Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “TIME FUNCTION”

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 1,405 records · Page 78
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Efficient Modeling of Structural, Electronic, and Optical Properties of Silver and Gold Metal Nanoclusters and Alloys Using Optimized SCC-DFTB Parameters

Computation of optical properties using conventional time-dependent density functional theory (TD-DFT) is time-consuming and memory-intensive. In this study, we investigate the accuracy and efficiency of the density functional tight binding (DFTB) framework with newly optimized Slater–Koster (SK) parameters for modeling the structural, electronic properties, and absorption spectra of silver and gold nanoclusters and their alloys. Our investigation of the ground state (GS) properties demonstrates that the newly developed GS-SK parameters enable DFTB to closely approximate DFT-calculated bond lengths for octahedron, tetrahedron, icosahedra, and truncated octahedron with sizes Ag n /Au n (n = 19, 20, 38, 55), nanoclusters and Ag 20 /Au 20 nanoalloys, with a maximum deviation of approximately 0.15 Å. Formation energy results indicate that the GS-SK parameters can closely estimate changes in formation energies with alloy composition, and the comparison of electronic structures for Ag 20 , Au 20 , and AgAu alloy nanoclusters using the DFTB approximation reveals good agreement in the projected density of states (DOS) profiles and energy levels. A second set of SK parameters, ES-SK, has been developed to describe excited state (ES) properties, including the absorption spectra of silver octahedron Ag 19 , tetrahedral Ag n (n = 20, 56, 84), truncated octahedron Ag 38 , and icosahedra Ag 55 closed-shell clusters and their gold and alloy counterparts over a broad range of alloy compositions. This parametrization uses TD-DFTB calculations and fine-tunes the d and p eigenvalues by comparing them to reference absorption spectra from first-principles TD-DFT. This enables the generation of absorption spectra that closely match the reference spectra when plasmon excitation is dominant, as demonstrated by studying the plasmonic properties of icosahedral Ag n and Au n (n = 309 and 561) nanoparticles. This includes the rapid loss in plasmon quality when Au partially replaces Ag in alloy clusters. Furthermore, these results provide a foundation for addressing computational bottlenecks in plasmonics and with new prospects for applications in the quantum plasmonics for bimetallic alloys.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2006

The Supercritical Pile Model for GRBs

We present the spectral and temporal radiative signatures expected within the Supercritical Pile model of Gamma Ray Bursts (GRB). This model is motivated by the need for a process that provides the dissipation necessary in GRB and presents a well defined scheme for converting the energy stored in the relativistic protons of the Relativistic Blast Waves (RBW) associated with GRB into radiation; at the same time it leads to spectra which exhibit a peak in the burst nuF(sub nu) distribution at an energy E(sub p) approximately equal to 1 MeV in the observer s frame, in agreement with observation and largely independent of the Lorentz factor GAMMA of the associated relativistic outflow. Furthermore, this scheme does not require (but does not preclude) acceleration of particles at the shock other than that provided by the isotropization of the flow bulk kinetic energy on the RBW frame. In the present paper we model in detail the evolution of protons, electrons and photons from a RBW to produce detailed spectra of the prompt GRB phase as a function of time from across a very broad range spanning roughly 4 log10 GAMMA decades in frequency. The model spectra are in general agreement with observations and provide a means for the delineating of the model parameters through direct comparison with trends observed in GRB properties.

Kazanas, Demos↗
NASA NTRS2005

The Supercritical Pile Model for GRBs

We present the spectral and temporal radiative signatures expected within the "Supercritical Pile" model of Gamma Ray Bursts (GRB). This model is motivated by the need for a process that provides the dissipation necessary in GRB and presents a well defined scheme for converting the energy stored in the relativistic protons of the Relativistic Blast Waves (RBW) associated with GRB into radiation; at the same time it leads to spectra which exhibit a peak in the burst nuF(sub nu) distribution at an energy E(sub p) approx. equal to 1 MeV in the observer s frame, in agreement with observation and largely independent of the Lorentz factor r of the associated relativistic outflow. Futhermore, this scheme does not require (but does not preclude) acceleration of particles at the shock other than that provided by the isotropization of the flow bulk kinetic energy on the RBW frame. In the present paper we model in detail the evolution of protons, electrons and photons from a RBW to produce detailed spectra of the prompt GRB phase as a function of time from across a very broad range spanning roughly 4 log10Gamma decades in frequency. The model spectra are in general agreement with observations and provide a means for the delineating of the model parameters through direct comparison with trends observed in GRB properties.

Kazanas, D.↗
DOE OSTI2017

Monitoring reinforcement corrosion and corrosion-induced cracking by X-ray microcomputed tomography method

X-ray microcomputed tomography (X-ray μCT) method is proposed to trace steel corrosion and corrosion-induced cracking in cement paste. Experimental results show it can track the time-dependent development of steel corrosion and corrosion products, as well as the subsequent initiation and propagation of corrosion-induced cracks. Furthermore, the information of corrosion pits, corrosion products, and corrosion-induced cracks can be clearly obtained from the whole specimen by this novel method. Additionally, SEM/EDS results agree closely with image analyses by X-ray μCT. This method provides a new angle to investigate the reinforcement corrosion process and can help to improve the numerical analysis of corrosion-induced damage in reinforced concrete structures. - Highlights: • Reinforcement corrosion and corrosion-induced cracking is traced by X-ray μCT method. • The development of corrosion products can be determined as a function of time and space. • Subsequent initiation and propagation of corrosion-induced cracks can be monitored. • The time-dependent corrosion process can be quantitative analyzed by X-ray μCT measurement.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Scattering in the Ising model with the quantum Lanczos algorithm *

Abstract Time evolution and scattering simulation in phenomenological models are of great interest for testing and validating the potential for near-term quantum computers to simulate quantum field theories. Here, we simulate one-particle propagation and two-particle scattering in the one-dimensional transverse Ising model for 3 and 4 spatial sites with periodic boundary conditions on a quantum computer. We use the quantum Lanczos algorithm to obtain all energy levels and corresponding eigenstates of the system. We simplify the quantum computation by taking advantage of the symmetries of the system. These results enable us to compute one- and two-particle transition amplitudes, particle numbers for spatial sites, and the transverse magnetization as functions of time. The quantum circuits were executed on various IBM Q superconducting hardware. The experimental results are in very good agreement with the values obtained using exact diagonalization.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1991

Physical aging in comets

The question of physical aging in cometary nuclei is addressed in order to elucidate the relationship between the past conditions in the protosolar nebula and the present state of the cometary nucleus, and to understand the processes that will physically and chemically alter the nucleus as a function of time. Attention is given to some of the processes that might be responsible for causing aging in comets, namely, radiation damage in the upper layers of the nucleus during the long residences in the Oort cloud, processing from heating and collisions within the Oort cloud, loss of highly volatile species from the nucleus on the first passage through the inner solar system, buildup of a dusty mantle, which can eventually prohibit further sublimation, and a change in the porosity, and hence the thermal properties, of the nucleus. Recent observations suggest that there are distinct differences between 'fresh' Oort cloud comets and thermally processed periodic comets with respect to intrinsic brightness and rate of change of activity as a function of distance.

Meech, Karen J.↗
DOE OSTI2018

Attrition of hematite particles for chemical looping combustion in a conical jet cup

The attrition of hematite particles for use in the chemical looping combustion process was investigated using a cold flow jet cup test. Jet cup attrition experiments are commonly used for bulk attrition testing of fluidized bed catalyst. The results indicate that the particle attrition in the jet cup cold flow experiments arises from surface abrasion due to particle-particle and particle-wall interactions. Experiments indicate that the measured cumulative mass loss increases with attrition time. However, the attrition rate decreases sharply at the early stage of attrition, and gradually, the rate decline slows and approaches a constant value with increasing attrition time. Furthermore, the influence of inlet gas velocity and solid inventory is discussed. As inlet gas velocities increase, the measured cumulative mass loss also increases. However, as the solid inventory increases, the cumulative mass loss decreases. The results also show that the jet cup experiments quantitatively compare with low magnitude tangential forces which is an indication of attrition through abrasion as the primary mechanism. It is determined through particle size distributions before and after which show a small shift of the main peaks with no peak broadening while producing a small number of fines. By using the mass of abraded fines and the widely-used Archard model for abrasive attrition, the specific wear rate coefficient can be predicted as a function of time. The wear coefficient calculation further identifies that the abrasion mechanism as the primary mechanism of attrition.

42 ENGINEERING↗
NASA NTRS1987

Displacements of the earth's surface due to atmospheric loading - Effects of gravity and baseline measurements

Atmospheric mass loads and deforms the earth's crust. By performing a convolution sum between daily, global barometric pressure data and mass loading Green's functions, the time dependent effects of atmospheric loading, including those associated with short-term synoptic storms, on surface point positioning measurements and surface gravity observations are estimated. The response for both an oceanless earth and an earth with an inverted barometer ocean is calculated. Load responses for near-coastal stations are significantly affected by the inclusion of an inverted barometer ocean. Peak-to-peak vertical displacements are frequently 15-20 mm with accompanying gravity perturbations of 3-6 micro Gal. Baseline changes can be as large as 20 mm or more. The perturbations are largest at higher latitudes and during winter months. These amplitudes are consistent with the results of Rabbel and Zschau (1985), who modeled synoptic pressure disturbances as Gaussian functions of radius around a central point. Deformation can be adequately computed using real pressure data from points within about 1000 km of the station. Knowledge of local pressure, alone, is not sufficient. Rabbel and Zschau's hypothesized corrections for these displacements, which use local pressure and the regionally averaged pressure, prove accurate at points well inland but are, in general, inadequate within a few hundred kilometers of the coast.

Van Dam, T. M.↗
DOE OSTI2015

X-Ray Diffraction of Slag-Based Sodium Salt Waste Forms - 15513

Cementitious materials are used to solidify and stabilize aqueous based radioactive waste containing sodium salts. The types and proportions of cementitious ingredients used to treat aqueous radioactive waste streams containing sodium salts depend on the performance objectives for the waste forms and the compositions of the waste streams. This paper documents sample preparation and x-ray diffraction results for a series of materials made with water or highly alkaline sodium salt simulated waste water and cementitious binders. The objective of this study was to: 1) generate a base line for the evolution of the waste form as a function of time and conditions, 2) design new binders based on mineralogy of the binder, 3) understand and predict anion and cation leaching behavior of contaminants of concern, and 4) predict performance of the waste forms for which phase solubility and thermodynamic data are available. Characterization of the mineralogy is also important for understanding the buffering effects that the waste form has on infiltrating water / leachates. In summary, mixtures of Type II portland cement, Grade 100 ground granulated blast furnace slag (GGBFS) and carbon burn-out (CBO) Class F Fly ash which were hydrated with water contained hydrated phase assemblages typical of those reported in the literature. The calcium silicate hydrate phase assemblage in samples hydrated with the alkaline 4.4 M sodium salt simulated waste solution was found to be a function of the (CaO + MgO) / (SiO{sub 2} + Al{sub 2}O{sub 3}) ratio of the samples characterized. No significant differences were detected in samples cured 2 months and 14 months in sealed containers at ambient indoor temperatures. Slag and a blend of slag and cement hydrated with caustic 4.4 M Na salt solution resulted in the most crystalline matrix. In addition to poorly ordered C-S-H, these samples contained fairly well ordered C-S-H I (a precursor of 14A tobermorite) and 11 A Al-substituted tobermorite. These crystalline C-S-H phases did not form or were present in only trace amounts in slag blends containing about 45 to 62 mass percent fly ash. These slag-Class F fly ash blends had a higher silica plus alumina content relative to lime and magnesia than the blends that produced C-S-H I and Al-substituted tobermorite. The calcium silicate binder in the 10:45:45 mixture of cement: slag: fly ash was made up of poorly ordered C-S-H. The sample cured for 14 months may contain a small amount of the more crystalline calcium silicate hydrate phases. Layered double hydroxides in the hydrotalcite (magnesium-aluminum carbonate hydroxide) and hydrocalumite / AFm phases (calcium aluminum hydroxide) were present in mixtures containing slag. The specific phase(s) were not identified because these phases form solid solutions and have a considerable amount of overlap in their x-ray patterns. Sodium nitrate was the only sodium salt phase identified in x-ray diffraction patterns of the samples hydrated with salt solution. Drying during x-ray diffraction sample preparation may have resulted in precipitation of the sodium nitrate or it may have been present in the samples prior to x-ray sample preparation. Sodium sulfate, aluminate, and carbonate may have been incorporated in the structures of the layered double hydroxide (AFm) type phases. These mixed metal layered double hydroxides make up an important fraction of the matrix in the slag containing blends hydrated with caustic salt solution. They are among the few oxide-based phases that exhibit substantial, permanent anion exchange capacity [Kirkpatrick, et al. 1999, Plamer, et al., 2009, and Zhang and Reardon, 2003]. They also contribute to the structural properties of cementitious matrices [Taylor, 1997]. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Fermi and Swift Observations of GRB 190114C: Tracing the Evolution of High-energy Emission from Prompt to Afterglow

We report on the observations of gamma-ray burst (GRB) 190114C by the Fermi Gamma-ray Space Telescope and the Neil Gehrels Swift Observatory . The prompt gamma-ray emission was detected by the Fermi GRB Monitor (GBM), the Fermi Large Area Telescope (LAT), and the Swift Burst Alert Telescope (BAT) and the long-lived afterglow emission was subsequently observed by the GBM, LAT, Swift X-ray Telescope (XRT), and Swift UV Optical Telescope. The early-time observations reveal multiple emission components that evolve independently, with a delayed power-law component that exhibits significant spectral attenuation above 40 MeV in the first few seconds of the burst. This power-law component transitions to a harder spectrum that is consistent with the afterglow emission observed by the XRT at later times. This afterglow component is clearly identifiable in the GBM and BAT light curves as a slowly fading emission component on which the rest of the prompt emission is superimposed. As a result, we are able to observe the transition from internal-shock- to external-shock-dominated emission. We find that the temporal and spectral evolution of the broadband afterglow emission can be well modeled as synchrotron emission from a forward shock propagating into a wind-like circumstellar environment. We estimate the initial bulk Lorentz factor using the observed high-energy spectral cutoff. Considering the onset of the afterglow component, we constrain the deceleration radius at which this forward shock begins to radiate in order to estimate the maximum synchrotron energy as a function of time. We find that even in the LAT energy range, there exist high-energy photons that are in tension with the theoretical maximum energy that can be achieved through synchrotron emission from a shock. These violations of the maximum synchrotron energy are further compounded by the detection of very high-energy (VHE) emission above 300 GeV by MAGIC concurrent with our observations. We conclude that the observations of VHE photons from GRB 190114C necessitates either an additional emission mechanism at very high energies that is hidden in the synchrotron component in the LAT energy range, an acceleration mechanism that imparts energy to the particles at a rate that is faster than the electron synchrotron energy-loss rate, or revisions of the fundamental assumptions used in estimating the maximum photon energy attainable through the synchrotron process.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2014

A Super-Resolution Algorithm for Enhancement of FLASH LIDAR Data: Flight Test Results

This paper describes the results of a 3D super-resolution algorithm applied to the range data obtained from a recent Flash Lidar helicopter flight test. The flight test was conducted by the NASA's Autonomous Landing and Hazard Avoidance Technology (ALHAT) project over a simulated lunar terrain facility at NASA Kennedy Space Center. ALHAT is developing the technology for safe autonomous landing on the surface of celestial bodies: Moon, Mars, asteroids. One of the test objectives was to verify the ability of 3D super-resolution technique to generate high resolution digital elevation models (DEMs) and to determine time resolved relative positions and orientations of the vehicle. 3D super-resolution algorithm was developed earlier and tested in computational modeling, and laboratory experiments, and in a few dynamic experiments using a moving truck. Prior to the helicopter flight test campaign, a 100mX100m hazard field was constructed having most of the relevant extraterrestrial hazard: slopes, rocks, and craters with different sizes. Data were collected during the flight and then processed by the super-resolution code. The detailed DEM of the hazard field was constructed using independent measurement to be used for comparison. ALHAT navigation system data were used to verify abilities of super-resolution method to provide accurate relative navigation information. Namely, the 6 degree of freedom state vector of the instrument as a function of time was restored from super-resolution data. The results of comparisons show that the super-resolution method can construct high quality DEMs and allows for identifying hazards like rocks and craters within the accordance of ALHAT requirements.

Bulyshev, Alexander↗
NASA NTRS2020

Fermi and Swift Observations of GRB 190114C: Tracing the Evolution of High-energy Emission from Prompt to Afterglow

We report on the observations of gamma-ray burst (GRB) 190114C by the Fermi Gamma-ray Space Telescope and the Neil Gehrels Swift Observatory. The prompt gamma-ray emission was detected by the Fermi GRB Monitor (GBM), the Fermi Large Area Telescope (LAT), and the Swift Burst Alert Telescope (BAT) and the long-lived afterglow emission was subsequently observed by the GBM, LAT, Swift X-ray Telescope (XRT), and Swift UV Optical Telescope. The early-time observations reveal multiple emission components that evolve independently, with a delayed power-law component that exhibits significant spectral attenuation above 40 MeV in the first few seconds of the burst. This power-law component transitions to a harder spectrum that is consistent with the afterglow emission observed by the XRT at later times. This afterglow component is clearly identifiable in the GBM and BAT light curves as a slowly fading emission component on which the rest of the prompt emission is superimposed. As a result, we are able to observe the transition from internal-shock- to external-shock-dominated emission. We find that the temporal and spectral evolution of the broadband afterglow emission can be well modeled as synchrotron emission from a forward shock propagating into a wind-like circumstellar environment. We estimate the initial bulk Lorentz factor using the observed high-energy spectral cutoff. Considering the onset of the afterglow component, we constrain the deceleration radius at which this forward shock begins to radiate in order to estimate the maximum synchrotron energy as a function of time. We find that even in the LAT energy range, there exist high-energy photons that are in tension with the theoretical maximum energy that can be achieved through synchrotron emission from a shock. These violations of the maximum synchrotron energy are further compounded by the detection of very high-energy (VHE) emission above 300 GeV by MAGIC concurrent with our observations. We conclude that the observations of VHE photons from GRB 190114C necessitates either an additional emission mechanism at very high energies that is hidden in the synchrotron component in the LAT energy range, an acceleration mechanism that imparts energy to the particles at a rate that is faster than the electron synchrotron energy-loss rate, or revisions of the fundamental assumptions used in estimating the maximum photon energy attainable through the synchrotron process.

M. Ajello↗
NASA NTRSDate not supplied

Simulation Studies for an Urban Air Mobility Aircraft using Hardware-In-Loop Experiments

Urban Air Mobility seeks to transport passengers, deliver cargo, and provide emergency medical transportation in major metropolitan areas. This will be accomplished with distributed electric powered vertical takeoff and landing aircraft vehicles. The low specific energy of the current generation lithium-ion battery packs limit the operational range of the electric aircraft. Limited range impacts safety by reducing the amount of time available for analyzing the potential impact of errors and failures and responding to them, and for flying to an alternative landing area or returning to the base. It is therefore critical to understand the impact of flight and environmental conditions on the onboard lithium-ion battery pack’s health. With this as the motivation, the procedure for evaluating the performance of battery packs in a laboratory setting and the results obtained using this procedure on battery packs subject to power draw characteristics of a simulated flight of a NASA conceptual quadrotor aircraft model are described. The fully charged battery is allowed to discharge at specific C-rates based on the power draw profile during the experiment, and the current and voltages are recorded as a function of time. Observed results under different operating conditions and mission profiles are discussed.

UAM↗
NASA NTRS1992

Real-time obstacle avoidance using harmonic potential functions

This paper presents a new formulation of the artificial potential approach to the obstacle avoidance problem for a mobile robot or a manipulator in a known environment. Previous formulations of artificial potentials for obstacle avoidance have exhibited local minima in a cluttered environment. To build an artificial potential field, harmonic functions that completely eliminate local minima even for a cluttered environment are used. The panel method is employed to represent arbitrarily shaped obstacles and to derive the potential over the whole space. Based on this potential function, an elegant control strategy is proposed for the real-time control of a robot. The harmonic potential, the panel method, and the control strategy are tested with a bar-shaped mobile robot and a three-degree-of-freedom planar redundant manipulator.

Kim, Jin-Oh↗
NASA NTRSDate not supplied

Uncertainty Propagation in Pre-Flight Prediction of Unmanned Aerial Vehicle Separation Violation

Current forecasts on the future of aeronautics suggest an in- creasing number of unmanned aerial vehicles entering the low- altitude airspace in the next decades (FAA, 2018; Kopardekar et al., 2016). Small vehicles for package delivery as well as larger vehicles for urban air mobility will change the airspace drastically, increasing density of operations both in time, i.e. high number of take-off and landings per unit time, and in space, operating in dense urban environment. This scenario poses challenges to the current approach to air traffic control, and large efforts from academia, industry and regulatory bodies are dedicated to the development of new traffic management strategies that leverage higher computing and simulating capabilities available today. In this paper, we propose a simple look-ahead approach to predict potential minimum separation violations at the strategic level, that is before vehicles start flying, depending on the predefined 4D trajectories and uncertainty affecting the wind acting along those routes. The wind field is extracted from the NOAA North America Mesoscale Forecast System and interpolated using Gaussian process regression, while uncertainty affecting the expected cruise airspeed is propagated through error intervals. The approach allows the prediction of aircraft separation as a function of time, highlighting potential safety violations that would go undetected if uncertainty affecting the expected 4D trajectories is not considered. The paper will also discuss issues related to accuracy and scalability of the approach to multiple vehicle operations.

Trajectory Prediction↗
NASA NTRS1994

Cometary Coma Chemical Composition (C4) Mission

Cometary exploration remains of great importance to virtually all of space science. Because comets are presumed to be remnants of the early solar nebula, they are expected to provide fundamental knowledge as to the origin and development of the solar system as well as to be key to understanding of the source of volatiles and even life itself in the inner solar system. Clearly the time for a detailed study of the composition of these apparent messages from the past has come. A comet rendezvous mission, the Cometary Coma Chemical Composition (C4) Mission, is now being studied as a candidate for the new Discovery program. This mission is a highly-focussed and usefully-limited subset of the Cometary Rendezvous Asteroid Flyby (CRAF) Mission. The C4 mission will concentrate on measurements that will produce an understanding of the composition and physical makeup of a cometary nucleus. The core science goals of the C4 mission are 1) to determine the chemical, elemental, and isotopic composition of a cometary nucleus and 2) to characterize the chemical and isotopic nature of its atmosphere. A related goal is to obtain temporal information about the development of the cometary coma as a function of time and orbital position. The four short-period comets -- Tempel 1, Tempel 2, Churyumov-Gerasimenko, and Wirtanen -which all appear to have acceptable dust production rates, were identified as candidate targets. Mission opportunities have been identified beginning as early as 1998. Tempel I with a launch in 1999, however, remains the baseline comet for studies of and planning the C4 mission. The C4 mission incorporates two science instruments and two engineering instruments in the payload to obtain the desired measurements. The science instruments include an advanced version of the Cometary Ice and Dust Experiment (CIDEX), a mini-CIDEX with a sample collection system, an X-ray Fluorescence Spectrometer and a Pyrolysis-Gas Chromatograph, and a simplified version of the Neutral Gas and Ion Mass Spectrometer (NIGMS). Both of these instruments have substantial heritage as they are based on those developed for the CRAF Mission. The engineering instruments include a simplified Comet Dust Environmental Monitor (SCODEM) and a navigational Camera, NAVCAM. While neither of the instruments will be permitted to establish science requirements, it is anticipated that significant science return will be accomplished Radio science will also be included.

Carle, Glenn C.↗
DOE OSTI2019

Analysis of the Spectral Stability of the Generalized Runge–Kutta Methods Applied to Initial-Boundary-Value Problems for Equations of the Parabolic Type. II. Implicit Methods

We consider specific realizations of different implicit generalized Runge–Kutta methods as applied to the numerical integration with respect to time of initial-boundary-value problems for the second-order parabolic equations and investigate their spectral stability. It is shown that all implicit generalized Runge–Kutta methods are unconditionally spectrally stable but some of them have the conditional property of monotonicity of the numerical solution with respect to time. The functions of spectral stability of the implicit generalized Runge–Kutta methods are rational. We compare the analytic solution of the nonstationary one-dimensional problem of heat conduction with the numerical solutions of this problem obtained by different implicit generalized Runge–Kutta methods. It is shown that, in this case, the application of the one-stage Radau methods with subsequent discretization of the problem with respect to the space variable leads to the classical forward finite difference scheme (Laasonen scheme), whereas the use of the one-stage Gauss–Legendre method leads to a six-point symmetric scheme (Crank–Nicolson scheme). It is shown that diagonally implicit generalized Nørsett and Burrage methods are realized in almost the same way as the one-stage Radau and Gauss–Legendre methods but their accuracy in the time step is 10–1000 times higher. On the basis of comparison of the numerical and analytic solutions, we conclude that, in order to get practically suitable numerical solutions without any restrictions on the time step, it is reasonable to use one- and three-stage generalized Radau methods or two- and four-stage Lobatto IIIC methods. All other explicit and implicit generalized Runge–Kutta methods require certain restrictions imposed on the time step.

42 ENGINEERING↗
NASA NTRS2012

External Surface Changes Observed on the International Space Station (ISS) Through 2012

As the International Space Station (ISS) surpasses 13 years of on-orbit operation, 11 of those years continuously inhabited, external surfaces of the vehicle have shown a wide variety of visible environmental effects. Throughout, the ISS program has maintained a significant effort to routinely document the vehicle external surface condition and to monitor those changes with time. The impacts of micrometeoroids and orbital debris, surface changes from molecular contamination of various sources, and the effects of ultraviolet radiation and atomic oxygen have all been noted. The tremendous size and complexity of the ISS vehicle has yielded a wide variety of observations of interest to the spacecraft materials engineer concerning long-term, low earth orbit (LEO) space environmental effects (SEE). In addition, inadvertent materials substitutions have been identified because of these environmental effects, as well as inadequate contamination control practices likely occurring during hardware manufacture and assembly. Some of the observations from our photography are purely artifacts of the unusual lighting conditions and environments that exist in space. A compilation of ISS on-orbit photography representing all of these aspects is presented, demonstrating the various SEE and their impacts as a function of time in LEO, including interpretations of those effects.

Golden, Johnny L.↗