Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “DIFFERENTIAL OPERATOR”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

High gain, large area, and solar blind avalanche photodiodes based on Al-rich AlGaN grown on AlN substrates

We demonstrate large area (25 000 μm2) Al-rich AlGaN-based avalanche photodiodes (APDs) grown on single crystal AlN substrates operating with differential (the difference in photocurrent and dark current) signal gain of 100 000 at 90 pW (<1 μW cm−2) illumination with very low dark currents <0.1 pA at room temperature under ambient light. The high gain in large area AlGaN APDs is attributed to a high breakdown voltage at 340 V, corresponding to very high breakdown fields ∼9 MV cm−1 as a consequence of low threading and screw dislocation densities < 103 cm−2. The maximum charge collection efficiency of 30% was determined at 255 nm, corresponding to the bandgap of Al0.65Ga0.35N, with a response of 0.06 A/W. No response was detected for λ > 280 nm, establishing solar blindness of the device.

Reddy, Pramod (ORCID:0000000285561178)↗
DOE OSTI2023

Transformer Health Monitoring via Synchrophasors

Traditional transformer protection schemes such as differential protection operate once the transformer is in a critical state. Proactive means of transformer health evaluation such as Sweep Frequency Response Analysis, can only be performed periodically with the transformer out-of-service. This work presents a framework where the health and structural integrity of transformers is monitored via synchrophasors in real-time. Synchrophasors and subspace estimation techniques are used to build reduced-order models which are then analyzed across multiple domains. A diagnostics algorithm is developed and tested via Matlab simulations. Test results are promising, opening up new prospects in transformer protection research.

cyber-physical security↗
DOE OSTI2025

STILGAR End-of-Project Report

The Subsurface Tunnel Imaging LeveraGed by Analysis of Rayleigh wave ellipticity (STILGAR) project demonstrated an integrated geophysical approach for detecting, locating, and characterizing underground structural changes using dense seismic arrays and advanced inversion techniques. Field campaigns were conducted at two operational mines—the Redmond salt mine (Utah) and Graymont Pleasant Gap limestone mine (Pennsylvania)—providing real-world testbeds for monitoring anthropogenic subsurface activity. At the Redmond salt mine, seismic interferometry combined with back-projection inversion successfully identified continuous, low-amplitude signals from mining operations. The approach differentiated stationary from migrating anthropogenic sources, captured daily operational cycles, and validated the potential of passive seismic monitoring for remote detection of underground activity. At the Graymont Pleasant Gap mine, two dense seismic deployments in the spring and fall of 2023 generated over 4 TB of high-resolution data. Key outcomes included the relocation of 199 underground and 8 surface explosions with accuracies within tens of meters and the development of a 3D P-wave velocity model using the triple-difference tomography algorithm (tomoTD) that resolved major structural features such as the mine entrance, low-velocity tunnels, and roof-collapse areas. Ambient noise cross-correlation and back-projection analyses revealed persistent sources linked to ongoing mining activity, whereas horizontal-to-vertical spectral ratio (HVSR) and ellipticity studies confirmed stable site responses across seasons and identified soil thickness trends consistent with regional erosional and depositional processes. Checkerboard and sensitivity tests further validated the robustness of the tomographic results. Overall, the findings emphasize that although significant progress has been made in subsurface imaging, further work is needed to enhance the detection and localization of underground structures. Accurate imaging requires higher frequencies, yet anthropogenic sources tend to dominate the seismic record at those frequencies, and high-frequency surface waves are affected by higher modes that complicate interpretation. The improved detection and localization of human-induced signals enabled detailed temporal and spatial mapping of daily mine operations, demonstrating the feasibility of continuous anthropogenic source monitoring. Sensitivity to signals from nontraditional sources, such as fan operations, highlights the broader applicability of this approach to other industrial environments in which continuous and impulsive signals are present. The field campaigns produced a substantial volume of high-quality seismic data, supporting the development and testing of new methods for seismic source characterization and subsurface imaging. Future deployments should include sensors capable of recording lower frequencies to probe deeper structures, increase bandwidth to enhance resolution and sensitivity to both shallow and deep targets, and collect additional large-scale datasets to refine imaging and source characterization techniques. Moreover, conducting 3D modeling studies of seismic wavefields at higher frequencies will provide a better understanding of wave scattering and cavity–wavefield interactions in complex underground environments. In conclusion, the STILGAR project demonstrated that integrated seismic monitoring can effectively characterize underground operations, capturing both natural and anthropogenic signals. The approaches developed provide a foundation for improved detection, localization, and imaging of subsurface structures and are directly transferable to broader industrial monitoring applications.

58 GEOSCIENCES↗
DOE OSTI2020

Ion Number Density Quantification Utilizing Pulsing Frequency in Negative Differential Resistance (NDR) Regime of Microplasma Operation

A mathematical model is presented for quantifying the ion number density over a range of discharge current in microplasma discharges. The ion number density is determined from measured discharge voltage, current, pulsing frequency, and trace impurity that is injected into the system deliberately. Experiments are conducted in pure helium with nitrogen being introduced as the trace species. The ion number density is estimated over a range of discharge current and is compared with multidimensional simulation results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Pulse compression photoconductive semiconductor switches

A photoconductive switch that uses materials that support negative differential mobility, whose operation leverages the pulse compression of a charge could to generate the “on” time of the pulse in combination with the speed of light to generate the “off” time of the pulse, is described. In one example, a method of operating a photoconductive switch, which includes two electrodes and a light absorbing material positioned therebetween, includes selecting a value for one or more parameters comprising a voltage for generation of an electric field, a spot size of a laser pulse, a temporal pulse width of the laser pulse, or an intensity of the laser pulse, wherein the selected value(s) for the one or more parameters enable the switch to operate in a region where the light absorbing material exhibits negative differential mobility, and illuminating the light absorbing material with the laser pulse to generate a charge cloud within the light absorbing material.

Voss, Lars F.↗
DOE OSTI2020

On differentiable local bounds preserving stabilization for Euler equations

This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integration is used in the case of the transient form. A differentiable local bounds preserving method has been developed, which combines a Rusanov artificial diffusion operator and a differentiable shock detector. Nonlinear stabilization schemes are usually stiff and highly nonlinear. This issue is mitigated by the differentiability properties of the proposed method. Moreover, in order to further improve the nonlinear convergence, we also propose a continuation method for a subset of the stabilization parameters. The resulting method has been successfully applied to steady and transient problems with complex shock patterns. Numerical experiments show that it is able to provide sharp and well resolved shocks. Furthermore, the importance of the differentiability is assessed by comparing the new scheme with its non-differentiable counterpart. Numerical experiments suggest that, for up to moderate nonlinear tolerances, the method exhibits improved robustness and nonlinear convergence behavior for steady problems. Additionally, in the case of transient problem, we also observe a reduction in the computational cost.

42 ENGINEERING↗
DOE OSTI2020

Bilevel Parameter Optimization for Nonlocal Image Denoising Models

We propose a bilevel optimization approach for the determination of parameters in nonlocal image denoising. We consider both spatial weights in front of the fidelity term, as well as weights within the kernel of the nonlocal operator. In both cases we investigate the differentiability of the solution operator in function spaces and derive a first order optimality system that characterizes local minima. For the numerical solution of the problems, we propose a second-order optimization algorithm in combination with a finite element discretization of the nonlocal denoising models and a computational strategy for the solution of the resulting dense linear systems. Several experiments are run in order to show the suitability of our approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Bilevel parameter optimization for learning nonlocal image denoising models

We propose a bilevel optimization approach for the estimation of parameters in nonlocal image denoising models. The parameters we consider are both the space-dependent fidelity weight and weights within the kernel of the nonlocal operator. In both cases we investigate the differentiability of the solution operator in function spaces and derive a first order optimality system that characterizes local minima. For the numerical solution of the problems, we propose a second-order trust-region algorithm in combination with a finite element discretization of the nonlocal denoising models and we introduce a computational strategy for the solution of the resulting dense linear systems. Several experiments illustrate the applicability and effectiveness of our approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Non-intrusive data-driven model reduction for differential–algebraic equations derived from lifting transformations

In this paper we present a non-intrusive data-driven approach for model reduction of nonlinear systems. The approach considers the particular case of nonlinear partial differential equations (PDEs) that form systems of partial differential–algebraic equations (PDAEs) when lifted to polynomial form. Such systems arise, for example, when the governing equations include Arrhenius reaction terms (e.g., in reacting flow models) and thermodynamic terms (e.g., the Helmholtz free energy terms in a phase-field solidification model). Using the known structured form of the lifted algebraic equations, the approach computes the reduced operators for the algebraic equations explicitly, using straightforward linear algebra operations on the basis matrices. The reduced operators for the differential equations are inferred from lifted snapshot data using operator inference, which solves a linear least squares regression problem. The approach is illustrated for the nonlinear model of solidification of a pure material. The lifting transformations reformulate the solidification PDEs as a system of PDAEs that have cubic structure. The operators of the lifted system for this solidification example have affine dependence on key process parameters, permitting us to learn a parametric reduced model with operator inference. Numerical experiments show the effectiveness of the resulting reduced models in capturing key aspects of the solidification dynamics.

42 ENGINEERING↗
DOE OSTI2022

Improved Architectures and Training Algorithms for Deep Operator Networks

Operator learning techniques have recently emerged as a powerful tool for learning maps between infinite-dimensional Banach spaces. Trained under appropriate constraints, they can also be effective in learning the solution operator of partial differential equations (PDEs) in an entirely self-supervised manner. In this work we analyze the training dynamics of deep operator networks (DeepONets) through the lens of Neural Tangent Kernel theory, and reveal a bias that favors the approximation of functions with larger magnitudes. To correct this bias we propose to adaptively re-weight the importance of each training example, and demonstrate how this procedure can effectively balance the magnitude of back-propagated gradients during training via gradient descent. We also propose a novel network architecture that is more resilient to vanishing gradient pathologies. Taken together, our developments provide new insights into the training of DeepONets and consistently improve their predictive accuracy by a factor of 10-50x, demonstrated in the challenging setting of learning PDE solution operators in the absence of paired input-output observations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Liouville operators over the Hardy space

The role of Liouville operators in the study of dynamical systems through the use of occupation measures has been an active area of research in control theory over the past decade. This article investigates Liouville operators over the Hardy space, which encode complex ordinary differential equations in an operator over a reproducing kernel Hilbert space.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

GMLS-Nets: A Framework for Learning from Unstructured Data

Data fields sampled on irregularly spaced points arise in many applications in the sciences and engineering. For regular grids, Convolutional Neural Networks (CNNs) have been successfully used to gaining benefits from weight sharing and invariances. We generalize CNNs by introducing methods for data on unstructured point clouds based on Generalized Moving Least Squares (GMLS). GMLS is a non-parametric technique for estimating linear bounded functionals from scattered data, and has recently been used in the literature for solving partial differential equations. By parameterizing the GMLS estimator, we obtain learning methods for operators with unstructured stencils. In GMLS-Nets the necessary calculations are local, readily parallelizable, and the estimator is supported by a rigorous approximation theory. We show how the framework may be used for unstructured physical data sets to perform functional regression to identify associated differential operators and to regress quantities of interest. The results suggest the architectures to be an attractive foundation for data-driven model development in scientific machine learning applications

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Detailed study of the eikonal reaction theory for the breakup of one-neutron halo nuclei

Background: One-neutron removal reactions are used to study the single-particle structure of unstable nuclei, and in particular the exotic halo nuclei. The eikonal reaction theory (ERT) has been developed by Yahiro, Ogata, and Minomo [Prog. Theor. Phys. 126, 167 (2011)] to include dynamical effects, which are missing in the usual eikonal description of these reactions. Encouraging results have been obtained for total breakup cross sections in comparison to more elaborate reaction models. Purpose: Here, we extend these comparisons to more differential breakup cross sections expressed as functions of the relative energy or parallel momentum between the core and halo neutron. Method: ERT predictions of these cross sections are compared to state-of-the-art calculations. Results: The hypotheses upon which the ERT is based are confirmed and their range of validity is made clearer. The actual ordering of the evolution operators affects ERT differential cross sections and a specific choice leads to excellent agreement with the reference calculation. Dynamical effects in the treatment of the neutron-target interaction can be significant in the parallel-momentum observable. Conclusions: The role of the different interactions in the dynamics of breakup reactions of one-neutron halo nuclei are better understood and improvements to the ERT are suggested.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Operability thresholds for thermally damaged EBW detonators

Operability thresholds that differentiate between functional RP-87 exploding bridge wire (EBW) detonators and nonfunctional RP-87 EBW detonators (duds) were determined by measuring the time delay between initiation and early wall movement (function time). The detonators were inserted into an externally heated hollow cylinder of aluminum and fired with current flow from a charged capacitor using an exploding bridge wire (EBW initiated). Functioning detonators responded like unheated pristine detonators when the function time was 4 μs or less. The operability thresholds of the detonators were characterized with a simple decomposition cookoff model calibrated using a modified version of the Sandia Instrumented Thermal Ignition (SITI) experiment. These thresholds are based on the calculated state of the PETN when the detonators fire. The operability threshold is proportional to the positive temperature difference (ΔT) between the maximum temperature within the PETN and the onset of decomposition (~406 K). Furthermore, the temperature difference alone was not sufficient to define the operability threshold. The operability threshold was also proportional to the time that the PETN had been at elevated temperatures. That is, failure was proportional to both temperature and reaction rate. The reacted gas fraction is used in the current work for the reaction correlation. Melting of PETN also had a significant effect on the operability threshold. Detonator failure occurred when the maximum temperature exceeded the nominal melting point of PETN (414 K) for 45±5 s or more.

42 ENGINEERING↗