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Results for “Linearity preservation”

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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Direct driving of electronic and phononic degrees of freedom in a honeycomb bilayer with infrared light

Here, we study theoretically AB-stacked honeycomb bilayers driven by light in resonance with an infrared phonon within a tight-binding description. We characterize the phonon properties of honeycomb bilayers with group theory and construct an electronic time-dependent tight-binding model for the system following photoexcitation in resonance with an infrared phonon. We adopt an atomically adiabatic approximation [V. Mohanty and E. J. Heller, Proc. Natl. Acad. Sci. 116, 18316 (2019)] to describe classically vibrating nuclei, but obtain the Floquet quasienergy spectrum associated with the time-dependent model exactly. We introduce a general scheme to disentangle the complex low-frequency Floquet spectrum to elucidate the relevant Floquet bands. As a prototypical example, we consider bilayer graphene. We find that light in the low-frequency regime can induce a band gap in the quasienergy spectrum in the vicinity of the $K$ points even if it is linearly polarized, in contrast with the expectations within the Born-Oppenheimer approximation and the high-frequency regime. Finally, we analyze the diabaticity of the driven electron and driven phonon processes and find contrasting effects on the autocorrelation functions at the same driving frequency: Driven phonons preserve the character of the initial state while driven electrons exhibit strong deviations within a few drive cycles. The procedure outlined here can be applied to other materials to describe the combined effects of low-frequency light on phonons and electrons.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

AutoReP: Automatic ReLU Replacement for Fast Private Network Inference

The proliferation of the Machine-Learning-As-A-Service (MLaaS) market has brought to light a number of clients’ data privacy and security concerns. One promising solution is private inference (PI) techniques using cryptographic primitives. These techniques often come with high computation and communication overhead associated with the non-linear operator such as ReLU. Several approaches have been developed in reducing the number of ReLU operations, however, they either require a heuristic threshold selection or introduce significant accuracy drop. This work presents AutoReP, a gradient-based framework for non-linear operators reduction that aims to mitigate these concerns from a systematic perspective. AutoReP automates the process of discrete selection of ReLU and polynomial functions on neurons to accelerate PI applications. We also introduce distribution-aware polynomial approximation (DaPa) to accurately approximate ReLUs under given distribution, preserving model expressivity. Our experimental results demonstrate significant accuracy improvements of 6.12% (94.31%, 12.9K ReLU budget, CIFAR-10), 8.39% (74.92%, 12.9K ReLU budget, CIFAR-100), and 9.45% (63.69%, 55K ReLU budget, Tiny-ImageNet) over current state-of-the-art methods, e.g., SNL. Morever, AutoReP is applied to EfficientNet-B2 on ImageNet dataset, and achieved 75.55% accuracy with 176.1 × ReLU budget reduction.

Peng, Hongwu↗
DOE OSTI2022

Time-discretization of a plasma-neutral MHD model with a semi-implicit leapfrog algorithm

The semi-implicit leapfrog time-discretization is a workhorse algorithm for initial-value MHD codes to bridge between vastly separated time scales. Inclusion of atomic interactions with neutrals breaks the functional structure of the MHD equations that exploited by the leapfrog. In this work, we address how to best integrate atomic physics into the semi-implicit leapfrog. Following the Crank-Nicolson method, one approach is to time-center the atomic interactions in the linear solver and use a Newton method to include the nonlinear contributions. Alternatively, another family of methods are based on operator-splitting the terms associated with the atomic interactions using a Strang-splitting technique. These methods naturally break equations into constituent ODE and PDE parts and preserve the structure exploited by the semi-implicit leapfrog. We study the accuracy and efficiency of these methods through a battery of 0D and 1D cases and show that a second-order-in-time Douglas-Rachford inspired coupling between the ODE and PDE advances is effective in reducing the time-discretization error to be comparable to that of Crank-Nicolson with Newton iteration of the nonlinear terms. Splitting ODE and PDE parts results in independent matrix solves for each field which reduces the computational cost considerably and provides parallelization over species relative to Crank-Nicolson.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Tri-Level Linear Programming Model for Automatic Load Shedding Using Spectral Clustering

Traditional load shedding schemes can be inadequate in grids with high renewable penetration, leading to unstable events and unnecessary grid islanding. Although for both manual and automatic operating modes load shedding areas have been predefined by grid operators, they have remained fixed, and may be sub-optimal due to dynamic operating conditions. In this work, a distributed tri-level linear programming model for automatic load shedding to avoid system islanding is presented. Preventing islanding is preferred because it reduces the need for additional load shedding besides the disconnection of transmission lines between islands. This is crucial as maintaining the local generation-demand balance is necessary to preserve frequency stability. Furthermore, uneven distribution of generation resources among islands can lead to increased load shedding, causing economic and reliability challenges. This issue is further compounded in modern power systems heavily dependent on non-dispatchable resources like wind and solar. The upper-level model uses complex power flow measurements to determine the system areas to shed load depending on actual operating conditions using a spectral clustering approach. The mid-level model estimates the area system state, while the lower-level model determines the locations and load values to be shed. The solution is practical and promising for real-world applications.

Baquedano-Aguilar, Mario D.↗
NASA NTRS1979

Serenitatis multi-ringed basin - Regional geology and basin ring interpretation

New topographic data allow a reassessment of the ring structure and distribution of facies of the Serenitatis basin (SB) and correlation with the younger and essentially same-size Orientale basin. Three major rings of the main (southern) SB are mapped: the Linne ring, outlined by mare ridges, average diameter 420 km; the Haemus ring, outlined by basin-facing scarps and massifs with crenulated borders, 610 km; and the Vitruvius ring, outlined by basin-facing linear scarps and massifs, 880 km. The second ring is interpreted as the rim of the transient cavity, while Serenitatis ejecta should be present in significant amounts at the junction of the Serenitatis and Imbrium third rings. The new reconstruction indicates that portions of the SB are better preserved than previously thought, consistent with recent stratigraphic and sample studies that suggest an age (as young as 3.87 plus or minus 0.04 b.y.) for SB which is older than, but close to, the time of formation of the Imbrium basin.

Head, J. W., III↗
DOE OSTI2023

Semi-Implicit Computation of Fast Modes in a Scheme Integrating Slow Modes by a Leapfrog Method Based on a Selective Implicit Time Filter

Abstract A scheme for integration of atmospheric equations containing terms with differing time scales is developed. The method employs a filtered leapfrog scheme utilizing a fourth-order implicit time filter with one function evaluation per time step to compute slow-propagating phenomena such as advection and rotation. The terms involving fast-propagating modes are handled implicitly with an unconditionally stable method that permits application of larger time steps and faster computations compared to fully explicit treatment. Implementation using explicit and recurrent formulation is provided. Stability analysis demonstrates that the method is conditionally stable for any combination of frequencies involved in the slow and fast terms as they approach the origin. The implicit filter used in the method damps the computational modes without noticeably sacrificing the accuracy of the physical mode. TheO[(Δt 4 )] accuracy for amplitude errors achieved by the implicitly filtered leapfrog is preserved in applications where terms responsible for fast propagation are integrated with a semi-implicit method. Detailed formulation of the method for soundproof nonhydrostatic anelastic equations is provided. Procedures for implementation in global spectral shallow-water models are also given. Examples comparing numerical and analytical solutions for linear gravity waves demonstrate the accuracy of the scheme. The performance is also shown in more practical nonlinear applications, where numerical solutions accomplished by the method are evaluated against those computed from a scheme where the slow terms are handled by the third-order Runge–Kutta scheme. It demonstrates that the method is able to accurately resolve fine-scale dynamics of Kelvin–Helmholtz shear instabilities, the evolution of density current, and nonlinear drifts of twin tropical cyclones.

Meteorology & Atmospheric Sciences↗
NASA NTRS1981

Theory, computation, and application of exponential splines

A generalization of the semiclassical cubic spline known in the literature as the exponential spline is discussed. In actuality, the exponential spline represents a continuum of interpolants ranging from the cubic spline to the linear spline. A particular member of this family is uniquely specified by the choice of certain tension parameters. The theoretical underpinnings of the exponential spline are outlined. This development roughly parallels the existing theory for cubic splines. The primary extension lies in the ability of the exponential spline to preserve convexity and monotonicity present in the data. Next, the numerical computation of the exponential spline is discussed. A variety of numerical devices are employed to produce a stable and robust algorithm. An algorithm for the selection of tension parameters that will produce a shape preserving approximant is developed. A sequence of selected curve-fitting examples are presented which clearly demonstrate the advantages of exponential splines over cubic splines.

Mccartin, B. J.↗
NASA NTRS2002

A Two-Dimensional Linear Bicharacteristic FDTD Method

The linear bicharacteristic scheme (LBS) was originally developed to improve unsteady solutions in computational acoustics and aeroacoustics. The LBS has previously been extended to treat lossy materials for one-dimensional problems. It is a classical leapfrog algorithm, but is combined with upwind bias in the spatial derivatives. This approach preserves the time-reversibility of the leapfrog algorithm, which results in no dissipation, and it permits more flexibility by the ability to adopt a characteristic based method. The use of characteristic variables allows the LBS to include the Perfectly Matched Layer boundary condition with no added storage or complexity. The LBS offers a central storage approach with lower dispersion than the Yee algorithm, plus it generalizes much easier to nonuniform grids. It has previously been applied to two and three-dimensional free-space electromagnetic propagation and scattering problems. This paper extends the LBS to the two-dimensional case. Results are presented for point source radiation problems, and the FDTD algorithm is chosen as a convenient reference for comparison.

Beggs, John H.↗
DOE OSTI2020

Assessment of Demographic, Genetic, and Imaging Variables Associated With Brain Resilience and Cognitive Resilience to Pathological Tau in Patients With Alzheimer Disease

Importance: Better understanding is needed of the degree to which individuals tolerate Alzheimer disease (AD)-like pathological tau with respect to brain structure (brain resilience) and cognition (cognitive resilience). Objective: To examine the demographic (age, sex, and educational level), genetic (APOE-ε4 status), and neuroimaging (white matter hyperintensities and cortical thickness) factors associated with interindividual differences in brain and cognitive resilience to tau positron emission tomography (PET) load and to changes in global cognition over time. Design, setting, an participants: In this cross-sectional, longitudinal study, tau PET was performed from June 1, 2014, to November 30, 2017, and global cognition monitored for a mean [SD] interval of 2.0 [1.8] years at 3 dementia centers in South Korea, Sweden, and the United States. The study included amyloid-β-positive participants with mild cognitive impairment or AD dementia. Data analysis was performed from October 26, 2018, to December 11, 2019. Exposures: Standard dementia screening, cognitive testing, brain magnetic resonance imaging, amyloid-β PET and cerebrospinal fluid analysis, and flortaucipir (tau) labeled with fluor-18 (18F) PET. Main outcomes and measures: Separate linear regression models were performed between whole cortex [18F]flortaucipir uptake and cortical thickness, and standardized residuals were used to obtain a measure of brain resilience. The same procedure was performed for whole cortex [18F]flortaucipir uptake vs Mini-Mental State Examination (MMSE) as a measure of cognitive resilience. Bivariate and multivariable linear regression models were conducted with age, sex, educational level, APOE-ε4 status, white matter hyperintensity volumes, and cortical thickness as independent variables and brain and cognitive resilience measures as dependent variables. Linear mixed models were performed to examine whether changes in MMSE scores over time differed as a function of a combined brain and cognitive resilience variable. Results: A total of 260 participants (145 [55.8%] female; mean [SD] age, 69.2 [9.5] years; mean [SD] MMSE score, 21.9 [5.5]) were included in the study. In multivariable models, women (standardized β = -0.15, P = .02) and young patients (standardized β = -0.20, P = .006) had greater brain resilience to pathological tau. Higher educational level (standardized β = 0.23, P < .001) and global cortical thickness (standardized β = 0.23, P < .001) were associated with greater cognitive resilience to pathological tau. Linear mixed models indicated a significant interaction of brain resilience × cognitive resilience × time on MMSE (β [SE] = -0.235 [0.111], P = .03), with steepest slopes for individuals with both low brain and cognitive resilience. Conclusions and relevance: Results of this study suggest that women and young patients with AD have relative preservation of brain structure when exposed to neocortical pathological tau. Interindividual differences in resilience to pathological tau may be important to disease progression because participants with both low brain and cognitive resilience had the most rapid cognitive decline over time.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Ladder symmetries of black holes. Implications for love numbers and no-hair theorems

It is well known that asymptotically flat black holes in general relativity have a vanishing static, conservative tidal response. Here, we show that this is a result of linearly realized symmetries governing static (spin 0,1,2) perturbations around black holes. The symmetries have a geometric origin: in the scalar case, they arise from the (E)AdS isometries of a dimensionally reduced black hole spacetime. Underlying the symmetries is a ladder structure which can be used to construct the full tower of solutions, and derive their general properties: (1) solutions that decay with radius spontaneously break the symmetries, and must diverge at the horizon; (2) solutions regular at the horizon respect the symmetries, and take the form of a finite polynomial that grows with radius. Taken together, these two properties imply that static response coefficients — and in particular Love numbers — vanish. Moreover, property (1) is consistent with the absence of black holes with linear (perturbative) hair. We also discuss the manifestation of these symmetries in the effective point particle description of a black hole, showing explicitly that for scalar probes the worldline couplings associated with a non-trivial tidal response and scalar hair must vanish in order for the symmetries to be preserved.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Downscaled hyper-resolution (400 m) gridded datasets of daily precipitation and temperature (2008–2019) for the East–Taylor subbasin (western United States)

Abstract. High-resolution gridded datasets of meteorological variables are needed in order to resolve fine-scale hydrological gradients in complex mountainous terrain. Across the United States, the highest available spatial resolution of gridded datasets of daily meteorological records is approximately 800 m. This work presents gridded datasets of daily precipitation and mean temperature for the East–Taylor subbasin (in the western United States) covering a 12-year period (2008–2019) at a high spatial resolution (400 m). The datasets are generated using a downscaling framework that uses data-driven models to learn relationships between climate variables and topography. We observe that downscaled datasets of precipitation and mean temperature exhibit smoother spatial gradients (while preserving the spatial variability) when compared to their coarser counterparts. Additionally, we also observe that when downscaled datasets are upscaled to the original resolution (800 m), the mean residual error is almost zero, ensuring no bias when compared with the original data. Furthermore, the downscaled datasets are observed to be linearly related to elevation, which is consistent with the methodology underlying the original 800 m product. Finally, we validate the spatial patterns exhibited by downscaled datasets via an example use case that models lidar-derived estimates of snowpack. The presented dataset constitutes a valuable resource to resolve fine-scale hydrological gradients in the mountainous terrain of the East–Taylor subbasin, which is an important study area in the context of water security for the southwestern United States and Mexico. The dataset is publicly available at https://doi.org/10.15485/1822259 (Mital et al., 2021).

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2014

Development of a Linear Ion Trap Mass Spectrometer (LITMS) Investigation for Future Planetary Surface Missions

Future surface missions to Mars and other planetary bodies will benefit from continued advances in miniature sensor and sample handling technologies that enable high-performance chemical analyses of natural samples. Fine-scale (approx.1 mm and below) analyses of rock surfaces and interiors, such as exposed on a drill core, will permit (1) the detection of habitability markers including complex organics in association with their original depositional environment, and (2) the characterization of successive layers and gradients that can reveal the time-evolution of those environments. In particular, if broad-based and highly-sensitive mass spectrometry techniques could be brought to such scales, the resulting planetary science capability would be truly powerful. The Linear Ion Trap Mass Spectrometer (LITMS) investigation is designed to conduct fine-scale organic and inorganic analyses of short (approx.5-10 cm) rock cores such as could be acquired by a planetary lander or rover arm-based drill. LITMS combines both pyrolysis/gas chromatograph mass spectrometry (GCMS) of sub-sampled core fines, and laser desorption mass spectrometry (LDMS) of the intact core surface, using a common mass analyzer, enhanced from the design used in the Mars Organic Molecule Analyzer (MOMA) instrument on the 2018 ExoMars rover. LITMS additionally features developments based on the Sample Analysis at Mars (SAM) investigation on MSL and recent NASA-funded prototype efforts in laser mass spectrometry, pyrolysis, and precision subsampling. LITMS brings these combined capabilities to achieve its four measurement objectives: (1) Organics: Broad Survey Detect organic molecules over a wide range of molecular weight, volatility, electronegativity, concentration, and host mineralogy. (2) Organic: Molecular Structure Characterize internal molecular structure to identify individual compounds, and reveal functionalization and processing. (3) Inorganic Host Environment Assess the local chemical/mineralogical makeup of organic host phases to help determine deposition and preservation factors. (4) Chemical Stratigraphy Analyze the fine spatial distribution and variation of key species with depth.

Mars↗
NASA NTRS1982

Vortices in turbulence

Theoretical and experimental results of studies to determine the flow parameters and structures of plane mixing layers are reported. Smoke visualization, combined with hot-wire anemometry, sheets of laser light, and photography were used to gather data from the wall flow. The behavior of vortex rods was examined, noting that the rods persisted only if new vortex energy was supplied from the sublayer. A power spectral density was defined for the velocity fluctuations, as was a hierarchy of velocity scales for geometrically similar vortices. The length scale grows linearly with downstream distance, where the flow structures are fed by longitudinal vortices. A model is developed for vortex pairing in sequential order from the bottom of the mixing layer outward in a repetitive process involving vortex stretching. The model is actually a migration strategy that satisfies the flow self-preservation constraints.

Perry, A. E.↗
NASA NTRS1986

Geologic periodicities and the Galaxy

New geologic and astronomical developments are reviewed that have recently led to the proposal of various Galactic theories to explain the temporal pattern of impact craters on earth. Linear and harmonic time series analyses have revealed that two dominant periodicities about equal to 33 + or - 3 Myr and 260 + or - 25 Myr underlie the geologic record of terrestrial impact cratering and global tectonic phenomena. It is argued that purely terrestrial mechanisms cannot account for the cratering cycles as being preservational artifacts; cratering rather appears to influence tectonism, possibly through perturbations of mantle convection. Galactic models proposed to explain the two long-term periodicities are reviewed critically. The most likely explanation for the 33 Myr cycle involves the comparatively stable half period of vertical oscillation of the solar system about the Galactic plane. The 260 Myr cycle may be related to rare encounters with Galactic spiral arms during the revolution of the solar system around the Galactic center.

Rampino, Michael R.↗
NASA NTRS1996

Periodic Time-Domain Nonlocal Nonreflecting Boundary Conditions for Duct Acoustics

Periodic time-domain boundary conditions are formulated for direct numerical simulation of acoustic waves in ducts without flow. Well-developed frequency-domain boundary conditions are transformed into the time domain. The formulation is presented here in one space dimension and time; however, this formulation has an advantage in that its extension to variable-area, higher dimensional, and acoustically treated ducts is rigorous and straightforward. The boundary condition simulates a nonreflecting wave field in an infinite uniform duct and is implemented by impulse-response operators that are applied at the boundary of the computational domain. These operators are generated by convolution integrals of the corresponding frequency-domain operators. The acoustic solution is obtained by advancing the Euler equations to a periodic state with the MacCormack scheme. The MacCormack scheme utilizes the boundary condition to limit the computational space and preserve the radiation boundary condition. The success of the boundary condition is attributed to the fact that it is nonreflecting to periodic acoustic waves. In addition, transient waves can pass rapidly out of the solution domain. The boundary condition is tested for a pure tone and a multitone source in a linear setting. The effects of various initial conditions are assessed. Computational solutions with the boundary condition are consistent with the known solutions for nonreflecting wave fields in an infinite uniform duct.

Watson, Willie R.↗
DOE OSTI2023

Data-driven, structure-preserving approximations to entropy-based moment closures for kinetic equations

In this study, we present a data-driven approach for approximating entropy-based closures of moment systems from kinetic equations. The proposed closure learns the entropy function by fitting the map between the moments and the entropy of the moment system, and thus does not depend on the spacetime discretization of the moment system or specific problem configurations such as initial and boundary conditions. With convex and C 2 approximations, this data-driven closure inherits several structural properties from entropy-based closures, such as entropy dissipation, hyperbolicity, and H-Theorem. We construct convex approximations to the Maxwell–Boltzmann entropy using convex splines and neural networks, test them on the plane source benchmark problem for linear transport in slab geometry, and compare the results to the standard, entropy-based systems which solve a convex optimization problem to find the closure. Numerical results indicate that these data-driven closures provide accurate solutions in much less computation time than that required by the optimization routine.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems

In this work, we present Lift & Learn, a physics-informed method for learning low-dimensional models for large-scale dynamical systems. The method exploits knowledge of a system’s governing equations to identify a coordinate transformation in which the system dynamics have quadratic structure. This transformation is called a lifting map because it often adds auxiliary variables to the system state. The lifting map is applied to data obtained by evaluating a model for the original nonlinear system. This lifted data is projected onto its leading principal components, and low-dimensional linear and quadratic matrix operators are fit to the lifted reduced data using a least-squares operator inference procedure. Analysis of our method shows that the Lift & Learn models are able to capture the system physics in the lifted coordinates at least as accurately as traditional intrusive model reduction approaches. This preservation of system physics makes the Lift & Learn models robust to changes in inputs. Numerical experiments on the FitzHugh–Nagumo neuron activation model and the compressible Euler equations demonstrate the generalizability of our model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Phase-Only Beam Broadening of Contiguous Uniform Subarrayed Arrays

In modern antenna systems, beam broadening of subarrayed arrays provides continuous coverage of a wide angular extent in a cost-effective manner. While many methods have been published that address beam broadening of traditional (non-subarrayed) arrays, there is a knowledge gap in the published literature with respect to efficient beam broadening of contiguous uniform subarrayed arrays. This article presents efficient methods for beam broadening of contiguous uniform subarrayed arrays where the excitation of each element is not individually controlled, but the elements of the array are grouped together as subarrays to have the same element excitations. Particularly, this article focuses on phase-only optimization to preserve maximum power output. Additionally, three modilied iterative Fourier transform (IFT) methods and one genetic algorithm (GA) are presented to efliciently search the vast solution space of possible phase settings for a solution that satislies the desired broadened pattern. These methods are evaluated on idealized 1 x 40 and 1 x 80 linear arrays with live element subarrays and 40 x 40 and 80 x 80 element rectangular arrays with 5 x 5 element subarrays. The proposed modilied IFT methods are found to be faster than the GA approach, while the GA approach only offers a few percentage points of better effectiveness.

42 ENGINEERING↗