SEARCH · Search NASA

Results for “continuous approaches”

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.

SourceResearch connectionFrom yearThrough year

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

At least 307 records · Page 17

All sources NASA NTRS DOE OSTI

NASA NTRS2016

Explorations of Quantum-Classical Approaches to Scheduling a Mars Lander Activity Problem

An effective approach to solving problems involving mixed (continuous and discrete) variables and constraints, such as hybrid systems, is to decompose them into subproblems and integrate dedicated solvers geared toward those subproblems. Here, we introduce a new framework based on a tree search algorithm to solve hybrid discrete-continuous problems that incorporates: (1) a quantum annealer that samples from the configuration space for the discrete portion and provides information about the quality of the samples, and (2) a classical computer that makes use of information from the quantum annealer to prune and focus the search as well as check a continuous constraint. We consider four variants of our algorithm, each with progressively more guidance from the results provided by the quantum annealer. We empirically test our algorithm and compare the variants on a simplified Mars Lander task scheduling problem. Variants with more guidance from the quantum annealer have better performance.

scheduling↗

NASA NTRSDate not supplied

The Stratospheric Aerosol and Gas Experiment (SAGE) IV Pathfinder

Atmospheric aerosols and ozone are designated as observing system priorities in the 2017–2027 Decadal Survey report [1]. Accurate records of stratospheric aerosols are a vital piece of the puzzle regarding climate change. Stratospheric ozone has been the subject of observation and research for decades. Its importance is exhibited in the United States Clean Air Act [2], which mandates that NASA monitor atmospheric ozone. Measurements from satellites provided data on the initial decline of ozone in the late 1970s and early 1980s that supported the adoption of the Montreal Protocol, and current observations hint at a potential recovery. Adequate determination of that recovery requires continuous and, in the case of multiple instruments, overlapping data records. However, most current satellite systems are well beyond their expected lifetimes, and so we look towards the future of satellite observations of stratospheric ozone and aerosols to develop the Stratospheric Aerosol and Gas Experiment (SAGE) IV Pathfinder. Enabled by the NASA Earth Science Technology Office (ESTO)’s Instrument Incubator Program (IIP), the SAGE IV Pathfinder project has developed and validated a prototype demonstration that paves the way for a future SAGE IV spaceflight mission. Utilizing solar occultation imaging, SAGE IV will be capable of measuring ozone, aerosol, and other trace gas species with the same quality as previous SAGE instruments but with greatly improved pointing knowledge. Furthermore, current technological advancements allow SAGE IV to fit within a CubeSat framework and make use of commercial hardware, significantly reducing the size and cost when compared with traditional missions and enabling sustainability of future measurements. SAGE IV will meet the definition of the newly-recommended Venture-Continuity missions by “bringing forward innovative approaches to sustain measurements at lower costs”. The latest results from development of the SAGE IV Pathfinder are presented. [1] “Thriving on Our Changing Planet: A Decadal Strategy for Earth Observation from Space,” National Academies of Sciences, Engineering, and Medicine, 2018. [2] “United State Clean Air Act,” 42 U.S.C. 767 1b(d)(2).

Robert Damadeo↗

NASA NTRSDate not supplied

Growing the success of Small Satellite missions through community learning

The successful utilization of small satellites for scientific missions relies on continual infusion of technology innovations, creative approaches, and new capabilities, all of which advance at a very rapid pace. Achieving these advancements requires open and efficient exchange of results, experiences, and ideas. Community learning is particularly challenging in this fast-growing community involving an increasingly diverse set of players from all sectors: industry, academia, government, and the public at large. Building and cultivating a community of practices around small satellite technology development and mission implementation are key objectives for NASA’s Small Spacecraft Systems Virtual Institute (S3VI). The institute has developed and provides access to a large collection of products, tools, and activities to advance clear communications and coordination regarding small spacecraft undertakings across NASA, to provide mission enabling information to the smallsat research community, to engage with stakeholders in industry, government, academia and the general public, and to support the overall small spacecraft community. New and updated offerings by the S3VI include: The2021 NASA State of the Art Report of Small Spacecraft Technology, the Small Spacecraft Reliability Initiative Knowledge Base, and the “MISSION ACCOMPLISHED”webinar series. These and other institute products will help scientists and engineers planning future missions answer pertinent questions, such as: What is the state of the art of small spacecraft technology that can be used?What are some best practices that other experts and teams can recommend? What did previous missions accomplish? What lessons could be learned from previous missions? What flight-proven parts are available? What emerging technologies could be taken advantage of? A status will be presented on S3VI activities facilitating community learning within the small satellite science community through the collection, sharing, and exchange of experiences with small satellite mission development and execution across all NASA mission areas.

Moretto Jorgensen, T↗

NASA NTRSDate not supplied

Growing the Success of Small Satellite Missions Through Community Learning

The successful utilization of small satellites for scientific missions relies on continual infusion of technology innovations, creative approaches, and new capabilities, all of which advance at a very rapid pace. Achieving these advancements requires open and efficient exchange of results, experiences, and ideas. Community learning is particularly challenging in this fast-growing community involving an increasingly diverse set of players from all sectors: industry, academia, government, and the public at large. Building and cultivating a community of practices around small satellite technology development and mission implementation are key objectives for NASA’s Small Spacecraft Systems Virtual Institute (S3VI). The institute has developed and provides access to a large collection of products, tools, and activities to advance clear communications and coordination regarding small spacecraft undertakings across NASA, to provide mission enabling information to the smallsat research community, to engage with stakeholders in industry, government, academia and the general public, and to support the overall small spacecraft community. New and updated offerings by the S3VI include: The2021 NASA State of the Art Report of Small Spacecraft Technology, the Small Spacecraft Reliability Initiative Knowledge Base, and the “MISSION ACCOMPLISHED” webinar series. These and other institute products will help scientists and engineers planning future missions answer pertinent questions, such as: What is the state of the art of small spacecraft technology that can be used? What are some best practices that other experts and teams can recommend? What did previous missions accomplish? What lessons could be learned from previous missions? What flight-proven parts are available? What emerging technologies could be taken advantage of? A status will be presented on S3VI activities facilitating community learning within the small satellite science community through the collection, sharing, and exchange of experiences with small satellite mission development and execution across all NASA mission areas.

Small Satellite↗

NASA NTRS2022

Preparations for the Launch, Cruise, and Orbital Operations Phases of the Psyche Mission

“Psyche: Journey to a Metal World” was selected in 2017 as the 14th mission in NASA’s Discovery program. The mission uses an electric propulsion (EP) system to rendezvous with and orbit the large metal asteroid (16) Psyche. Spacecraft development is a hybrid approach with deep-space avionics provided by the Jet Propulsion Laboratory (JPL) and a solar electric propulsion chassis based on Maxar’s 1300-series GEO communications satellites. The payload suite is comprised of a magnetometer, multispectral imager, and gamma ray & neutron spectrometer science instruments and the Deep Space Optical Communications advanced technology demonstration.The spacecraft is currently in the final integration and test phase to support a planned launch period open in August 2022. With under a year until liftoff, final pre-liftoff preparations are underway for the mission’s major in-flight Phases. The Launch Phase is the mission’s only critical event as the vehicle autonomously deploys the solar arrays and delivers the spacecraft to a safe state. Following a planned 70-day Initial Checkout Phase, the spacecraft thrusts with the EP system through the majority of a 3.5-year Cruise Phase, which includes a Mars gravity assist, to rendezvous with (16) Psyche. The Approach Phase uses optical navigation while continuing to thrust with the EP engines to deliver the spacecraft into orbit. Orbital Operations are baselined for 20 months as the spacecraft steps through four progressively lower orbital altitudes to study the largest M-type asteroid in the solar system.

Hart, William↗

NASA NTRSDate not supplied

NASA GPM Status and Future Activities

Global Precipitation Measuremen↗

NASA NTRSDate not supplied

A Proposed Clock Synchronization Method for the Solar System Internet

Networked communications in space are necessary to achieve scalability in terms of the number of communicating nodes but also in terms of the overall system complexity. A key component to such a system is the ability to synchronize clocks, which is the focus of this paper. The so-called Solar System Internet (SSI) will be built upon Delay Tolerant Networking (DTN), which, in analogy to the Internet Protocol (IP), can be considered a suite of protocols necessary for networking in the space domain. Therefore, our goal is to extend this suite to include a DTN clock synchronization capability, analogous to the Network Time Protocol (NTP) used in the Internet. A motivating example of a network in space is NASA’s LunaNet, a vision for a multi-hop multi-path network extending to the moon wherein not all nodes will have direct connections to an authoritative reference clock. In this paper, we propose a general clock synchronization methodology and algorithm that could be used for LunaNet as well as more elaborate time-varying networks. In recent years, DTN has benefited from modeling efforts founded on the mathematical tool of sheaves. Here we continue this work to provide an approach to clock synchronization. Due to the time-varying nature of space networks, absolute consensus is not possible. However, the sheaf Laplacian provides a practical, distributed approach to approximating consensus by allowing data to diffuse through the network. In particular, the sheaf Laplacian is readily computable, lending our approach to implementation. Our approach is well suited to handle the difficulties of space networks. For instance, differences in clock accuracy mean certain nodes are more authoritative than others; we can account for these differences through hierarchies in the network, generalizing the strata in NTP. Furthermore, just as error estimation is an integral part of NTP, we are able to give concrete error bounds for our approach. Indeed, different applications (e.g., communications schedules, pointing, navigation, distributed science) will have different requirements, hence it is necessary to maintain clocks within a given tolerance. We outline some of the necessary steps to turn our approach into a practical network protocol that could be used in DTN, and we conclude the paper with suggestions for future research.

Michael Moy↗

NASA NTRSDate not supplied

NASA GPM Status and Future Activities

The joint U.S.-Japan Global Precipitation Measurement (GPM) mission is approaching a decade of operations, and continues to pursue research, dataset production, and outreach related to precipitation. Key activities over the last year were the release of an improved “Version 07” of all GPM precipitation and latent heating products, boosting the orbit of the GPM Core Observatory (GPM CO) to 435 km, and improving quality control on precipitation retrievals from the GPM constellation of passive microwave satellites. This presentation summarizes key improvements to the GPM products and provides some examples of the changes between Versions 06 and 07 in algorithm performance. One important operational change that affected Version 07 is that the scanning strategy for the Ka-band radar channel changed in May 2018; all products that depend on Ka were revised to accommodate this change. For example, in Version 07 the Goddard Profiling (GPROF) algorithm has implemented improvements in regions where orographic enhancement and suppression take place and where the surface is snowy/icy, and again covers radiometers reaching back to 1987. The Combined Radar Radiometer Algorithm (CORRA) now incorporates modified drop-size distribution constraints that substantially reduce bias. Revisions to the Convective-Stratiform Heating (CSH) algorithm employ new radiative transfer retrievals as well as accounting for terrain in the vertical coordinates. Each algorithm was adjusted to ensure continuity for each product across the boundary in 2014 between the predecessor Tropical Rainfall Measuring Mission (TRMM) and the GPM CO. The U.S. Science Team’s Integrated Multi-satellitE Retrievals for GPM (IMERG) was upgraded to account for distortions in the probability density function of regional precipitation rates due to weighted averaging in the Kalman filter used for “morphing” the passive microwave data. Maintaining the GPM CO orbital altitude in the the current very active solar cycle has been forcing the use of more fuel than planned and consequently shortening the forecasted life of the mission from the early 2030's to the late 2020's. It was considered vital to regain some of this lifetime to ensure overlap with the upcoming Atmosphere Observing System mission to provide crosscalibration of instruments. To accomplish this, the orbital altitude was raised from 400 to 435 km on 7-8 November 2023. Thereafter, the primary GPM CO algorithms had to be revised to account for the change in observing parameters. By meeting time this action should be complete. Recently, a screening algorithm based on auto-encoding was developed that uncovered 162 orbits (out of the many thousands of orbits across all years and all satellites) of passive microwave retrievals that had highly anomalous values. Removing these defective retrievals has improved the integrity of both the GPROF and IMERG records. However, the nature of the IMERG processing interacted sufficiently badly with the now-discovered anomalous orbits that it was necessary to completely reprocess the IMERG Final Run record, now labeled Version 07B. The presentation also considers major issues that require continued attention, including the use of machine learning algorithms and the operational challenge of swarms of “small”, perhaps short-lived satellites.

GPM↗

NASA NTRSDate not supplied

Enhancements, Verification, and VMS Integration of VTOL Concept Vehicle Simulation Models

Advanced Rotorcraft Technology (ART) and the NASA Ames Aeromechanics branch have jointly developed FLIGHTLAB simulation models for Advanced Air Mobility (AAM) VTOL concept vehicles. The overarching purpose of the simulation model development is to establish a set of well defined reference vehicles for FLIGHTLAB users and the rotorcraft community. The ongoing research effort and enhancement of these AAM simulation models to fulfill the role of quality reference vehicles is this paper’s focus. The content of this paper expands on the established characteristics of these AAM models in three primary areas. First, enhancement of the lift+cruise and tiltwing models with elastic airframe properties is discussed. The process of setting up the elastic airframe model in FLIGHTLAB, as well as the impacts on flight characteristics are explained. The introduction of the elastic airframe modeling allows these models to be used in flight dynamics, loads, and vibration analysis of the configuration designs. Next, linear model generation from the enhanced simulation model is covered. Confirming the validity of the linearized models is of importance, as these linear models are utilized for flight control design and tuning for these experimental configurations. For the final focus, the progress towards implementation of these models into the NASA Ames Vertical Motion Simulator (VMS) is described. This task seeks to demonstrate the procedures of integrating a FLIGHTLAB flight simulation in the VMS environment, test fully integrated simulation with communication between flight dynamics, control, and propulsion models, and explore the essential aspects of simulation model integration in a full flight simulator environment. This includes I/O definition, initialization, trim, flying, etc. By expanding the capabilities of the AAM simulation models, they continue to develop as valuable and approachable modeling references.

VMS↗

NASA NTRSDate not supplied

NASA Progress on the Development and Qualification of a 12-kW Hall-Effect, Solar Electric Propulsion Thruster

The National Aeronautics and Space Administration (NASA) continues to evolve the human exploration approach for beyond low-Earth orbit and in a manner involving international, academic, and industry partners. The center of this approach is NASA’s Gateway program that will establish a permanent human presence in lunar orbit for human cislunar science, operations, and lunar surface access to eventually land the next American astronauts on the south pole of the Moon. In support of the effort, NASA’s Space Technology Mission Directorate (STMD) began a project to increase the state of the art for the Hall-Effect Solar Electric Propulsion (SEP) technology. The resulting Advanced Electric Propulsion System (AEPS) project has developed a 12 kW Hall-effect thruster in support of the Gateway program. The project is managed by the NASA Glenn Research Center (GRC), supported by the NASA Jet Propulsion Laboratory (JPL) with development, qualification & flight hardware all supplied by L3 Harris Aerojet Rocketdyne (AR). Development of the 12-kW Hall thruster electric propulsion system began with maturation of the Hall Effect Rocket with Magnetic Shielding (HERMeS) Technology Demonstration Units (TDUs). The technology development was then transitioned to AR via the AEPS contract, which built and tested two Engineering Test Unit (ETU) thrusters and multiple critical components. The project transitioned to the production of the three flight thrusters and entered qualification testing at the component and thruster levels.

Electric Propulsion↗

NASA NTRSDate not supplied

NASA Progress on the Development and Qualification of a 12-kW Hall-Effect, Solar Electric Propulsion Thruster

Electric Propulsion↗

NASA NTRS1993

Nonreflective boundary conditions for high-order methods

A different approach to nonreflective boundary conditions for the Euler equations is presented. This work is motivated by a need for in and outflow boundary conditions that do not limit the useful accuracy of high-order accurate methods. The primary interest is in the propagation and convection of continuous acoustic and convective waves. This new approach employs the exact solution to finite waves to relate interior values and ambient conditions to boundary values. The method is first presented in one dimension and then generalized to multidimensions. Grid refinement studies are used to demonstrate high-order convergence for both one-dimensional and two-dimensional flows.

Atkins, H. L.↗

NASA NTRS1994

Nonreflective boundary conditions for high-order methods

A different approach to nonreflective boundary conditions for the Euler equations is presented. This work is motivated by a need for inflow and outflow boundary conditions that do not limit the useful accuracy of high-order accurate methods. The primary interest is in the propagation and convection of continuous acoustic and convective waves. This new approach employs the exact solution to finite waves to relate interior values and ambient conditions to boundary values. The method is first presented in one dimension and then generalized to multidimensions. Grid refinement studies are used to demonstrate high-order convergence for both one-dimensional and two-dimensional flows.

Atkins, H.↗

NASA NTRS1997

Maneuver design for Galileo Jupiter approach and orbital operations

Following the successful release of the Galileo probe, the navigation efforts were focused on the implementation of the critical Io approach and the Jupiter orbit insertion strategy. The actual in-flight events on the approach phase affected the strategy. The most significant event was the onboard tape recorder anomaly, and it is shown that this anomaly affected the plans and assumptions of the navigation strategy for the approach and orbit insertion. The analysis, constraints, contingency planning and design evolution of trajectory correction maneuvers which enabled the continuation of the mission, are reported on. The Jupiter approach and initial orbit navigation strategy is presented in order to verify the viability of the strategy under nominal circumstances, and future mission operations plans are described.

Wilson, Michael G.↗

NASA NTRS2016

Unmanned Aircraft Systems Traffic Management (UTM) Safely Enabling UAS Operations in Low-Altitude Airspace

Unmanned Aircraft System (UAS) Traffic Management (UTM) Enabling Civilian Low-Altitude Airspace and Unmanned Aircraft System Operations What is the problem? Many beneficial civilian applications of UAS have been proposed, from goods delivery and infrastructure surveillance, to search and rescue, and agricultural monitoring. Currently, there is no established infrastructure to enable and safely manage the widespread use of low-altitude airspace and UAS operations, regardless of the type of UAS. A UAS traffic management (UTM) system for low-altitude airspace may be needed, perhaps leveraging concepts from the system of roads, lanes, stop signs, rules and lights that govern vehicles on the ground today, whether the vehicles are driven by humans or are automated. What system technologies is NASA exploring? Building on its legacy of work in air traffic management for crewed aircraft, NASA is researching prototype technologies for a UAS Traffic Management (UTM) system that could develop airspace integration requirements for enabling safe, efficient low-altitude operations. While incorporating lessons learned from the today's well-established air traffic management system, which was a response that grew out of a mid-air collision over the Grand Canyon in the early days of commercial aviation, the UTM system would enable safe and efficient low-altitude airspace operations by providing services such as airspace design, corridors, dynamic geofencing, severe weather and wind avoidance, congestion management, terrain avoidance, route planning and re-routing, separation management, sequencing and spacing, and contingency management. One of the attributes of the UTM system is that it would not require human operators to monitor every vehicle continuously. The system could provide to human managers the data to make strategic decisions related to initiation, continuation, and termination of airspace operations. This approach would ensure that only authenticated UAS could operate in the airspace. In its most mature form, the UTM system could be developed using autonomicity characteristics that include self-configuration, self-optimization and self-protection. The self-configuration aspect could determine whether the operations should continue given the current andor predicted windweather conditions. NASA envisions concepts for two types of possible UTM systems. The first type would be a Portable UTM system, which would move from between geographical areas and support operations such as precision agriculture and disaster relief. The second type of system would be a Persistent UTM system, which would support low-altitude operations and provide continuous coverage for a geographical area. Either system would require persistent communication, navigation, and surveillance (CNS) coverage to track, ensure, and monitor conformance. What is NASA doing to test the technologies? NASA's near-term goal is the development and demonstration of a possible future UTM system that could safely enable low-altitude airspace and UAS operations. Working alongside many committed government, industry and academic partners, NASA is leading the research, development and testing that is taking place in a series of activities called Technology Capability Levels (TCL), each increasing in complexity. UTM TCL1 concluded field testing in August 2015 and is undergoing additional testing at an FAA site.

UTM Low-altitude↗

NASA NTRS2003

Various Numerical Applications on Tropical Convective Systems Using a Cloud Resolving Model

In recent years, increasing attention has been given to cloud resolving models (CRMs or cloud ensemble models-CEMs) for their ability to simulate the radiative-convective system, which plays a significant role in determining the regional heat and moisture budgets in the Tropics. The growing popularity of CRM usage can be credited to its inclusion of crucial and physically relatively realistic features such as explicit cloud-scale dynamics, sophisticated microphysical processes, and explicit cloud-radiation interaction. On the other hand, impacts of the environmental conditions (for example, the large-scale wind fields, heat and moisture advections as well as sea surface temperature) on the convective system can also be plausibly investigated using the CRMs with imposed explicit forcing. In this paper, by basically using a Goddard Cumulus Ensemble (GCE) model, three different studies on tropical convective systems are briefly presented. Each of these studies serves a different goal as well as uses a different approach. In the first study, which uses more of an idealized approach, the respective impacts of the large-scale horizontal wind shear and surface fluxes on the modeled tropical quasi-equilibrium states of temperature and water vapor are examined. In this 2-D study, the imposed large-scale horizontal wind shear is ideally either nudged (wind shear maintained strong) or mixed (wind shear weakened), while the minimum surface wind speed used for computing surface fluxes varies among various numerical experiments. For the second study, a handful of real tropical episodes (TRMM Kwajalein Experiment - KWAJEX, 1999; TRMM South China Sea Monsoon Experiment - SCSMEX, 1998) have been simulated such that several major atmospheric characteristics such as the rainfall amount and its associated stratiform contribution, the Qlheat and Q2/moisture budgets are investigated. In this study, the observed large-scale heat and moisture advections are continuously applied to the 2-D model. The modeled cloud generated from such an approach is termed continuously forced convection or continuous large-scale forced convection. A third study, which focuses on the respective impact of atmospheric components on upper Ocean heat and salt budgets, will be presented in the end. Unlike the two previous 2-D studies, this study employs the 3-D GCE-simulated diabatic source terms (using TOGA COARE observations) - radiation (longwave and shortwave), surface fluxes (sensible and latent heat, and wind stress), and precipitation as input for the Ocean mixed-layer (OML) model.

Shie, C.-L.↗

NASA NTRS2011

Macro vs. Micro: Relating the Spectral Properties of Vesta and the HED Meteorite

We present the main results obtained comparing the visible-near infrared (VIS-NIR) spectra Vesta s surface with howardites, eucrites, diogenites (HED). HEDs are commonly associated with Vesta s composition based on spectral similarities. Because of such association, much effort is being made to merge the information from HEDs as well as Vestoids - with that from Vesta to characterize the lithologic diversity of the surface of this asteroid and to infer clues regarding its thermal history. However, while the HEDs are a class of meteorites well studied in the laboratory, the only spectral data available for Vesta until now were telescopic observations which are limited in terms of observation conditions, spatial resolution and Signal to Noise Ratio. The Dawn spacecraft, orbiting around Vesta since July 2011, is performing detailed observations of this body and thus improving our knowledge of its properties. Dawn s scientific payload includes an imaging spectrometer, VIR-MS, sensitive to the VIS-NIR spectral range. VIR-MS began acquiring spectra during the approach phase started in May 2011 and will continue its observations through July 2012 when the spacecraft will depart Vesta to travel to Ceres. The VIR-MS spatial resolution depends upon the mission phase (approach, survey, high altitude, low altitude). However, spectra acquired by VIR-MS have already exceeded the spatial resolution of ground-based telescopic observations, with resolution in the approach phase ranging from 2.5 up to 0.8 km/pixel. Moreover, the observations are uniformly distributed in latitude and longitude allowing us to have a global view of Vesta s crust spectral properties. Using the information provided by VIR spectra, we studied the distribution of the spectral heterogeneities on the surface and we used our findings to perform a comparison with HEDs spectra in the VIS-NIR spectral range searching for analogies and/or incompatibilities. In our analysis, we focused on a method to compare the results obtained at microscopic scale on HEDs samples and the one obtained at macroscopic scale on the surface of Vesta. Finally, we discuss our results in the context of vestan thermal history. The intent of this study is to improve our understanding of the connection between Vesta and the HED samples, which is one of the primary Dawn scientific objectives. This work is supported by an Italian Space Agency (ASI) grant and by NASA through the Dawn project and a Dawn at Vesta Participating Scientist grant.

Ammannito, E.↗

NASA NTRS1995

Time-domain approach for the transient responses in stratified viscoelastic Earth models

We have developed the numerical algorithm for the computation of transient viscoelastic responses in the time domain for a radially stratified Earth model. Stratifications in both the elastic parameters and the viscosity profile have been considered. The particular viscosity profile employed has a viscosity maximum with a constrast of O(100) in the mid lower mantle. The distribution of relaxation times reveals the presence of a continuous spectrum situated between O(100) and O(exp 4) years. The principal mode is embedded within this continuous spectrum. From this initial-value approach we have found that for the low degree harmonics the non-modal contributions are comparable to the modal contributions. For this viscosity model the differences between the time-domain and normal-mode results are found to decrease strongly with increasing angular order. These calculations also show that a time-dependent effective relaxation time can be defined, which can be bounded by the relaxation times of the principal modes.

Hanyk, L.↗