrap experimental observations with the prior knowledge of materials structure to get information on certain nonobserved properties, and demonstrate linear causal analysis for PFM observables. We further demonstrate that the strength of individual causal links between complex descriptors can be ascertained using the deep kernel learning (DKL) model. In this DKL analysis, we use the prior information on domain structure within the image to predict the physical properties. This analysis demonstrates the correlative relationships between morphology, piezoresponse, elastic property, etc., at nanoscale. The prediction of morphology and other physical parameters illustrates a mutual interaction between surface condition and physical properties in ferroelectric materials. Overall, this analysis is universal and can be extended to explore the correlative relationships of other multichannel data sets, and allow for high-fidelity reconstruction of underpinning functionalities and physical mechanisms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Spectral Analysis of Linear Models of Viscoelasticity

In this paper, we examine Volterra integrodifferential equations with unbounded operator coefficients in Hilbert spaces. Equations considered are abstract hyperbolic equations perturbed by terms containing Volterra integral operators. These equations can be realized as partial integrodifferential equations that appear in the theory of viscoelasticity (see [2, 5]), as Gurtin–Pipkin integrodifferential equations (see [1, 7]) that describe finite-speed heat transfer in materials with memory. They also appear in averaging problems for multiphase media (Darcy’s law.

97 MATHEMATICS AND COMPUTING↗