Results for “operator complexity” — Page 84

NASA NTRS2006

Marsviewer

Marsviewer is a multi-platform application designed to aid in quality control, browsing, and analysis of original science product images (Experiment Data Records, or EDRs) and derived image data products (Reduced Data Records, or RDRs) returned by the Mars Explorer Rover (MER) mission. Marsviewer offers an abstraction of the products organization via a file finder. For example, the application understands the file structure and filename conventions of the MER Operational Storage Server, helping the user to navigate this complex file system to find desired images. Marsviewer also works with a flat file system, remote-operations file systems, image-archive file systems, and others. All EDRs found for a given solar day (Sol) are displayed in a list, optionally with thumbnail images. Once the user selects an image from the list, a tabbed pane conveniently displays the original source image and all associated RDRs. Marsviewer provides the option of overlaying derived images upon the source image, resulting in an easier-to-interpret color representation of the data. Display manipulations such as zoom, data range adjustment, contrast enhancement, and contour control are available. Image metadata (labels) from the current image can be displayed and searched. The architecture of the program is extensible: new types of RDRs can be installed and new file finders can be added to adapt the program to different file structures and different filename conventions. This keeps the application flexible and provides an opportunity for reuse with future rover missions.

Toole, Nicholas↗

NASA NTRS2020

Unsupervised Anomaly Detection in High-Dimensional Flight Data Using Convolutional Variational Auto-Encoder

The modern National Airspace System (NAS) is an extremely safe system and the aviation industry has experienced a steady decrease in fatalities over the years. This can be attributed to both improved flight critical systems with redundant hardware and software protections, as well as an increased focus on active monitoring and response to real time and historically identified vulnerabilities by implementing more resilient procedures and protocols. The main approach for identifying vulnerabilities in operations leverages domain expertise using knowledge about how the system should behave within the expected tolerances to known safety margins. This approach works well when the system has a well-defined operating condition. However, the operations in the NAS can be highly complex with various nuances that render it difficult to clearly pre-define all known safety vulnerabilities. With the advancement of data science and machine learning techniques, the potential to automatically identify emerging vulnerabilities in the observed operations has become more practical in recent years. The state-of-the-art anomaly detection approaches in aerospace data usually rely on supervised or semi-supervised learning. However, in many real-world problems such as flight safety, creating labels for the data requires huge amount of effort and is largely impractical. To address this challenge, we developed a Convolutional Variational Auto-Encoder (CVAE), which is an unsupervised learning approach for anomaly detection in high-dimensional heterogeneous time-series data. We validate performance of CVAE compared to the state-of-the-art supervised learning approach as well as unsupervised clustering-based approach using KMeans++ and kernel-based approach using One-Class Support Vector Machine (OC-SVM) on Yahoo!'s benchmark time series anomaly detection data. Finally, we showcase performance of CVAE on a case study of identifying anomalies in the first 60 seconds of commercial flights' take-offs using Flight Operational Quality Assurance (FOQA) data.

Memarzadeh, Milad↗

NASA NTRSDate not supplied

Unsupervised Anomaly Detection in High-Dimensional Flight Data Using Convolutional Variational Auto-Encoder

The modern National Airspace System (NAS) is an extremely safe system. The industry has experienced a steady decrease in fatalities over the years. This can be contributed to both improved flight critical systems with redundant hardware and software protections as well as an increased focus on active monitoring and response to real time and historically identified vulnerabilities by implementing more resilient procedures and protocols. The main practice for identifying vulnerabilities in operations leverages domain expertise using knowledge about how the system should behave with the expected tolerances to known safety margins. This approach works well when the system has a well-defined operating condition. However, the operations in the NAS can be highly complex with various nuances that render it difficult to clearly pre-define all known safety vulnerabilities. With the advancement of data science and machine learning techniques, the potential to automatically identify emerging vulnerabilities in the observed operations has become more practical in recent years. The state-of-the-art anomaly detection approaches in aerospace data usually rely on supervised or semi-supervised learning. However, in many real-world problems such as flight safety creating labels for the data requires huge amount of efforts and is largely expensive. As a result, in this article, we develop a Convolutional Variational Auto-Encoder (CVAE), an unsupervised learning approach for anomaly detection in high-dimensional heterogeneous time-series data. We validate performance of CVAE compared to the state-of-the-art supervised learning approach (as an upper bound) as well as an supervised clustering based on K-Means (as a lower bound) on Yahoo!'s benchmark time series anomaly detection data. Finally, we showcase performance of CVAE on a case study of identifying anomalies in the first 60 seconds of commercial flights' take-offs using Flight Operational Quality Assurance (FOQA) data.

Milad Memarzadeh↗

NASA NTRS2019

Advancing Aircraft Operations in a Net-Centric Environment with the Incorporation of Increasingly Autonomous Systems and Human Teaming

NextGen has begun the modernization of the nation’s air transportation system, with goals to improve system safety, increase operation efficiency and capacity, provide enhanced predictability, resilience and robustness. With these improvements, NextGen is poised to handle significant increases in air traffic operations, more than twice the number recorded in 2016, by 2025.1 NextGen is evolving toward collaborative decision-making across many agents, including automation, by use of a Net-Centric architecture, which in itself creates a very complex environment in which the navigation and operation of aircraft are to take place. An intricate environment such as this, coupled with the expected upsurge of air traffic operations generates concern respecting the ability of the human-agent to both fly and manage aircraft within. Therefore, it is both necessary and practical to begin the process of increasingly autonomous systems within the cockpit that will act independently to assist the human-agent achieve the overall goal of NextGen. However, the straightforward technological development and implementation of intelligent machines into the cockpit is only part of what is necessary to maintain, at minimum, or improve human-agent functionality, as desired, while operating in NextGen. The full integration of Increasingly Autonomous Systems (IAS) within the cockpit can only be accomplished when the IAS works in concert with the human, formulating trust between the two, thereby establishing a team atmosphere. Imperative to cockpit implementation is ensuring the proper performance of the IAS by the development team and the human-agent with which it will be paired when given a specific piloting, navigation, or observational task. Described in this paper are the steps taken, at NASA Langley Research Center, during the second and third phases of the development of an IAS, the Traffic Data Manager (TDM), its verification and validation by human-agents, and the foundational development of Human Autonomy Teaming (HAT) between the two.

Houston, Vincent E.↗

NASA NTRS1972

Planning, Management, and Economics of Airport Operation

An overview of the role of the airport in the transportation complex and in the community is presented. The establishment of the airport including its requirements in regional planning and the operation of the airport as a social and economic force are discussed.

Wiley, J.↗

NASA NTRS2011

A Parametric Testing Environment for Finding the Operational Envelopes of Simulated Guidance Algorithms

The ever-increasing size and complexity of aerospace systems often drive developers to validate using modeling and Monte Carlo simulations confined around expected points of operation in a hyper-dimensional parameter space. This paper describes an alternative that explores large regions of the parameter space with explicit coverage guarantees, searching for n parameter relations that characterize a system's performance envelope.

Parametric testing↗

NASA NTRS2021

Aerosol and Cloud Detection Using Machine Learning Algorithms and Space-Based Lidar Data

Clouds and aerosols play a significant role in determining the overall atmospheric radiation budget, yet remain a key uncertainty in understanding and predicting the future climate system. In addition to their impact on the Earth’s climate system, aerosols from volcanic eruptions, wildfires, man-made pollution events and dust storms are hazardous to aviation safety and human health. Space-based lidar systems provide critical information about the vertical distributions of clouds and aerosols that greatly improve our understanding of the climate system. However, daytime data from backscatter lidars, such as the Cloud-Aerosol Transport System (CATS) on the International Space Station (ISS), must be averaged during science processing at the expense of spatial resolution to obtain sufficient signal-to-noise ratio (SNR) for accurately detecting atmospheric features. For example, 50% of all atmospheric features reported in daytime operational CATS data products require averaging to 60 km for detection. Furthermore, the single-wavelength nature of the CATS primary operation mode makes accurately typing these features challenging in complex scenes. This paper presents machine learning (ML) techniques that, when applied to CATS data, (1) increased the 1064 nm SNR by 75%, (2) increased the number of layers detected (any resolution) by 30%, and (3) enabled detection of 40% more atmospheric features during daytime operations at a horizontal resolution of 5 km compared to the 60 km horizontal resolution often required for daytime CATS operational data products. A Convolutional Neural Network (CNN) trained using CATS standard data products also demonstrated the potential for improved cloud-aerosol discrimination compared to the operational CATS algorithms for cloud edges and complex near-surface scenes during daytime.

lidar↗

NASA NTRS1993

Spatial operator algebra for flexible multibody dynamics

This paper presents an approach to modeling the dynamics of flexible multibody systems such as flexible spacecraft and limber space robotic systems. A large number of degrees of freedom and complex dynamic interactions are typical in these systems. This paper uses spatial operators to develop efficient recursive algorithms for the dynamics of these systems. This approach very efficiently manages complexity by means of a hierarchy of mathematical operations.

Jain, A.↗

NASA NTRS1996

Human-Centered Aviation Automation: Principles and Guidelines

This document presents principles and guidelines for human-centered automation in aircraft and in the aviation system. Drawing upon operational experience with highly automated aircraft, it describes classes of problems that have occurred in these vehicles, the effects of advanced automation on the human operators of the aviation system, and ways in which these problems may be avoided in the design of future aircraft and air traffic management automation. Many incidents and a few serious accidents suggest that these problems are related to automation complexity, autonomy, coupling, and opacity, or inadequate feedback to operators. An automation philosophy that emphasizes improved communication, coordination and cooperation between the human and machine elements of this complex, distributed system is required to improve the safety and efficiency of aviation operations in the future.

Billings, Charles E.↗

NASA NTRS2008

Computational Analyses in Support of Sub-scale Diffuser Testing for the A-3 Facility: Steady Predictions - Part 1

Simulation technology can play an important role in rocket engine test facility design and development by assessing risks, providing analysis of dynamic pressure and thermal loads, identifying failure modes and predicting anomalous behavior of critical systems. Advanced numerical tools assume greater significance in supporting testing and design of high altitude testing facilities and plume induced testing environments of high thrust engines because of the greater inter-dependence and synergy in the functioning of the different sub-systems. This is especially true for facilities such as the proposed A-3 facility at NASA SSC because of a challenging operating envelope linked to variable throttle conditions at relatively low chamber pressures. Facility designs in this case will require a complex network of diffuser ducts, steam ejector trains, fast operating valves, cooling water systems and flow diverters that need to be characterized for steady state performance. In this paper, we will demonstrate with the use of CFD analyses s advanced capability to evaluate supersonic diffuser and steam ejector performance in a sub-scale A-3 facility at NASA Stennis Space Center (SSC) where extensive testing was performed. Furthermore, the focus in this paper relates to modeling of critical sub-systems and components used in facilities such as the A-3 facility. The work here will address deficiencies in empirical models and current CFD analyses that are used for design of supersonic diffusers/turning vanes/ejectors as well as analyses for confined plumes and venting processes. The primary areas that will be addressed are: (1) supersonic diffuser performance including analyses of thermal loads (2) accurate shock capturing in the diffuser duct; (3) effect of turning duct on the performance of the facility (4) prediction of mass flow rates and performance classification for steam ejectors (5) comparisons with test data from sub-scale diffuser testing and assessment of confidence levels in CFD based flowpath modeling of the facility. The analyses tools used here expand on the multi-element unstructured CFD which has been tailored and validated for impingement dynamics of dry plumes, complex valve/feed systems, and high pressure propellant delivery systems used in engine and component test stands at NASA SSC. The analyses performed in the evaluation of the sub-scale diffuser facility explored several important factors that influence modeling and understanding of facility operation such as (a) importance of modeling the facility with Real Gas approximation, (b) approximating the cluster of steam ejector nozzles as a single annular nozzle, (c) existence of mixed subsonic/supersonic flow downstream of the turning duct, and (d) inadequacy of two-equation turbulence models in predicting the correct pressurization in the turning duct and expansion of the second stage steam ejectors. The procedure used for modeling the facility was as follows: (i) The engine, test cell and first stage ejectors were simulated with an axisymmetric approximation (ii) the turning duct, second stage ejectors and the piping downstream of the second stage ejectors were analyzed with a three-dimensional simulation utilizing a half-plane symmetry approximation. The solution i.e. primitive variables such as pressure, velocity components, temperature and turbulence quantities were passed from the first computational domain and specified as a supersonic boundary condition for the second simulation. (iii) The third domain comprised of the exit diffuser and the region in the vicinity of the facility (primary included to get the correct shock structure at the exit of the facility and entrainment characteristics). The first set of simulations comprising the engine, test cell and first stage ejectors was carried out both as a turbulent real gas calculation as well as a turbulent perfect gas calculation. A comparison for the two cases (Real Turbulent and Perfect gas turbulent) of the Ma Number distribution and temperature distributions are shown in Figures 1 and 2 respectively. The Mach Number distribution shows small yet distinct differences between the two cases such as locations of shocks/shock reflections and a slightly different impingement point on the wall of the diffuser from the expansion at the exit of the nozzle. Similarly the temperature distribution indicates different flow recirculation patterns in the test cell. Both cases capture all the essential flow phenomena such as the shock-boundary layer interaction, plume expansion, expansion of the first stage ejectors, mixing between the engine plume and the first stage ejector flow and pressurization due to the first stage ejectors. The final paper will discuss thermal loads on the walls of the diffuser and cooling mechanisms investigated.

Allgood, Daniel C.↗

NASA NTRS2010

Computational Analyses in Support of Sub-scale Diffuser Testing for the A-3 Facility: Steady Predictions - Part 1

Simulation technology can play an important role in rocket engine test facility design and development by assessing risks, providing analysis of dynamic pressure and thermal loads, identifying failure modes and predicting anomalous behavior of critical systems. Advanced numerical tools assume greater significance in supporting testing and design of high altitude testing facilities and plume induced testing environments of high thrust engines because of the greater inter-dependence and synergy in the functioning of the different sub-systems. This is especially true for facilities such as the proposed A-3 facility at NASA SSC because of a challenging operating envelope linked to variable throttle conditions at relatively low chamber pressures. Facility designs in this case will require a complex network of diffuser ducts, steam ejector trains, fast operating valves, cooling water systems and flow diverters that need to be characterized for steady state performance. In this paper, we will demonstrate with the use of CFD analyses s advanced capability to evaluate supersonic diffuser and steam ejector performance in a sub-scale A-3 facility at NASA Stennis Space Center (SSC) where extensive testing was performed. Furthermore, the focus in this paper relates to modeling of critical sub-systems and components used in facilities such as the A-3 facility. The work here will address deficiencies in empirical models and current CFD analyses that are used for design of supersonic diffusers/turning vanes/ejectors as well as analyses for confined plumes and venting processes. The primary areas that will be addressed are: (1) supersonic diffuser performance including analyses of thermal loads (2) accurate shock capturing in the diffuser duct; (3) effect of turning duct on the performance of the facility (4) prediction of mass flow rates and performance classification for steam ejectors (5) comparisons with test data from sub-scale diffuser testing and assessment of confidence levels in CFD based flowpath modeling of the facility. The analyses tools used here expand on the multi-element unstructured CFD which has been tailored and validated for impingement dynamics of dry plumes, complex valve/feed systems, and high pressure propellant delivery systems used in engine and component test stands at NASA SSC. The analyses performed in the evaluation of the sub-scale diffuser facility explored several important factors that influence modeling and understanding of facility operation such as (a) importance of modeling the facility with Real Gas approximation, (b) approximating the cluster of steam ejector nozzles as a single annular nozzle, (c) existence of mixed subsonic/supersonic flow downstream of the turning duct, and (d) inadequacy of two-equation turbulence models in predicting the correct pressurization in the turning duct and expansion of the second stage steam ejectors. The procedure used for modeling the facility was as follows: (i) The engine, test cell and first stage ejectors were simulated with an axisymmetric approximation (ii) the turning duct, second stage ejectors and the piping downstream of the second stage ejectors were analyzed with a three-dimensional simulation utilizing a half-plane symmetry approximation. The solution i.e. primitive variables such as pressure, velocity components, temperature and turbulence quantities were passed from the first computational domain and specified as a supersonic boundary condition for the second simulation. (iii) The third domain comprised of the exit diffuser and the region in the vicinity of the facility (primary included to get the correct shock structure at the exit of the facility and entrainment characteristics). The first set of simulations comprising the engine, test cell and first stage ejectors was carried out both as a turbulent real gas calculation as well as a turbulent perfect gas calculation. A comparison for the two cases (Real Turbulent and Perfect gas turbulent) of the Ma Number distribution and temperature distributions are shown in Figures 1 and 2 respectively.

Allgood, Daniel C.↗

DOE OSTI2021

A surrogate-model-based approach for estimating the first and second-order moments of offshore wind power

Power curve, the functional relationship that governs the process of converting a set of weather variables experienced by a wind turbine into electric power, is widely used in the wind industry to estimate power output for planning and operational purposes. Existing methods for power curve estimation have three main limitations: (i) they mostly rely on wind speed as the sole input, thus ignoring the secondary, yet possibly significant effects of other environmental factors, (ii) they largely overlook the complex marine environment in which offshore turbines operate, potentially compromising their value in offshore wind energy applications, and (ii) they solely focus on the first-order properties of wind power, with little (or null) information about the variation around the mean behavior, which is important for ensuring reliable grid integration, asset health monitoring, and energy storage, among others. In light of that, this study investigates the impact of several wind-and wave-related factors on offshore wind power variability, with the ultimate goal of accurately predicting its first two moments. Further, our approach couples OpenFAST—a multi-physics wind turbine simulator—with Gaussian Process (GP) regression to reveal the underlying relationships governing offshore weather-to-power conversion. We first find that a multi-input power curve which captures the combined impact of wind speed, direction, and air density, can provide double-digit improvements, in terms of prediction accuracy, relative to univariate methods which rely on wind speed as the sole explanatory variable (e.g. the standard method of bins). Wave-related variables are found not important for predicting the average power output, but interestingly, appear to be extremely relevant in describing the fluctuation of the offshore power around its mean. Tested on real-world data collected at the New York/New Jersey bight, our proposed multi-input models demonstrate a high explanatory power in predicting the first two moments of offshore wind generation, testifying their potential value to the offshore wind industry.

17 WIND ENERGY↗

NASA NTRS2002

Method for Locating a Concealed Object

Apparatus and methods are disclosed for detecting anomalies in microwave penetrable material that may be used for locating plastic mines or pipes underneath the ground. A transmitter is positioned at a plurality of different positions above the ground. A microwave signal is transmitted that is stepped over a plurality of frequencies. At each position, a plurality of reflections are received corresponding to each of the plurality of frequencies that were transmitted. A complex target vector may be produced at each position that contains complex values corresponding to magnitude, phase, and time delay for each of the plurality of reflections received at that location. A complex reference data vector may be produced, either based on predetermined values or based on data from the received plurality of reflections. A comparison is made between the complex target vector and the complex reference data vector to produce a channel vector. In one embodiment, an operator may be applied to the channel vector such as a complex filter matrix or to add a complex conjugate. A response signal is produced and anomalies are detected by variations in the response signal with respect to the plurality of positions.

G Dickey Arndt↗

NASA NTRS2015

Retrieval of Aerosol Microphysical Properties from AERONET Photo-Polarimetric Measurements. 2: A New Research Algorithm and Case Demonstration

A new research algorithm is presented here as the second part of a two-part study to retrieve aerosol microphysical properties from the multispectral and multiangular photopolarimetric measurements taken by Aerosol Robotic Network's (AERONET's) new-generation Sun photometer. The algorithm uses an advanced UNified and Linearized Vector Radiative Transfer Model and incorporates a statistical optimization approach.While the new algorithmhas heritage from AERONET operational inversion algorithm in constraining a priori and retrieval smoothness, it has two new features. First, the new algorithmretrieves the effective radius, effective variance, and total volume of aerosols associated with a continuous bimodal particle size distribution (PSD) function, while the AERONET operational algorithm retrieves aerosol volume over 22 size bins. Second, our algorithm retrieves complex refractive indices for both fine and coarsemodes,while the AERONET operational algorithm assumes a size-independent aerosol refractive index. Mode-resolved refractive indices can improve the estimate of the single-scattering albedo (SSA) for each aerosol mode and thus facilitate the validation of satellite products and chemistry transport models. We applied the algorithm to a suite of real cases over Beijing_RADI site and found that our retrievals are overall consistent with AERONET operational inversions but can offer mode-resolved refractive index and SSA with acceptable accuracy for the aerosol composed by spherical particles. Along with the retrieval using both radiance and polarization, we also performed radiance-only retrieval to demonstrate the improvements by adding polarization in the inversion. Contrast analysis indicates that with polarization, retrieval error can be reduced by over 50% in PSD parameters, 10-30% in the refractive index, and 10-40% in SSA, which is consistent with theoretical analysis presented in the companion paper of this two-part study.

aerosol retrieval algorithm↗

NASA NTRS2019

Effectiveness of Redundant Communications Systems in Maintaining Operational Control of Small Unmanned Aircraft

NASA has been researching prototype technologies for an Unmanned Aircraft System (UAS) Traffic Management (UTM) system to facilitate enabling of safe and efficient civilian low-altitude airspace and UAS operations, in a series of Technical Capability Levels (TCL) activities that are increasingly complex. In TCL1, completed in 2015, visual line-of-sight operations such as agriculture, firefighting and infrastructure monitoring were addressed with a focus on geofencing and operations scheduling. Technologies and requirements needed for beyond visual line-of-sight (BVLOS) operations in sparsely populated areas were examined in TCL2 in 2016, and those for operations over moderately populated areas in TCL3 in 2017 and 2018. TCL4 will build on the earlier TCLs and focus on technologies and requirements for operations in higher-density urban areas for tasks such as news gathering, package delivery and for managing large-scale contingencies. This paper describes a communications test conducted in TCL3 and discusses insights gained from the test. In the test, operators were directed to equip UAS with redundant Command and Control (C2) communications systems, send a maneuver command to Unmanned Aircraft (UA) via the primary system, then verify execution of the sent command. This exercise was repeated with each redundant system. The test was designed to assess effectiveness of redundant C2 systems in maintaining operational control of UA. Several UAS were configured with varying arrangements to achieve redundancy, including two identical radio modems using the same frequency band, WiFi and Long-Term Evolution (LTE) cellular modems, etc. From the test, digital data such as time maneuver command sent, time maneuver verified, etc., were collected. Descriptions of methods to detect loss of C2 communications and contingency steps for such event were collected and assessed. The final paper will include a detailed analysis of the collected data leading to the following insights. First, effectiveness of redundant C2 systems depends on several factors, such as operational environment and communications service availability. For example, use of two identical point-to-point radio to connect operator and UA on the same frequency band can be effective in mitigating radio malfunction when operating in an environment where possibility of Radio Frequency (RF) interference is low, such as over open plains. However, the same arrangement may not be effective where high level of RF transmissions in broad spectrum ranges can be expected, such as over or near urban areas. For redundant systems that consist of external communications services, such as cellular and satellite communications network, redundancy is maintained only in the areas where more than one services are available. Therefore, UAS operators should have the means to plan for and monitor the performance of external communications services they are relying on to control UA. Second, communications performance needs, such as the minimum data transfer rate and the maximum tolerable latency, should be assessed to reflect the potential hazard that can come from loss of UA control. For example, UA operations over desolate area pose less hazard to people than operations over densely populated area and performance need for the former would be less than the latter.

Jung, Jaewoo↗

DOE OSTI2019

Implementation of Augmented Teleautonomy on a Hydraulic Manipulator for Nuclear Facility D and D - 19602

Robotic and remote system have been used in nuclear applications to keep the human workers from high radiation environment and enhance task performance. However, applications in the more unstructured nuclear environments present more formidable challenges to robotics and remote systems. In particular, remote operation tasks for nuclear facility D and D (or dismantling) requires dexterous manipulation of heavy objects with simple and rugged robotic equipment. To address such challenge, this paper presents a new teleoperation method of augmented teleautonomy for remote operation of tools for D and D tasks. Rather than imposing complex functionalities on the slave robot, focused innovation is directed to providing effective operator aids in such a way as to draw more performance out of human operators. In this regard, the development entails the implementation of an enhanced telerobotic operation method by incorporating multi-modal augmented reality operator aids and autonomous motion primitives. This paper presents the relevant technology development utilizing a mixed-reality telerobotic test bed, and system integration and demonstration with a rugged, hydraulic slave robot system. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2018

Computational and Experimental Validation of the Serviceability of RBMK Core Elements Under Graphite Stack Distortion Conditions

Computational and experimental validation of the serviceability of zirconium channels in the reactor core according to strength criteria was conducted in order to ensure safe operation of the RBMK reactor facility under graphite stack deformation conditions. A complex of computational and experimental studies confirmed that the requirements of the operative federal norms and regulations for objects using nuclear power are met.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2018

Analytic in a Sector Resolving Families of Operators for Degenerate Evolution Fractional Equations

We introduce a class of pairs of operators defining a linear homogeneous degenerate evolution fractional differential equation in a Banach space. Reflexive Banach spaces are represented as the direct sums of the phase space of the equation and the kernel of the operator at the fractional derivative. In a sector of the complex plane containing the positive half-axis, we construct an analytic family of resolving operators that degenerate only on the kernel. The results are used in the study of the solvability of initial-boundary value problems for partial differential equations containing fractional time-derivatives and polynomials in the Laplace operator with respect to the spatial variable.

97 MATHEMATICS AND COMPUTING↗