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DOE OSTI2026

A finite viscoelastic constitutive model for low to high strain rate response of elastomers with application of strain rate-induced glass transition

Amorphous elastomers exhibit significant rate-stiffening and unique viscous flow characteristics across a wide range of strain rates, often undergoing glass transition above a strain rate threshold. We have developed a thermodynamically-consistent and micromechanically-inspired constitutive model for soft elastomeric materials to capture the rate-dependent stress-strain behavior and hysteresis when subjected to low to high strain rates. Here, our proposed constitutive model encapsulates the viscous flow of materials through molecular motion at low strain rates and local rearrangement and alignment of the molecules trying to overcome the intermolecular resistance at high strain rates, essentially covering the glass transition. We applied our constitutive model to uniaxial compression experiments performed at low and high strain rates for polyborosiloxane (PBS) to identify the material parameters, and subsequently, performed numerical simulations of single and multi-cycle compression, stress relaxation, and small amplitude oscillatory tension-compression. Our analyses indicate that the model predicts higher total energy dissipation with increasing strain rate; however, dissipation associated with molecular relaxation decreases (forming a cusp) because, beyond a crossover strain rate, intermolecular rearrangement and alignment become dominant, which is consistent with the onset of the glass transition. For cyclic loading-unloading, we observed that dissipation over a cycle remains constant at low strain rates but decreases non-monotonically at high strain rates before becoming constant, with the peak stress over the cycle becoming higher, which can be interpreted as more loading being carried elastically by the polymer network as the intermolecular rearrangement process occurs. Additionally, our model was able to predict the qualitative nature of the storage modulus and loss modulus in the limit of small strain over a wide range of frequency sweeps.

36 MATERIALS SCIENCE↗

NASA NTRS2005

Rate of Iron Transfer Through the Horse Spleen Ferritin Shell Determined by the Rate of Formation of Prussian Blue and Fe-desferrioxamine Within the Ferritin Cavity

Iron (2+ and 3+) is believed to transfer through the three-fold channels in the ferritin shell during iron deposition and release in animal ferritins. However, the rate of iron transit in and out through these channels has not been reported. The recent synthesis of [Fe(CN)(sub 6)](3-), Prussian Blue (PB) and desferrioxamine (DES) all trapped within the horse spleen ferritin (HoSF) interior makes these measurements feasible. We report the rate of Fe(2+) penetrating into the ferritin interior by adding external Fe(2+) to [Fe(CN)(sub 6)](3-) encapsulated in the HoSF interior and measuring the rate of formation of the resulting encapsulated PB. The rate at which Fe(2+) reacts with [Fe(CN)(sub 6)](3-) in the HoSF interior is much slower than the formation of free PB in solution and is proceeded by a lag period. We assume this lag period and the difference in rate represent the transfer of Fe(2+) through the HoSF protein shell. The calculated diffusion coefficient, D approx. 5.8 x 10(exp -20) square meters per second corresponds to the measured lag time of 10-20 s before PB forms within the HoSF interior. The activation energy for Fe(2+) transfer from the outside solution through the protein shell was determined to be 52.9 kJ/mol by conducting the reactions at 10 to approximately 40 C. The reaction of Fe(3+) with encapsulated [Fe(CN)6](4-) also readily forms PB in the HoSF interior, but the rate is faster than the corresponding Fe(2+) reaction. The rate for Fe(3+) transfer through the ferritin shell was confirmed by measuring the rate of the formation of Fe-DES inside HoSF and an activation energy of 58.4 kJ/mol was determined. An attempt was made to determine the rate of iron (2+ and 3+) transit out from the ferritin interior by adding excess bipyridine or DES to PB trapped within the HoSF interior. However, the reactions are slow and occur at almost identical rates for free and HoSF-encapsulated PB, indicating that the transfer of iron from the interior through the protein shell is faster than the rate-limiting step of PB dissociation. The method described in this work presents a novel way of determining the rate of transfer of iron and possibly other small molecules through the ferritin shell.

Zhang, Bo↗

NASA NTRS1994

Advantages of estimating rate corrections during dynamic propagation of spacecraft rates: Applications to real-time attitude determination of SAMPEX

This paper describes real-time attitude determination results for the Solar, Anomalous, and Magnetospheric Particle Explorer (SAMPEX), a gyroless spacecraft, using a Kalman filter/Euler equation approach denoted the real-time sequential filter (RTSF). The RTSF is an extended Kalman filter whose state vector includes the attitude quaternion and corrections to the rates, which are modeled as Markov processes with small time constants. The rate corrections impart a significant robustness to the RTSF against errors in modeling the environmental and control torques, as well as errors in the initial attitude and rates, while maintaining a small state vector. SAMPLEX flight data from various mission phases are used to demonstrate the robustness of the RTSF against a priori attitude and rate errors of up to 90 deg and 0.5 deg/sec, respectively, as well as a sensitivity of 0.0003 deg/sec in estimating rate corrections in torque computations. In contrast, it is shown that the RTSF attitude estimates without the rate corrections can degrade rapidly. RTSF advantages over single-frame attitude determination algorithms are also demonstrated through (1) substantial improvements in attitude solutions during sun-magnetic field coalignment and (2) magnetic-field-only attitude and rate estimation during the spacecraft's sun-acquisition mode. A robust magnetometer-only attitude-and-rate determination method is also developed to provide for the contingency when both sun data as well as a priori knowledge of the spacecraft state are unavailable. This method includes a deterministic algorithm used to initialize the RTSF with coarse estimates of the spacecraft attitude and rates. The combined algorithm has been found effective, yielding accuracies of 1.5 deg in attitude and 0.01 deg/sec in the rates and convergence times as little as 400 sec.

Challa, M. S.↗

NASA NTRS1993

On the variation of the sun's X ray background flux and its relation to the sun's flaring rate, energetic event rate, and the solar cycle

Daily averages of the sun's X-ray background flux as measured by the GOES satellite are combined to yield monthly means and 'smoothed' monthly means (12-month moving averages) for the interval January 1986 through May 1992 (minimum rise, maximum, and initial decline of solar cycle 22). These averages are then compared directly to the sun's optical flaring rate, energetic event rate, and the usual markers of the solar cycle (e.g., sunspot number, total corrected sunspot area, and 10.7-cm solar radio flux, number of groups, and number of spots). The results of this analysis support previous findings that there exists a remarkably close positive relationship between the optical flaring rate and the X-ray background flux rate (the independent variable), and that the X-ray background flux rate can be used as a proxy for the solar cycle. Additionally, this study has found that a strong positive relationship exists between the energetic event rate and the X-ray background flux rate (the independent variable), and that the lag between the maxima of the rates of optical flaring and X-ray background flux reported for cycle 21 did not recur for cycle 22.

Wilson, Robert M.↗

NASA NTRS1994

A comparison of eastern North American seismic strain-rates to glacial rebound strain-rates

Glacial rebound strain-rates computed using a simple Laurentide glacial loading model are of the order of 10(exp -9) per year within the region of glaciation and extending several hundred kilometers beyond. The horizontal strain-rates receive approximately equal contributions from horizontal and vertical velocities, a consequence of the spherical geometry adopted for the Earth model. In the eastern United States and southeastern Canada the computed strain-rates are 1-3 orders of magnitude greater than an estimate of the average seismic strain-rate (Anderson, 1986) and approximately 1 order of magnitude greater than predicted erosional strain-rates. The predicted glacial rebound strain-rates are not, in general, oriented in such a way as to augment the observed state of deviatoric stress, possibly explaining why the seismic strain-rates are much smaller than the glacial rebound strain-rates. An exception to this may be seismically active regions in the St. Lawrence valley.

James, Thomas S.↗

NASA NTRS1989

Estimation of the rate of volcanism on Venus from reaction rate measurements

Laboratory rate data for the reaction between SO2 and calcite to form anhydrite are presented. If this reaction rate represents the SO2 reaction rate on Venus, then all SO2 in the Venusian atmosphere will disappear in 1.9 Myr unless volcanism replenishes the lost SO2. The required volcanism rate, which depends on the sulfur content of the erupted material, is in the range 0.4-11 cu km of magma erupted per year. The Venus surface composition at the Venera 13, 14, and Vega 2 landing sites implies a volcanism rate of about 1 cu km/yr. This geochemically estimated rate can be used to determine if either (or neither) of two discordant geophysically estimated rates is correct. It also suggests that Venus may be less volcanically active than the earth.

Fegley, Bruce, Jr.↗

NASA NTRS1993

Rain-rate data base development and rain-rate climate analysis

The single-year rain-rate distribution data available within the archives of Consultative Committee for International Radio (CCIR) Study Group 5 were compiled into a data base for use in rain-rate climate modeling and for the preparation of predictions of attenuation statistics. The four year set of tip-time sequences provided by J. Goldhirsh for locations near Wallops Island were processed to compile monthly and annual distributions of rain rate and of event durations for intervals above and below preset thresholds. A four-year data set of tropical rain-rate tip-time sequences were acquired from the NASA TRMM program for 30 gauges near Darwin, Australia. They were also processed for inclusion in the CCIR data base and the expanded data base for monthly observations at the University of Oklahoma. The empirical rain-rate distributions (edfs) accepted for inclusion in the CCIR data base were used to estimate parameters for several rain-rate distribution models: the lognormal model, the Crane two-component model, and the three parameter model proposed by Moupfuma. The intent of this segment of the study is to obtain a limited set of parameters that can be mapped globally for use in rain attenuation predictions. If the form of the distribution can be established, then perhaps available climatological data can be used to estimate the parameters rather than requiring years of rain-rate observations to set the parameters. The two-component model provided the best fit to the Wallops Island data but the Moupfuma model provided the best fit to the Darwin data.

Crane, Robert K.↗

DOE OSTI2025

SENSEI at SNOLAB: Single-Electron Event Rate and Implications for Dark Matter

We present results from data acquired by the SENSEI experiment at SNOLAB after a major upgrade in May 2023, which includes deploying 16 new sensors and replacing the copper trays that house the CCDs with a new light-tight design. We observe a single-electron event rate of (1.39±0.11)×10^{-5} e^{-}/pix/day, corresponding to (39.8±3.1) e^{-}/gram/day. This is an order-of-magnitude improvement compared to the previous lowest single-electron rate in a silicon detector and the lowest for any photon detector in the wavelength range between near-infrared and ultraviolet. We use these data to obtain a 90% confidence level upper bound of 1.53×10^{-5} e^{-}/pix/day and to set constraints on sub-GeV dark matter candidates that produce single-electron events. We hypothesize that the data taken at SNOLAB in the previous run, with an older tray design for the sensors, contained a larger rate of single-electron events due to light leaks. We test this hypothesis using data from the SENSEI detector located in the MINOS cavern at Fermilab.

dark matter↗

NASA NTRS1979

Asteroid rotation. I - Tabulation and analysis of rates, pole positions and shapes. II - A theory for the collisional evolution of rotation rates

Rotation properties and shape data for 182 asteroids are compiled and analyzed, and a collisional model for the evolution of the mean rotation rate of asteroids is proposed. Tabulations of asteroid rotation rates, taxonomic types, pole positions, sizes and shapes and plots of rotation frequency and light curve amplitude against size indicate that asteroid rotational frequency increases with decreasing size for all asteroids except those of the C or S classes. Light curve data also indicate that small asteroids are more irregular in shape than large asteroids. The dispersion in rotation rates observed is well represented by a three dimensional Maxwellian distribution, suggestive of collisional encounters between asteroids. In the proposed model, the rotation rate is found to tend toward an equilibrium value, at which spin-up due to infrequent, large collisions is balanced by a drag due to the larger number of small collisions. The lower mean rotation rate of C-type asteroids is attributed to a lower means density of that class, and the increase in rotation rate with decreasing size is interpreted as indicative of a substantial population of strong asteroids.

Harris, A. W.↗

NASA NTRS1988

Controlled-strain rate tests at very low strain rates of 2618 aluminum at 200 C

Constant strain rate tests and constant load creep tests were performed on 2618 aluminum at 200 C. The strain rates used in the constant strain rate tests were 10 to the minus 6, 10 to the minus 7, 10 to the minum 8, and 10 to the minus 9/sec. Due to the fact that the strain rates in both tests were comparable to each other, the similarities between them can therefore be studied. It was concluded that metals are essentially rate sensitive at elevated temperatures. The traditional definition of creep and plasticity used in the classical creep analysis is actually a reflection of the material behavior under different loading conditions. A constitutive equation based on the test data under one loading condition should work well for other loading conditions as long as the strain rates are in the same range as those under which the material constants are determined.

Ding, J. L.↗

NASA NTRS1995

Rate constants and temperature dependences for the reactions of hydroxyl radical with several halogenated methanes, ethanes, and propanes by relative rate measurements

Rate constants of 15 OH reactions with halogen-substituted alkanes, C1 to C3, were studied using a relative rate technique in the temperature range 283-403 K. Compounds studied were CHF2Cl (22), CHF2Br (22B), CH3F (41), CH2F2 (32), CHF3 (23), CHClFCCl2F (122a), CHCl2CF3 (123), CHClFCF3 (124), CH3CF3 (143a), CH3CH2F (161), CF3CHFCF3 (227ea), CF3CH2CF3 (236fa), CF3CHFCHF2 (236ea), and CHF2CF2CH2F (245ca). Using CH4, CH3CCl3, CF3CF2H, and C2H6 as primary reference standards (JPL 92-20 rate constants), absolute rate constants are derived. Results are in good agreement with previous experimental results for six of the compounds studied, including CHF2Cl, CHF2Br, CH2F2, CH3CF3, CHFClCFCl2, and CF3CHFCF3. For the remainder the relative rate constants are lower than those derived from experiments in which OH loss was used to measure the reaction rate. Comparisons of the derived Arrhenius A factors with previous literature transition-state calculations show order of magnitude agreement in most cases. However, the experimental A factors show a much closer proportionality to the number of H atoms in the molecule than is evident from the transition state calculations. For most of the compounds studied, an A factor of (8 +/- 3)E-13 cm(exp 3)/(molecule s) per C-H bond is observed. A new measurement of the ratio k(CH3CCl3)/k(CH4) is reported that is in good agreement with previous data.

Hsu, K.-J.↗

NASA NTRS1992

Dose rate, dose-equivalent rate, and quality factor in SLS-1

A tissue-equivalent proportional counter (TEPC) sensitive to the lineal energy range of 0.26-300 keV micrometer-1 was flown on STS-40 (39 degrees x 278 km x 296 km) inside the Spacelab. This instrument was previously flown on STS-31 but was modified to provide a finer resolution at lower lineal energies to better map the South Atlantic Anomaly (SAA) protons. The instrument was turned on 6 June 1991, and operated for 7470 min (124.5 h). The flight duration was characterized by a very large number of X-ray solar flares and enhanced magnetic field fluctuations; however, no significant dose from the solar particles was measured at the location of this instrument. The flight data can be separated into trapped and galactic cosmic radiation parts. The dose rate, dose-equivalent rate and quality factor for trapped radiation were 4.21 +/- 0.03 mrad day-1, 7.72 +/- 0.05 mrem day-1, and 1.83 +/- 0.1, respectively. The dose rate, dose-equivalent rate, and quality factor for galactic cosmic radiation were 5.34 +/- 0.03 mrad day-1, 14.63 +/- 0.06 mrem day-1, and 2.74 +/- 0.1, respectively. The overall quality factor for the flight was 2.38. The dose from the GCR is higher than from SAA protons because of the high inclination and low altitude of this flight. The AP8MAX model of the trapped radiation gives a dose rate of 2.43 mrad day-1 and a quality factor of 1.77. The CREME solar maximum model of galactic cosmic radiation gives a dose rate of 2.54 mrad day-1 and a quality factor of 2.91. Thus the AP8MAX model underestimates the dose by a factor of 1.8 whereas the CREME model leads to an underestimation of the dose by a factor of 2. A comparison of the LET spectra using the AP8MAX model and galactic cosmic radiation transport codes shows only a qualitative agreement.

NASA Discipline Number 00-00↗

NASA NTRS1984

Calculation of vaporization rates assuming various rate determining steps: Application to the resistojet

The various steps that could control the vaporization rate of a material are discussed. These steps include the actual vaporization, flow rate of matrix gas, chemical reaction, gas diffusion, and solid state diffusion. The applicable equations have been collected from diverse appropriate sources, and their use is explained. Rate equations are derived for conditions where more than one step is rate controlling. Calculations are made for two model materials: rhenium which vaporizes congruently, and tantalum carbide which vaporizes incongruently. The case of vaporization under thermal gradient conditions is also treated. The existence of a thermal gradient in the resistojet means that the vaporization rate of a material may be only one thousandth of that predicted under isothermal conditions. Calculations show that rhenium might have a 100,000 hr lifetime at temperature in a 2500 C resistojet. Tantalum carbide would have a life of only 660 sec under similar conditions.

May, C. E.↗

NASA NTRS1984

A Very Efficient Transfer Function Bounding Technique on Bit Error Rate for Viterbi Decoded, Rate 1/N Convolutional Codes

For rate 1/N convolutional codes, a recursive algorithm for finding the transfer function bound on bit error rate (BER) at the output of a Viterbi decoder is described. This technique is very fast and requires very little storage since all the unnecessary operations are eliminated. Using this technique, we find and plot bounds on the BER performance of known codes of rate 1/2 with K 18, rate 1/3 with K 14. When more than one reported code with the same parameter is known, we select the code that minimizes the required signal to noise ratio for a desired bit error rate of 0.000001. This criterion of determining goodness of a code had previously been found to be more useful than the maximum free distance criterion and was used in the code search procedures of very short constraint length codes. This very efficient technique can also be used for searches of longer constraint length codes.

Lee, P. J.↗

NASA NTRS1991

A comparison between computer-controlled and set work rate exercise based on target heart rate

Two methods are compared for observing the heart rate (HR), metabolic equivalents, and time in target HR zone (defined as the target HR + or - 5 bpm) during 20 min of exercise at a prescribed intensity of the maximum working capacity. In one method, called set-work rate exercise, the information from a graded exercise test is used to select a target HR and to calculate a corresponding constant work rate that should induce the desired HR. In the other method, the work rate is controlled by a computer algorithm to achieve and maintain a prescribed target HR. It is shown that computer-controlled exercise is an effective alternative to the traditional set work rate exercise, particularly when tight control of cardiovascular responses is necessary.

Pratt, Wanda M.↗

NASA NTRS1992

Reaction rate and energy-loss rate for photopair production by relativistic nuclei

The process of e(+/-) pair production by relativistic nuclei on ambient photons is considered. The process is important for cosmic-ray nuclei in interstellar and intergalactic space as well as in galactic and extragalactic compact objects. The rate of this process is given by an integral of the cross section over the photon angular and energy distribution. In the case of isotropic photons, the angular integration is performed to provide an expression for the rate at given photon energy in the nucleus rest frame. The total rate then becomes a single integral of that rate over the photon energy distribution. Formulas are also given for the fractional energy loss of a relativistic nucleus colliding with a photon of a given energy in the rest frame. The nucleus energy-loss rate is integrated over the photon angular distribution in the case of isotropic photons, and simple fits are provided.

Chodorowski, Michal J.↗

DOE OSTI2025

Modeling the differential rate for signal interactions in coincidence with noise fluctuations or large rate backgrounds

The characteristic energy of a relic dark matter interaction with a detector scales strongly with the putative dark matter mass. Consequently, experimental search sensitivity at the lightest masses will always come from interactions whose size is similar to noise fluctuations and low energy backgrounds in the detector. In this paper, we correctly calculate the net change in measured differential event rate due to low rate signal interactions that overlap in time with noise and backgrounds, accounting for both periods of time when the signal is coincident with noise/backgrounds and for the decreased amount of time in which only noise/backgrounds occur and we show that the introduction of random simulated signal events into the continuous raw data stream (a form of “salting”) provides a correct and practical implementation to estimate this net linear signal sensitivity. Unfortunately this does not apply to the situation with non negligible pileups as we show through explicit examples. Consequently, this exclusion technique should be complemented by less sensitive techniques that can separately exclude large rate, high pileup signal parameter space. An analysis threshold above the Gaussian-like noise component of the measured differential rate spectrum should also likely produce conservative limits. Though previous light mass dark matter searches did not correctly account for decreased background only live time effects in their signal sensitivity, conservative analysis choices likely protected their published limits from being nonconservative.

Li, Xinran↗

NASA NTRS1971

Saturn component failure rate and failure rate modifiers

Failure mode frequency ratios, environmental adjustment factors, and failure rates for mechanical and electromechanical component families are presented. The failure rates and failure rate modifiers resulted from a series of studies whose purpose was to provide design, tests, reliability, and systems engineers with accurate, up-to-date failure rate information. The results of the studies were achieved through an extensive engineering analysis of the Saturn Program test data and Unsatisfactory Condition Reports (UCR's) and the application of mathematical techniques developed for the studies.

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