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Numerical Integration of Viscoelastic Models

Accurate modeling of viscoelasticity remains an important consideration for a variety of materials (e.g. polymers and inorganic glasses). As such, over the previous decades a substantial body of work has been dedicated to developing appropriate constitutive models for viscoelasticity ranging from initial considerations of linear thermoviscoelasticity to more complex non-linear formulations incorporating fictive temperatures or potential energy clocks including the use of both internal state variable(ISV) and hereditary integral representations. Nonetheless, relatively limited (in comparison to plasticity) attention has been paid to the numerical integration of such schemes. In terms of integral based formulations, Taylor et al. first considered the problem of the integration of a linear viscoelasticity model. That work focused on the integration of the hereditary integrals and demonstrated improved performance of the new scheme with a custom finite element code over an existing finite difference reference. Chambers and Becker, using a free volume based shift factor, also considered the integration of the hereditary integrals and the impact on the problem of a pressurized thick-walled cylinder and developed an adaptive scheme to bound the error. Chambers later developed three-point Gauss and composite integration schemes for the hereditary integrals and noted improved accuracy. With respect to ISV-based schemes, formulations for the non-linear Schapery model have been proposed. However, in those efforts greater attention was paid to convergence of the non-linear solution scheme than impact of numerical integration. Various authors (e.g. Holzapfel and Simo and Hughes) have also studied the use of convolution integrals with differential forms of ISVs for temperature-independent formulations. Regardless, while the "potential energy clock" (PEC) and "simplified potential energy clock"(SPEC) models have been used to study a variety of non-linear responses (e.g.), limited attention has been paid to the numerical performance. As will be discussed later, the "clock" at the center of the formulations includes temperature and complex history dependence making the numerical integration of such a model even more challenging. Thus, in the current work an initial effort towards characterizing the numerical integration of the constitutive model through simplified problems is performed. To that end, in Section 2 the theory of the model is briefly presented while the numerical integration is discussed in Section 3. Results of various studies characterizing the numerical behavior and performance are then given in Section 4. Finally, some concluding remarks and thoughts for follow on works are provided in Section 5.

36 MATERIALS SCIENCE↗

Theory and Implementation of the Spectacular Nonlinear Viscoelastic Constitutive Model

This report is a comprehensive guide to the nonlinear viscoelastic Spectacular model, which is an isotropic, thermo-rheologically simple constitutive model for glass-forming materials, such as amorphous polymers. Spectacular is intermediate in complexity to the previous PEC and SPEC models (Potential Energy Clock and Simplified Potential Energy Clock models, respectively). The model form consists of two parts: a Helmholtz free energy functional and a nonlinear material clock that controls the rate of viscoelastic relaxation. The Helmholtz free energy is derived from a series expansion about a reference state. Expressions for the stress and entropy functionals are derived from the Helmholtz free energy following the Rational Mechanics approach. The material clock depends on a simplified expression for the potential energy, which itself is a functional of the temperature and strain histories. This report describes the thermo-mechanical theory of Spectacular, the numerical methods for time-integrating the model, model verification for its implementation in LAMÉ, a user guide for its implementation in LAMÉ, and ideas for future work. A number of appendices provide supplementary mathematical details and a description of the procedure used to derive the simplified potential energy from the full expression for the potential energy. The goal of this report is create a convenient point-of-entry for engineers who wish to learn more about Spectacular, but also to serve as a reference manual for advanced users of the model.

36 MATERIALS SCIENCE↗

NLR HPC Eagle GPU Node Metrics

Ganglia node metrics and iLO (Integrated Lights Out) power data captured from six representative Eagle GPU nodes The Eagle HPC operated at NLR from 2019 through 2024. Eagle was a 2,000-node, 8-petaflop system. This dataset is a representative sample of metrics for 6 of the GPU nodes. Each GPU node contained 2 CPUs and 2 GPUs. Data provided in compressed CSV format. Ganglia and iLO Power Time Series Fields ts: Timestamp dv: Device / Node - Rack and Unit - r103u17 == r(ack)103u(nit)17 mt: Metric (only present for Ganglia) vl: Value - Value in watts for iLO power (instantaneous value at sampling time) or specified Ganglia metric below Ganglia Metrics Metric name -- Metric description -- Unit cpu_aidle -- Percent of time since boot idle CPU -- Percent cpu_idle -- Percent CPU idle -- Percent cpu_nice -- Percent CPU nice -- Percent cpu_speed -- Speed in MHz of CPU -- MHz cpu_user -- Percent CPU user -- Percent cpu_wio -- The percentage of CPU Wait I/O -- Percent gpu0_bar1_memory -- Used GPU bar1 memory -- MB gpu0_decoder_util -- GPU decoder utilization -- Percent gpu0_ecc_db_error -- Total ECC error counts for the GPU -- Number gpu0_encoder_util -- GPU encoder utilization -- Percent gpu0_fan -- Fan speed -- RPM gpu0_fb_memory -- Used GPU framebuffer memory -- MB gpu0_graphics_clock_report -- Current clock speeds for the device -- MHz gpu0_mem_total -- Memory total -- MB gpu0_mem_util -- Memory utilization -- Percent gpu0_power_usage_report -- Power usage report -- Watts gpu0_temp -- GPU 1 temperature -- Celsius gpu1_bar1_memory -- Used GPU bar1 memory -- MB gpu1_decoder_util -- GPU decoder utilization -- Percent gpu1_ecc_db_error -- Total ECC error counts for the GPU -- Number gpu1_encoder_util -- GPU encoder utilization -- Percent gpu1_fan -- Fan speed -- RPM gpu1_fb_memory -- Used GPU framebuffer memory -- MB gpu1_graphics_clock_report -- Current clock speeds for the GPU -- MHz gpu1_mem_total -- Memory total -- MB gpu1_mem_util -- Memory utilization -- MB gpu1_power_usage_report -- Power usage report -- Watts gpu1_temp -- GPU 1 temperature -- Celsius ipmi_cpu1_temp -- CPU 1 temperature -- Celsius ipmi_cpu2_temp -- CPU 2 temperature -- Celsius ipmi_inlet_ambient_temp -- Temperature measured at intake -- Celsius ipmi_vr_p1_temp -- CPU 1 voltage regulator temperature -- Celsius ipmi_vr_p2_temp -- CPU 2 voltage regulator temperature -- Celsius mem_buffers -- Amount of buffered memory -- Bytes mem_cached -- Amount of cached memory -- Bytes mem_free -- Amount of available memory -- Bytes mem_shared -- Amount of shared memory -- Bytes mem_total -- Amount of available memory -- Bytes

97 MATHEMATICS AND COMPUTING↗

NIMBUS COMMAND SUBSYSTEM

All satellites have one common requirement, known as the command facility. This is usually a real-time direct RF link from a ground transmitter through the satellite receiver and decoder to a relay or controlled circuit. The more sophisticated research and operational satellites require a command facility which will permit storing of commands to activate systems at predetermined future times when the satellite is beyond the range of the command ground station. These satellites require an accurate clock and a source of precision frequencies. In the Nimbus spacecraft, all these functions are performed by an integrated command and clock subsystem, which includes the command clock and clock-receiver modules in the spacecraft, plus the associated command ground station. This paper will describe the functions and features of these various equipment's.

GROUND SUPPORT SYSTEM↗

Numerical computer peripheral interactive device with manual controls

A computer peripheral device is disclosed which includes a joystick whose displacement from a counter position along two axes X and Y in either a plus (+) or a minus (-) direction is sensed. The displacement magnitude in either direction controls the rate of clock pulses provided by a variable frequency clock. The clock pulses from the two clocks are accumulated in two separate counters, whose contents are displayed. The contents of the counters are suppliable to a computer to update the contents of specific cells which define the position of a cursor on a display which is under computer control.

Zygielbaum, A. I.↗

Four phase logic systems

A four-phase logic system is provided which includes at least four logic networks connected in parallel between a single power line and a reference potential. A four-phase clock generator generates four distinct clock signals from a single-phase clock input at data rate. Each logic network comprises a pair of complementary metal-oxide-semiconductor integrated transistors (CMOST). Each metal-oxide-Semiconductor transistor (MOST) in the pair is responsive to a clock signal which turns the transistor on or off. In each network, there is also at least one MOST which is responsive to a logic signal. The logic transistor is connected in cascade with the pair of CMOSTs.

Petersen, H. L.↗

Common time in a four-dimensional symmetry framework

Following the ideas of Poincare, Reichenbach, and Grunbaum concerning the convention of setting up clock systems, clock systems and light propagation are analyzed within the framework of four-dimensional symmetry. It is possible to construct a new four-dimensional symmetry framework incorporating common time: observers in different inertial frames of reference use one and the same clock system, which is located in any one of the frames. Consequently, simultaneity has a meaning independent of position and independent of frame of reference. A further consequence is that the two-way speeds of light alone are isotropic in any frame. By the choice of clock system there will be one frame in which the one-way speed of light is isotropic. This frame can be arbitrarily chosen. The difference between one-way speeds and two-way speeds of light signals is considered in detail.

Hsu, J. P.↗

Variations in propagation delay times for line ten (TV) based time transfers

Variation in the propagation delay for a 30 km TV (Line Ten) radio link was evaluated for a series of 30 independent measurements. Time marks from TV Channel 5 WTTG in Washington, D.C. were simultaneously measured at the Johns Hopkins University Applied Physics Laboratory and at the United States Naval Observatory against each stations' local cesium standard clocks. Differences in the stations' cesium clocks were determined by portable cesium clock transfers. Thirty independent timing determinations were made. The root mean square deviation in the propagation delay calculated from the timing determinations was 11 ns. The variations seen in the propagation delays are believed to be caused by environmental factors and by errors in the portable clock timing measurements. In correlating the propagation delay variations with local weather conditions, only a moderate dependence on air temperature and absolute humidity was found.

Chiu, M. C.↗

Investigations of laser pumped gas cell atomic frequency standard

The performance characteristics of a rubidium gas cell atomic frequency standard might be improved by replacing the standard rubidium discharge lamp with a single mode laser diode. Aspects of the laser pumped gas cell atomic clock studied include effects due to laser intensity, laser detuning, and the choice of the particular atomic absorption line. Results indicate that the performance of the gas cell clock may be improved by judicious choice of the operating parameters of the laser diode. The laser diode also proved to be a valuable tool in investigating the operation of the conventional gas cell clock. Results concerning linewidths, the light shift effect and the effect of isotopic spin exchange in the conventional gas cell clock are reported.

Volk, C. H.↗

Fast Asynchronous Data Communication Via Fiber Optics

Transmitter and receiver devised for asynchronous digital communication via optical fiber at rates above 100 Mb/s. Transmitter converts parallel data to serial for high-speed transmission; receiver recovers clock signal and converts data back to parallel. No phase-lock loops used. New receiver design avoids over-sampling altogether. Local sampling oscillator operating nominally at clock frequency generates N clock signals of equally spaced phase, used to clock incoming data into N separate shift registers.

Bergman, Larry A.↗

Optical Communication with Semiconductor Laser Diode

Theoretical and experimental performance limits of a free-space direct detection optical communication system were studied using a semiconductor laser diode as the optical transmitter and a silicon avalanche photodiode (APD) as the receiver photodetector. Optical systems using these components are under consideration as replacements for microwave satellite communication links. Optical pulse position modulation (PPM) was chosen as the signal format. An experimental system was constructed that used an aluminum gallium arsenide semiconductor laser diode as the transmitter and a silicon avalanche photodiode photodetector. The system used Q=4 PPM signaling at a source data rate of 25 megabits per second. The PPM signal format requires regeneration of PPM slot clock and word clock waveforms in the receiver. A nearly exact computational procedure was developed to compute receiver bit error rate without using the Gaussion approximation. A transition detector slot clock recovery system using a phase lock loop was developed and implemented. A novel word clock recovery system was also developed. It was found that the results of the nearly exact computational procedure agreed well with actual measurements of receiver performance. The receiver sensitivity achieved was the closest to the quantum limit yet reported for an optical communication system of this type.

Davidson, Frederic↗

Long Duration Exposure Facility (LDEF) attitude measurements of the interplanetary dust experiment

The Long Duration Exposure Facility (LDEF) Interplanetary Dust Experiment (IDE) was unique in providing a time history of impacts of micron-sized particles on six orthogonal faces of LDEF during the first year in orbit. The value of this time resolved data depended on and was enhanced by the proper operation of some basic LDEF systems. Thus, the value of the data is greatly enhanced when the location and orientation of LDEF is known for each time of impact. The location and velocity of LDEF as a function of time can be calculated from the 'two-line elements' published by GSFC during the first year of the LDEF mission. The attitude of LDEF was passively stabilized in a gravity-gradient mode and a magnetically anchored viscous damper was used to dissipate roll, pitch, and yaw motions. Finally, the IDE used a standard LDEF Experiment Power and Data System (EPDS) to collect and store data and also to provide a crystal derived clock pulse (1 count every 13.1072 seconds) for all IDE time measurements. All that remained for the IDE was to provide a system to calibrate the clock, eliminating accumulative errors, and also verify the attitude of LDEF. The IDE used solar cells on six orthogonal faces to observe the LDEF sunrise and provide data about the LDEF attitude. The data was recorded by the EPDS about 10 times per day for the first 345 days of the LDEF mission. This data consist of the number of IDE counts since the last LDEF sunrise and the status of the six solar cells (light or dark) at the time of the last IDE count. The EPDS determined the time that data was recorded and includes, with each record, the master EPDS clock counter (1 count every 1.6384 seconds) that provided the range and resolution for time measurements. The IDE solar cells provided data for an excellent clock calibration, meeting their primary purpose, and the time resolved LDEF attitude measurements that can be gleaned from this data are presented.

Kassel, Philip C., Jr.↗

Special purpose parallel computer architecture for real-time control and simulation in robotic applications

This is a real-time robotic controller and simulator which is a MIMD-SIMD parallel architecture for interfacing with an external host computer and providing a high degree of parallelism in computations for robotic control and simulation. It includes a host processor for receiving instructions from the external host computer and for transmitting answers to the external host computer. There are a plurality of SIMD microprocessors, each SIMD processor being a SIMD parallel processor capable of exploiting fine grain parallelism and further being able to operate asynchronously to form a MIMD architecture. Each SIMD processor comprises a SIMD architecture capable of performing two matrix-vector operations in parallel while fully exploiting parallelism in each operation. There is a system bus connecting the host processor to the plurality of SIMD microprocessors and a common clock providing a continuous sequence of clock pulses. There is also a ring structure interconnecting the plurality of SIMD microprocessors and connected to the clock for providing the clock pulses to the SIMD microprocessors and for providing a path for the flow of data and instructions between the SIMD microprocessors. The host processor includes logic for controlling the RRCS by interpreting instructions sent by the external host computer, decomposing the instructions into a series of computations to be performed by the SIMD microprocessors, using the system bus to distribute associated data among the SIMD microprocessors, and initiating activity of the SIMD microprocessors to perform the computations on the data by procedure call.

Fijany, Amir↗

Timing in private digital telecommunication networks

For proper operation of today's large digital private networks, high quality synchronization must be achieved. A general telecommunication performance objective is to maintain long-term frequency accuracy of ten parts per trillion at all synchronous digital equipment in the network. Many times, however, this is not achieved in private networks. Low quality clocks, errored transmission facilities, and incorrectly designed synchronization plans are often cause for poor performance. It is shown that properly-designed private networks can operate with long term frequency averages between ten parts per trillion to ten parts per million. These performance levels can adversely impact customer applications. The most demanding applications are digital and voice band data, encrypted voice, facsimile, and video. In a typical private network operating at 0.01 parts per million, the user would experience reduced data throughput, dropped encrypted calls, unreadable facsimile pages, or interrupted video transmission dozens of times per day. The major contribution to poor private network synchronization performance is the interaction of Customer Premises Equipment (CPE) clocks and the network facilities used to distribute timing. The performance of typical CPE clocks and facilities, and their impact on customer applications, are discussed. CPE clock performance issues, along with private network architectural constraints, make synchronization planning extremely difficult. Planning is usually costly and requires specialized expertise.

Abate, J. E.↗

A real-time prediction of UTC

The reference time scale for all scientific and technologic applications on the Earth, the Universal Coordinated Time (UTC), must be as stable, reliable, and accurate as possible. With this in view the BIPM and before it the BIH, have always calculated and then disseminated UTC with a delay of about 80 days. There are three fundamental reasons for doing this: (1) It takes some weeks for data, gathered from some 200 clocks spread world-wide, to be collected and for errors to be eliminated; (2) changes in clock rates can only be measured with high precision well after the fact; and (3) the measurement noise originating in time links, in particular using Loran-C, is smoothed out only when averaging over an extended period. Until mid-1992, the ultimate stability of UTC was reached at averaging times of about 100 days and corresponded to an Allan deviation sigma(sub y)(tau) of about 1,5x10(exp -14) then compared to the best primary clock in the world, the PTB CS2. For several years now, a predicted UTC has been computed by the USNO through an extrapolation of the values as published in deferred time by the BIPM. This is made available through the USNO Series 4, through the USNO Automated Data Service, and through GPS signals. Due to the instability of UTC, the poor predictability of the available clocks, and the intentional SA degradation of GPS signals, the real-time access to this extrapolated UTC has represented the true deferred-time UTC only to within several hundreds of nanoseconds.

Thomas, Claudine↗

Anticipated uncertainty budgets of PRARETIME and T2L2 techniques as applied to ExTRAS

The Experiment on Timing Ranging and Atmospheric Soundings, ExTRAS, was conceived jointly by the European Space Agency, ESA, and the Russian Space Agency, RSA. It is also designated the 'Hydrogen-maser in Space/Meteor-3M project'. The launch of the satellite is scheduled for early 1997. The package, to be flown on board a Russian meteorological satellite includes ultra-stable frequency and time sources, namely two active and auto-tuned hydrogen masers. Communication between the on-board hydrogen masers and the ground station clocks is effected by means of a microwave link using the modified version for time transfer of the Precise Range And Range-rate Equipment, PRARETIME, technique, and an optical link which uses the Time Transfer by Laser Link, T2L2, method. Both the PRARETIME and T2L2 techniques operate in a two-directional mode, which makes it possible to carry out accurate transmissions without precise knowledge of the satellite and station positions. Due to the exceptional quality of the on-board clocks and to the high performance of the communication techniques with the satellite, satellite clock monitoring and ground clocks synchronization are anticipated to be performed with uncertainties below 0.5 ns (1 sigma). Uncertainty budgets and related comments are presented.

Thomas, Claudine↗

Monte Carlo simulations of precise timekeeping in the Milstar communication satellite system

The Milstar communications satellite system will provide secure antijam communication capabilities for DOD operations into the next century. In order to accomplish this task, the Milstar system will employ precise timekeeping on its satellites and at its ground control stations. The constellation will consist of four satellites in geosynchronous orbit, each carrying a set of four rubidium (Rb) atomic clocks. Several times a day, during normal operation, the Mission Control Element (MCE) will collect timing information from the constellation, and after several days use this information to update the time and frequency of the satellite clocks. The MCE will maintain precise time with a cesium (Cs) atomic clock, synchronized to UTC(USNO) via a GPS receiver. We have developed a Monte Carlo simulation of Milstar's space segment timekeeping. The simulation includes the effects of: uplink/downlink time transfer noise; satellite crosslink time transfer noise; satellite diurnal temperature variations; satellite and ground station atomic clock noise; and also quantization limits regarding satellite time and frequency corrections. The Monte Carlo simulation capability has proven to be an invaluable tool in assessing the performance characteristics of various timekeeping algorithms proposed for Milstar, and also in highlighting the timekeeping capabilities of the system. Here, we provide a brief overview of the basic Milstar timekeeping architecture as it is presently envisioned. We then describe the Monte Carlo simulation of space segment timekeeping, and provide examples of the simulation's efficacy in resolving timekeeping issues.

Camparo, James C.↗

Experimental Study of Split-Path Transmission Load Sharing

Split-path transmissions are promising, attractive alternatives to the common planetary transmissions for helicopters. The split-path design offers two parallel paths for transmitting torque from the engine to the rotor. Ideally, the transmitted torque is shared equally between the two load paths; however, because of manufacturing tolerances, the design must be sized to allow for other than equal load sharing. To study the effect of tolerances, experiments were conducted using the NASA split-path test gearbox. Two gearboxes, nominally identical except for manufacturing tolerances, were tested. The clocking angle was considered to be a design parameter and used to adjust the load sharing of an otherwise fixed design. The torque carried in each path was measured for a matrix of input torques and clocking angles. The data were used to determine the optimal value and a tolerance for the clocking angles such that the most heavily loaded split path carried no greater than 53 percent of an input shaft torque of 367 N-m. The range of clocking angles satisfying this condition was -0.0012 +/- 0.0007 rad for box 1 and -0.0023 +/- 0.0009 rad for box 2. This study indicates that split-path gearboxes can be used successfully in rotorcraft and can be manufactured with existing technology.

Krantz, Timothy L.↗