Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “extrapolation”

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 307 records · Page 17

The Atomization Energy of Mg4

The atomization energy of Mg4 is determined using the MP2 and CCSD(T) levels of theory. Basis set incompleteness, basis set extrapolation, and core-valence effects are discussed. Our best atomization energy, including the zero-point energy and scalar relativistic effects, is 24.6+/-1.6 kcal per mol. Our computed and extrapolated values are compared with previous results, where it is observed that our extrapolated MP2 value is good agreement with the MP2-R12 value. The CCSD(T) and MP2 core effects are found to have the opposite signs.

Bauschlicher, Charles W., Jr.↗

TiCl, TiH and TiH+ Bond Energies, a Test of a Correlation Consistent Ti Basis Set

Correlation consistent basis sets are developed for Ti atom. The polarization functions are optimized for the average of the 3F and 5F states. One series of correlation consistent basis sets is for 3d and 4s correlation, while the second series includes 3s and 3p correlation as well as 3d and 4s correlation. These basis sets are tested using the Ti 3F-5F separation and the dissociation energies of TiCl X4Phi, TiH X4Phi, and TiH(+) X3Phi. The CCSD(T) complete basis set limit values are determined by extrapolation. The Douglas Kroll approach is used to compute the scalar relativistic effect. Spin-orbit effects are taken from experiment and/or computed at the CASSCF level. The Ti 3F-5F separation is in excellent agreement with experiment, while the TiCl, TiH, and TiH(+) bond energies are in good agreement with experiment. Extrapolation with the valence basis set is consistent with other atoms, while including 3s and 3p correlation appears to make extrapolation.

Bauschlicher, Charles W., Jr.↗

Scientific Objectives of the Critical Viscosity Experiment

In microgravity, the Critical Viscosity Experiment will measure the viscosity of xenon 15 times closer to the critical point than is possible on earth. The results are expected to include the first direct observation of the predicted power-law divergence of viscosity in a pure fluid and they will test calculations of the value of the exponent associated with the divergence. The results, when combined with Zeno's decay-rate data, will strengthen the test of mode coupling theory. Without microgravity viscosity data, the Zeno test will require an extrapolation of existing 1-g viscosity data by as much as factor of 100 in reduced temperature. By necessity, the extrapolation would use an incompletely verified theory of viscosity crossover. With the microgravity viscosity data, the reliance on crossover models will be negligible allowing a more reliable extrapolation. During the past year, new theoretical calculations for the viscosity exponent finally achieved consistency with the best experimental data for pure fluids. This report gives the justification for the proposed microgravity Critical Viscosity Experiment in this new context. This report also combines for the first time the best available light scattering data with our recent viscosity data to demonstrate the current status of tests of mode coupling theory.

Berg, R. F.↗

Reduction and Analysis of Phosphor Thermography Data With the IHEAT Software Package

Detailed aeroheating information is critical to the successful design of a thermal protection system (TPS) for an aerospace vehicle. This report describes NASA Langley Research Center's (LaRC) two-color relative-intensity phosphor thermography method and the IHEAT software package which is used for the efficient data reduction and analysis of the phosphor image data. Development of theory is provided for a new weighted two-color relative-intensity fluorescence theory for quantitatively determining surface temperatures on hypersonic wind tunnel models; an improved application of the one-dimensional conduction theory for use in determining global heating mappings; and extrapolation of wind tunnel data to flight surface temperatures. The phosphor methodology at LaRC is presented including descriptions of phosphor model fabrication, test facilities and phosphor video acquisition systems. A discussion of the calibration procedures, data reduction and data analysis is given. Estimates of the total uncertainties (with a 95% confidence level) associated with the phosphor technique are shown to be approximately 8 to 10 percent in the Langley's 31-Inch Mach 10 Tunnel and 7 to 10 percent in the 20-Inch Mach 6 Tunnel. A comparison with thin-film measurements using two-inch radius hemispheres shows the phosphor data to be within 7 percent of thin-film measurements and to agree even better with predictions via a LATCH computational fluid dynamics solution (CFD). Good agreement between phosphor data and LAURA CFD computations on the forebody of a vertical takeoff/vertical lander configuration at four angles of attack is also shown. In addition, a comparison is given between Mach 6 phosphor data and laminar and turbulent solutions generated using the LAURA, GASP and LATCH CFD codes. Finally, the extrapolation method developed in this report is applied to the X-34 configuration with good agreement between the phosphor extrapolation and LAURA flight surface temperature predictions. The phosphor process outlined in the paper is believed to provide the aerothermodynamic community with a valuable capability for rapidly obtaining (4 to 5 weeks) detailed heating information needed in TPS design.

Merski, N. Ronald↗

Implications for Core Formation of the Earth from High Pressure-Temperature Au Partitioning Experiments

Siderophile elements in the Earth.s mantle are depleted relative to chondrites. This is most pronounced for the highly siderophile elements (HSEs), which are approximately 400x lower than chondrites. Also remarkable is the relative chondritic abundances of the HSEs. This signature has been interpreted as representing their sequestration into an iron-rich core during the separation of metal from silicate liquids early in the Earth's history, followed by a late addition of chondritic material. Alternative efforts to explain this trace element signature have centered on element partitioning experiments at varying pressures, temperatures, and compositions (P-T-X). However, first results from experiments conducted at 1 bar did not match the observed mantle abundances, which motivated the model described above, a "late veneer" of chondritic material deposited on the earth and mixed into the upper mantle. Alternatively, the mantle trace element signature could be the result of equilibrium partitioning between metal and silicate in the deep mantle, under P-T-X conditions which are not yet completely identified. An earlier model determined that equilibrium between metal and silicate liquids could occur at a depth of approximately 700 km, 27(plus or minus 6) GPa and approximately 2000 (plus or minus 200) C, based on an extrapolation of partitioning data for a variety of moderately siderophile elements obtained at lower pressures and temperatures. Based on Ni-Co partitioning, the magma ocean may have been as deep as 1450 km. At present, only a small range of possible P-T-X trace element partitioning conditions has been explored, necessitating large extrapolations from experimental to mantle conditions for tests of equilibrium models. Our primary objective was to reduce or remove the additional uncertainty introduced by extrapolation by testing the equilibrium core formation hypothesis at P-T-X conditions appropriate to the mantle.

Danielson, L. R.↗

Apparent-Strain Correction for Combined Thermal and Mechanical Testing

Combined thermal and mechanical testing requires that the total strain be corrected for the coefficient of thermal expansion mismatch between the strain gage and the specimen or apparent strain when the temperature varies while a mechanical load is being applied. Collecting data for an apparent strain test becomes problematic as the specimen size increases. If the test specimen cannot be placed in a variable temperature test chamber to generate apparent strain data with no mechanical loads, coupons can be used to generate the required data. The coupons, however, must have the same strain gage type, coefficient of thermal expansion, and constraints as the specimen to be useful. Obtaining apparent-strain data at temperatures lower than -320 F is challenging due to the difficulty to maintain steady-state and uniform temperatures on a given specimen. Equations to correct for apparent strain in a real-time fashion and data from apparent-strain tests for composite and metallic specimens over a temperature range from -450 F to +250 F are presented in this paper. Three approaches to extrapolate apparent-strain data from -320 F to -430 F are presented and compared to the measured apparent-strain data. The first two approaches use a subset of the apparent-strain curves between -320 F and 100 F to extrapolate to -430 F, while the third approach extrapolates the apparent-strain curve over the temperature range of -320 F to +250 F to -430 F. The first two approaches are superior to the third approach but the use of either of the first two approaches is contingent upon the degree of non-linearity of the apparent-strain curve.

Johnson, Theodore F.↗

Measurement and Characterization of Space Shuttle Solid Rocket Motor Plume Acoustics

Lift-off acoustic environments generated by the future Ares I launch vehicle are assessed by the NASA Marshall Space Flight Center (MSFC) acoustics team using several prediction tools. This acoustic environment is directly caused by the Ares I First Stage booster, powered by the five-segment Reusable Solid Rocket Motor (RSRMV). The RSRMV is a larger-thrust derivative design from the currently used Space Shuttle solid rocket motor, the Reusable Solid Rocket Motor (RSRM). Lift-off acoustics is an integral part of the composite launch vibration environment affecting the Ares launch vehicle and must be assessed to help generate hardware qualification levels and ensure structural integrity of the vehicle during launch and lift-off. Available prediction tools that use free field noise source spectrums as a starting point for generation of lift-off acoustic environments are described in the monograph NASA SP-8072: "Acoustic Loads Generated by the Propulsion System." This monograph uses a reference database for free field noise source spectrums which consist of subscale rocket motor firings, oriented in horizontal static configurations. The phrase "subscale" is appropriate, since the thrust levels of rockets in the reference database are orders of magnitude lower than the current design thrust for the Ares launch family. Thus, extrapolation is needed to extend the various reference curves to match Ares-scale acoustic levels. This extrapolation process yields a subsequent amount of uncertainty added upon the acoustic environment predictions. As the Ares launch vehicle design schedule progresses, it is important to take every opportunity to lower prediction uncertainty and subsequently increase prediction accuracy. Never before in NASA s history has plume acoustics been measured for large scale solid rocket motors. Approximately twice a year, the RSRM prime vendor, ATK Launch Systems, static fires an assembled RSRM motor in a horizontal configuration at their test facility in Utah. The remaining RSRM static firings will take place on elevated terrain, with the nozzle exit plume being mostly undeflected and the landscape allowing placement of microphones within direct line of sight to the exhaust plume. These measurements will help assess the current extrapolation process by direct comparison between subscale and full scale solid rocket motor data.

Kenny, Jeremy↗

Lessons Learned from Assimilating Altimeter Data into a Coupled General Circulation Model with the GMAO Augmented Ensemble Kalman Filter

Satellite altimetry measurements have provided global, evenly distributed observations of the ocean surface since 1993. However, the difficulties introduced by the presence of model biases and the requirement that data assimilation systems extrapolate the sea surface height (SSH) information to the subsurface in order to estimate the temperature, salinity and currents make it difficult to optimally exploit these measurements. This talk investigates the potential of the altimetry data assimilation once the biases are accounted for with an ad hoc bias estimation scheme. Either steady-state or state-dependent multivariate background-error covariances from an ensemble of model integrations are used to address the problem of extrapolating the information to the sub-surface. The GMAO ocean data assimilation system applied to an ensemble of coupled model instances using the GEOS-5 AGCM coupled to MOM4 is used in the investigation. To model the background error covariances, the system relies on a hybrid ensemble approach in which a small number of dynamically evolved model trajectories is augmented on the one hand with past instances of the state vector along each trajectory and, on the other, with a steady state ensemble of error estimates from a time series of short-term model forecasts. A state-dependent adaptive error-covariance localization and inflation algorithm controls how the SSH information is extrapolated to the sub-surface. A two-step predictor corrector approach is used to assimilate future information. Independent (not-assimilated) temperature and salinity observations from Argo floats are used to validate the assimilation. A two-step projection method in which the system first calculates a SSH increment and then projects this increment vertically onto the temperature, salt and current fields is found to be most effective in reconstructing the sub-surface information. The performance of the system in reconstructing the sub-surface fields is particularly impressive for temperature, but not as satisfactory for salt.

Keppenne, Christian↗

3D Hail Size Distribution Interpolation/Extrapolation Algorithm

Radar data can usually detect hail; however, it is difficult for present day radar to accurately discriminate between hail and rain. Local ground-based hail sensors are much better at detecting hail against a rain background, and when incorporated with radar data, provide a much better local picture of a severe rain or hail event. The previous disdrometer interpolation/ extrapolation algorithm described a method to interpolate horizontally between multiple ground sensors (a minimum of three) and extrapolate vertically. This work is a modification to that approach that generates a purely extrapolated 3D spatial distribution when using a single sensor.

Lane, John↗

Impairment of Human Ocular Tracking with Low-Dose Alcohol

Previous studies have documented adverse effects of alcohol on oculomotor performance. For example, moderate-dose alcohol (yielding a Blood Alcohol Concentration or BAC of 0.04-0.1%) has been shown to decrease steady-state pursuit gain (Fransson et al., 2010, Clin Neurophysiol, 121(12): 2134; Moser et al., 1998, J Neurol, 245(8): 542; Roche & King, 2010, Psychopharmacology, 212(1): 33), to increase saccade latency (Moser et al., 1998, J Neurol, 245(8): 542; Roche & King, 2010, Psychopharmacology, 212(1): 33), to decrease peak saccadic velocity (Fransson et al., 2010, Clin Neurophysiol, 121(12): 2134; Roche & King, 2010, Psychopharmacology, 212(1): 33), and to increase the frequency of catch-up saccades (Moser et al., 1998, J Neurol, 245(8): 542). Here, we administered two doses of ethanol on different days, yielding moderate (0.06%) and low (0.02%) levels of initial BAC, to examine the effects on human ocular tracking over BACs ranging from 0.00 to 0.07%. Twelve subjects (8 females) participated in a 5-day study. Three days of at-home measurements of daily activity and sleep were monitored, followed by two laboratory days where, ~5 hours after awakening, we administered one of the two possible single doses of alcohol. Using a previously published paradigm (Liston & Stone, 2014, J Vis, 14(14): 12), we measured oculomotor performance multiple times throughout the day with three pre-dosing baseline runs and bi-hourly post-dosing test runs until the subject recorded a BAC of 0.00% for two hours. BAC was measured before each run using an Alco-Sensor IV breathalyzer (Intoximeters, Inc., St. Louis, MO). For each of the oculometric measures, for each subject, we computed the within-subject % deviation for each test run from their baseline averaged across their three pre-dosing runs. We then averaged the data across subjects in 0.01% BAC bins. Finally, we used linear regression to compute the slope and x-intercept (threshold) of the mean binned % deviation as a function of BAC. We found that pursuit initiation was impaired at very low BAC levels, with significant (p < 0.002) linear trends in latency (+1.3%/0.01%BAC) and initial acceleration (-4.6%/0.01%BAC) with extrapolated absolute thresholds at or below 0.01% BAC. We also found that steady-state tracking was impaired showing significant (p < 0.002) linear trends in gain (- 3.8%/0.01%BAC) and catch-up saccade amplitude (+9.1%/0.01%BAC), again with extrapolated absolute thresholds around 0.01% BAC. We also found a significant (p < 0.02) increase in pursuit direction noise (+9.8%/0.01%BAC) with an extrapolated absolute threshold below 0.01% BAC. Many aspects of ocular tracking are impaired in a dose-dependent manner beginning at a BAC level around 0.01%, with significant effects at levels lower than previously reported and up to 8-times lower than the legal limit for driving in most states.

human performance↗

Experimental Considerations for Estimating Degradation in PV Modules

Carefully controlled laboratory experiments and measurements can enable the determination of acceleration factors suitable for extrapolation to durability and performance of a fielded PV module. Ideally, a single mechanism can be identified with appropriate acceleration factors for extrapolation to the field. However, even with a single mechanism, the inherent uncertainty in these factors leads to uncertainty in the extrapolation which is greater the higher the acceleration factor. This course will explain how because of the wide range of acceleration factors for a given degradation mode, utilizing acceleration factors greater than about 10x will typically lead to unacceptable uncertainty in the results. Therefore, if even just a rank ordering of materials is desired, acceleration factors must be minimized which requires a good general understanding of the scale of the different acceleration factors for the degradation mode of interest. In this tutorial we will discuss what the different purposes are for many of the accelerated stress tests used today. E.g., what is a qualification test, a highly accelerated stress test, a rank ordering test, or a service life prediction test. We will discuss how one can understand the relationship between test results and expected field performance. A single accelerated stress test condition cannot duplicate outdoor exposure for all possible degradation pathways; therefore, one must use targeted evaluation of material properties at different stress levels to determine the relevant acceleration factors and fit it to a model. We will also discuss how to interpret the results of experiments understanding what is relevant/not relevant, or not e valuated in a test. There are many common error people make in their test interpretations because they push the stress levels to be too harsh. This creates biases and can mask the relevant failure modes and mechanisms or will erroneously lead one to over design materials against things that aren't relevant. Several case studies will be presented to illustrate appropriate interpretation of accelerated stress testing results.

degradation↗

The "PVLib" of Degradation: PVDeg

The Photovoltaic (PV) industry constantly aims for lower costs through higher-efficiency cells, improved module designs, and improvements in durability. This leads to the use of new materials, designs, and manufacturing processes, and not always with a sufficient amount of durability testing. To help drive down costs there is a desire to create modules that will last for up to 50 years of service life. To accomplish this, every degradation mode and mechanism must be identified and either eliminated or otherwise mitigated. This involves the extrapolation of laboratory results to the field conditions. There is a need to organize the existing degradation data into an accessible format and to provide industry relevant tools for extrapolation from laboratory to field conditions. While the basic equations used to model degradation are sometimes very simple, the full analysis involves calculations are cumbersome but ubiquitous for many degradation processes. A simplified, modeling framework to accomplish these repetitive processes will facilitate the analysis to help researchers keep up with the rapid pace of technological changes. In this talk, we will describe our progress creating the open-source tool PVDeg. This tool can be used to search for and analyze degradation information and extrapolate PV module performance and durability to field exposure. PVDeg simplifies many of the common foundational computational operations for obtaining meteorological data and using it to generate a model of the PV deployment. This prediction tool repository also contains various degradation models as well as a library of material parameters suitable for estimating the durability assessment of materials and components. We use an integration pipeline approach that allows us to leverage weather data from the National Solar Radiation Database, and other weather sources, to perform geospatial degradation analysis in the US and worldwide. We hope to become a repository that can be used for weathering and degradation analysis for various applications beyond the PV industry. During the talk, we will provide the PVPMC attendees the opportunity to interact with the tool via a Google Collab tutorial they can run on their phones or laptops.

durability↗

Computing the Critical Temperature of the Affine-Transformed $D=3$ Ising Model Using Masked Autoregressive Flow

The simple Ising model provides a rich environment to build and study lattice field theories. As part of an ongoing project to construct a conformal field theory (CFT) on an arbitrarily curved manifold, in this work we develop methods to measure the critical temperature $β_c$ of the affine-transformed Ising model on the face-centered cubic (FCC) lattice. The main challenge in this endeavor is finding a computationally efficient and accurate method of interpolating and extrapolating Monte Carlo observables with respect to coupling coefficients and temperature. Herein, we compare two such methods. A traditional statistical approach uses the multiple histogram (MH) method, while a newer machine learning approach uses a masked autoregressive flow (MAF) to estimate the underlying probability density function of a set of observables. While the MH method is specifically designed to interpolate and extrapolate Monte Carlo observables, we find that MAF is a viable alternative for measuring $β_c$ with a computational cost that scales more favorably. Furthermore, we comment on additional advantages of MAF relevant to our work, such as extrapolating in system volume.

Svenson, Kai [Texas U.]↗

A machine-learning-aided data recovery approach for predicting multi-material thermal behaviors in advanced test reactor capsules

Instrumented experiments conducted at test reactors are essential to the deployment of new advanced reactor systems. Designing new experiments and generating data on specific reactor conditions require significant investments in terms of both time and cost. Finite element analysis software can be used to create high-fidelity models of experiment environments in order to support the actual experiments, but computation time remains a concern in terms of applying outcomes to real-time usage of data (e.g., a digital twin [DT]). Here, the present research proposes a machine-learning (ML) aided approach to making temperature and displacement predictions based on the thickness of the outer gas gap on the experimental capsule used for in-pile demonstration of a novel new thermal conductivity probe in the Advanced Test Reactor (ATR). This capsule consisted of U10Zr fuel, a rodlet, sodium, and inner and outer capsules. Gas gaps existed between the fuel and the rodlet, and between the inner and the outer capsule. The learning data pertained to an experimental capsule's radial distributions of temperature and displacement, as obtained based on Abaqus and the physical features. For the first step of ML sequence, the temperature was predicted using three positional parameters. Next, the displacement was predicted using seven additional parameters. Each physical feature was normalized in order to be both nondimensional and standardized. The temperature and displacement predictions showed good agreement with the simulation results in all cases involving interpolation and extrapolation. Furthermore, data similarity enhancement increased the similarity between the training and the target data, thereby increasing the predictive accuracy of the ML models. In certain extrapolation cases involving limited original ML model accuracy, data similarity enhancement and data recovery was able to somewhat improve this accuracy.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

A continuum damage mechanics (CDM) based Wilshire model for creep deformation, damage, and rupture prediction

In this report, a new constitutive model is derived that combines the Wilshire equations with continuum damage mechanics (CDM) to enable the long-term prediction of creep deformation, damage, and rupture. The Wilshire equations have been demonstrated to accurately extrapolate the stress-rupture, minimum-creep-strain-rate, and time-to-strain of various alloys across decade of life. Recently, the time-to-creep-strain equation has been rearranged to predict creep deformation curves; however, the resulting equation is difficult to calibrate and does not track damage. The CDM-based Sinh constitutive model accurately predicts creep deformation, damage, and stress-rupture for a variety of alloys; however, it lacks an explicit description of stress and temperature co-dependence which limits interpolation and extrapolation ability. In this study, the Wilshire and the CDM-based Sinh equations are combined to create the “WCS” model. The WCS model combines the best features of each model while eliminating their deficiencies. Experimental data for alloy P91 is gathered and the WCS model is calibrated to the data. The WCS model accurately predicts the stress rupture, minimum-creep-strain-rate, creep deformation, and damage of alloy P91 across the experimental stress and temperature range as well as consistency in parametric simulations.

36 MATERIALS SCIENCE↗

Voltage Calculations in Secondary Distribution Networks via Physics-Inspired Neural Network Using Smart Meter Data

The increasing penetration of distributed energy resources (DERs) leads to voltage issues across distribution networks, necessitating voltage calculations by utilities. Electric model-free voltage calculation offers an enticing solution. However, most researches mainly focus on primary distribution networks ignoring secondary distribution networks and commonly overlook extreme voltage case calculations, which require the model’s extrapolation abilities. Here, in addressing the gaps, this paper presents a customized physics-inspired neural network (PINN) model, the structure of which is inspired by the derived coupled power flow model of primary-secondary distribution networks. To ensure precision and rapid convergence, a crafted training framework for the PINN model is proposed. The PINN’s “structure-mimetic” design enables superior extrapolation for unseen scenarios and enhances physical information awareness. We demonstrate this through two applications: hosting capacity analysis and customer-transformer connectivity. The effectiveness and advantages of the proposed PINN model are validated on two public testing systems and one utility distribution feeder model.

Distribution network↗

Toward Complete Characterization: Prospects for Directly Imaging Transiting Exoplanets

High-contrast direct imaging of exoplanets can provide many important observables, including measurements of the orbit, spectra that probe the lower layers of the atmosphere, and phase variations of the planet, but cannot directly measure planet radius or mass. Our future understanding of directly imaged exoplanets will therefore rely on extrapolated models of planetary atmospheres and bulk composition, which need robust calibration. We estimate the population of extrasolar planets that could serve as calibrators for these models. Critically, this population of “standard planets” must be accessible to both direct imaging and the transit method, allowing for radius measurement. We show that the search volume of a direct imaging mission eventually overcomes the transit probability falloff with semimajor axis, so that as long as cold planets are not exceedingly rare, the population of transiting planets and directly imageable planets overlaps. Using current extrapolations of Kepler occurrence rates, we estimate that ∼8 standard planets could be characterized shortward of 800 nm with an ambitious future direct imaging mission like LUVOIR-A and several dozen could be detected at the V band. We show the design space that would expand the sample size and discuss the extent to which ground- and space-based surveys could detect this small but crucial population of planets.

79 ASTRONOMY AND ASTROPHYSICS↗

A New Martian Crater Chronology: Implications for Jezero Crater

Crater chronologies are a fundamental tool to assess the relative and absolute ages of planetary surfaces when direct radiometric dating is not available. Martian crater chronologies are derived from lunar crater spatial densities on terrains with known radiometric ages, and thus they critically depend on the Moon-to-Mars extrapolation. This extrapolation requires knowledge of the time evolution of the impact flux, including contributions from various impactor populations, factors that are not trivially connected to the dynamical evolution of the early Solar System. In this paper, we will present a new Martian crater chronology based on current dynamical models, and consider the main sources of uncertainties (e.g., impactor size–frequency distribution; dynamical models with late and early instabilities, etc.). The resulting “envelope” of Martian crater chronologies significantly differs from previous chronologies. The new Martian crater chronology is discussed using two interesting applications: Jezero crater’s dark terrain (relevant to the NASA Mars 2020 mission) and the southern heavily cratered highlands. Our results indicate that Jezero’s dark terrain may have formed ∼3.1 Ga, i.e., up to 0.5 Gyr older than previously thought. In addition, available crater chronologies (including our own) overestimate the number of craters larger than 150 km on the southern highlands, suggesting either that large craters have been efficiently erased over Martian history or that dynamical models need further refinement. Further, our chronology constrains the age of Isidis basin to be 4.05–4.2 Ga and that of the Borealis basin to be 4.35–4.40 Ga; these are predictions that can be tested with future sample and return missions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗