On the Number of L2 Solutions of - y plus Q/t/y Equals Lambda y Where Q/t/ Is Complex Valued
Operator solutions for complex valued second order differential equation
DIFFERENTIAL OPERATOR↗
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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.
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Learning the solution operator of parametric partial differential equations with physics-informed DeepONets
Partial differential equations (PDEs) play a central role in the mathematical analysis and modeling of complex dynamic processes across all corners of science and engineering. Their solution often requires laborious analytical or computational tools, associated with a cost that is markedly amplified when different scenarios need to be investigated, for example, corresponding to different initial or boundary conditions, different inputs, etc. In this work, we introduce physics-informed DeepONets, a deep learning framework for learning the solution operator of arbitrary PDEs, even in the absence of any paired input-output training data. We illustrate the effectiveness of the proposed framework in rapidly predicting the solution of various types of parametric PDEs up to three orders of magnitude faster compared to conventional PDE solvers, setting a previously unexplored paradigm for modeling and simulation of nonlinear and nonequilibrium processes in science and engineering.
97 MATHEMATICS AND COMPUTING↗
Resummation of the Holstein-Primakoff expansion and differential equation approach to operator square roots
Not Available
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
A closed-loop control-loading system
Langley Differential Maneuvering Simulator (DMS) realistically simulates two aircraft operating in differential mode. It consists of two identical fixed-base cockpits and dome projection systems. Each projection system consists of sky/Earth projector and target-image generator and projector. Although programmable control forces are small part of overall system, they play large role in providing pilot with kinesthetic cues.
Ashworth, B. R.↗
Ask-The-Expert: Minimizing Human Review for Big Data Analytics Through Active Learning
In this CIF project, we worked toward semi-automating knowledge discovery from anomaly detection algorithms through the use of active learning. Active learning is an area of research within machine learning that uses an "expert in the loop" to learn from large data sets that have very few annotations or labels available, and where providing such labels is expensive. In our case, the task can be defined as the identification of safety events from flight operational data. Since traditional anomaly detection algorithms cannot differentiate between operationally relevant and irrelevant statistical anomalies, Subject Matter Experts (SMEs) have a lengthy and expensive burden of investigating every example identified by the detection algorithm, classifying and labeling them as relevant or irrelevant. Active learningidentifies the unlabeled example for which a label would most improve the classifier, asks the domain expert for a label, and repeats this process until there are no more resources (time, budget) available for labeling or a minimum required performance is reached. A positive label indicates an operationally significant safety event whereas a negative label indicates otherwise. Based on these few labels we propose to build an active learning system that utilizes the SME's time in the most effective manner by iteratively asking for labels for as few informative instances as possible. Our work was proposed to be a stepping stone toward implementation and deployment of the system with user interface to be pursued by the Aviation Operations and Safety Program (AOSP) given its interest in safety monitoring and discovery of safety incidents.
aviation safety↗
Linear differential
Apparatuses and methods of operating a linear differential (100, 600) are described herein. The linear differential (100, 600) contains a slide portion (102) with parallel right-hand and left-hand threaded rods (112, 114). Threaded onto the right-hand and left-hand threaded rods (112, 114) and attached to the slide portion (102) are right-hand and left-hand gears (116, 118). Meshed between the right-hand and left-hand gears (116, 118) and also attached to the slide portion (102) is a driven gear (200). An end effector (104) is attached to the driven gear (200) and is configured to translate along a translation axis (110) and rotate around a rotation axis (120).
Crawford, Anthony↗
A review of peridynamic theory and nonlocal operators along with their computer implementations
Not Available
97 MATHEMATICS AND COMPUTING↗
Convergence of Galerkin approximations for operator Riccati equations: A nonlinear evolution equation approach
An approximation and convergence theory was developed for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators on a separable Hilbert space. The Riccati equation was treated as a nonlinear evolution equation with dynamics described by a nonlinear monotone perturbation of a strongly coercive linear operator. A generic approximation result was proven for quasi-autonomous nonlinear evolution system involving accretive operators which was then used to demonstrate the Hilbert-Schmidt norm convergence of Galerkin approximations to the solution of the Riccati equation. The application of the results was illustrated in the context of a linear quadratic optimal control problem for a one dimensional heat equation.
Rosen, I. G.↗
Importance of hydrogen oxidation reaction current in quantifying hydrogen crossover in PEM water electrolyzers at high differential pressure
Understanding hydrogen permeation in proton exchange membrane water electrolyzers (PEMWEs) operating at high differential pressures (>25 bar) is critical towards developing effective gas recombination strategies that enable safe operation and high efficiency. Developing this understanding relies on accurate quantification of hydrogen crossover rates in water electrolyzers operating under such conditions. In this work, we show that PEMWEs operating at high differential pressures exhibit noticeable hydrogen oxidation reaction (HOR) currents. As the HOR consumes part of the permeated hydrogen at the anode, neglecting HOR currents leads to severe underestimation of the hydrogen crossover rate. We implemented a new method combining hydrogen oxidation current with online gas chromatography measurements to accurately quantify hydrogen crossover rates as a function of operating current density in PEMWEs operating at high differential pressures (10–30 bar g ).
25 ENERGY STORAGE↗
Linking structure to performance: Characterization of porous transport layers for high-pressure water electrolysis
Proton exchange membrane (PEM) water electrolysis is a promising technology to produce cost-efficient hydrogen. PEM electrolyzers offer a large current density range and the ability to operate at differential pressure which can be used to minimize both capital and operational expenditures. However, directly producing pressurized hydrogen at the cathode results in pushing the membrane against the anode porous transport layer (PTL). This can lead to detrimental effects, such as membrane deformation or ruptures, which depend on membrane properties as well as PTL material properties such as pore size, structure, and morphology. In this work, a range of sinter and felt-based commercial PTLs are evaluated for their contributions to the cell's electrochemical and H 2 crossover performance at cathode pressures up to 30 bar. X-ray tomography and post-operando optical microscopy are used to assess the morphology of the PTLs, and the PTL induced deformation experienced by the catalyst coated membrane (CCM), respectively. PTL samples with lower porosity were found to reduce both the cell voltage and the amount of H 2 permeating from the cathode to the anode exhaust, which was ascribed to improved catalyst layer contact and reduced membrane deformation, respectively. The best performing PTLs improved electrolyzer efficiency by ~1.5 kWh/kg H2 . Specifically, 1 kWh/kg H2 was gained due to reducing membrane deformation and decreasing H 2 crossover. The remainder 0.5 kWh/kg H2 were achieved by improving the electrical contact at the electrode/PTL interface which decreased cell voltage.
08 HYDROGEN↗
Operator inference with roll outs for learning reduced models from scarce and low-quality data
Data-driven modeling has become a key building block in computational science and engineering. However, data that are available in science and engineering are typically scarce, often polluted with noise and affected by measurement errors and other perturbations, which makes learning the dynamics of systems challenging. Here, in this work, we propose to combine data-driven modeling via operator inference with the dynamic training via roll outs of neural ordinary differential equations. Operator inference with roll outs inherits interpretability, scalability, and structure preservation of traditional operator inference while leveraging the dynamic training via roll outs over multiple time steps to increase stability and robustness for learning from low-quality and noisy data. Numerical experiments with data describing shallow water waves and surface quasi-geostrophic dynamics demonstrate that operator inference with roll outs provides predictive models from training trajectories even if data are sampled sparsely in time and polluted with noise of up to 10%.
97 MATHEMATICS AND COMPUTING↗
Ramp-integration technique for capacitance-type blade-tip clearance measurement
The analysis of a proposed new technique for capacitance type blade tip clearance measurement is presented. The capacitance between the blade tip and a mounted capacitance electrode within a guard ring forms one of the feedback elements of a high speed operational amplifier. The differential equation governing the operational amplifier circuit is formulated and solved for two types of inputs to the amplifier - a constant voltage and a ramp. The resultant solutions shows an output that contains a term that is proportional to the derivative of the product of the input voltage and the time constant of the feedback network. The blade tip clearance capacitance is obtained by subtracting the output of a balancing reference channel followed by integration. The proposed sampled data algorithm corrects the environmental effects and varying rotor speeds on-line, making the system suitable for turbine instrumentation. System requirements, block diagrams, and typical application are included.
Sarma, G. R.↗
Ramp-integration technique for capacitance-type blade-tip clearance measurement
The analysis of a proposed new technique for capacitance type blade tip clearance measurement is presented. The capacitance between the blade tip and a mounted capacitance electrode within a guard ring forms one of the feedback elements of a high speed operational amplifier. The differential equation governing the operational amplifier circuit is formulated and solved for two types of inputs to the amplifier - a constant voltage and a ramp. The resultant solution shows an output that contains a term that is proportional to the derivative of the product of the input voltage and the time constant of the feedback network. The blade tip clearance capacitance is obtained by subtracting the output of a balancing reference channel followed by integration. The proposed sampled data algorithm corrects for environmental effects and varying rotor speeds on-line, making the system suitable for turbine instrumentation. System requirements, block diagrams, and a typical application are included.
Sarma, Garimella R.↗
The operator theory of the pseudo-inverse. i - bounded operators.
Operator theory of pseudo-inverse generalized to encompass linear bounded operators on Hilbert spaces
HILBERT SPACE↗
Quantum theory of time-dependent phenomena treated by the evolution operator technique
Time dependent phenomena in nonrelativistic quantum theory treated by evolution operator technique
QUANTUM THEORY↗
The application of NAVSTAR Differential GPS to civil helicopter operations
Principles concerning the operation of the NAVSTAR Global Positioning Systems (GPS) are discussed. Selective availability issues concerning NAVSTAR GPS and differential GPS concepts are analyzed. Civil support and market potential for differential GPS are outlined. It is concluded that differential GPS provides a variation on the baseline GPS system, and gives an assured, uninterrupted level of accuracy for the civilian community.
Beser, J.↗
Using X-ray radiography to study oxygen flow in a proton exchange membrane electrolyzer operating under balanced pressure conditions
Of the various water electrolyzer technologies, the proton exchange membrane electrolyzer (PEMWE) is one of the best solutions for producing clean hydrogen without releasing CO 2 . In order to allow for widespread use of clean hydrogen, it is necessary to decrease its cost, which is intrinsically related to system operation. Current PEMWE plants operate in differential mode, directly pressurizing hydrogen and benefiting from thermodynamic compression, which increases overall system efficiency. However, high differential pressure above 30 bar can cause membrane stress, resulting in membrane creeping and failure. Pressurizing the water and operating at balanced pressure allows hydrogen to be produced at higher pressures while preserving the integrity of the membrane and porous layers. Nevertheless, the impact of pressurizing water on PEMWE performance must be better understood to maximize performance under balanced pressure conditions. Here, this study examined the impact of water pressure on two-phase flow. A high-pressure electrolyzer setup was developed to perform operando X-ray radiography and examine oxygen transport with high temporal resolution. The imaging segmentation process, developed to capture bubble properties in the channel, was applied to a specific experiment. The results clearly showed that as pressure increased up to 30 bars, the initial bubbly flow transitioned to slug flow, which led to channel saturation with oxygen. This work demonstrates that two-phase flow in an electrolyzer can be studied using X-ray radiography, which has the advantages of fast measurements and the ability to probe dense materials, such as those required for pressurized electrolyzers.
Balanced high pressure operation↗
Correlation of ISS Electric Potential Variations with Mission Operations
Orbiting approximately 400 km above the Earth, the International Space Station (ISS) is a unique research laboratory used to conduct ground-breaking science experiments in space. The ISS has eight Solar Array Wings (SAW), and each wing is 11.7 meters wide and 35.1 meters long. The SAWs are controlled individually to maximize power output, minimize stress to the ISS structure, and minimize interference with other ISS operations such as vehicle dockings and Extra-Vehicular Activities (EVA). The Solar Arrays are designed to operate at 160 Volts. These large, high power solar arrays are negatively grounded to the ISS and collect charged particles (predominately electrons) as they travel through the space plasma in the Earth's ionosphere. If not controlled, this collected charge causes floating potential variations which can result in arcing, causing injury to the crew during an EVA or damage to hardware [1]. The environmental catalysts for ISS floating potential variations include plasma density and temperature fluctuations and magnetic induction from the Earth's magnetic field. These alone are not enough to cause concern for ISS, but when they are coupled with the large positive potential on the solar arrays, floating potentials up to negative 95 Volts have been observed. Our goal is to differentiate the operationally induced fluctuations in floating potentials from the environmental causes. Differentiating will help to determine what charging can be controlled, and we can then design the proper operations controls for charge collection mitigation. Additionally, the knowledge of how high power solar arrays interact with the environment and what regulations or design techniques can be employed to minimize charging impacts can be applied to future programs.
Willis, Emily M.↗