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NASA NTRS2016

Cryovolcanic Emplacement of Domes on Europa

Here we explore the hypothesis that certain domes on Europa may have been produced by the extrusion of viscous cryolavas. A new mathematical method for the emplacement and relaxation of viscous lava domes is presented and applied to putative cryovolcanic domes on Europa. A similarity solution approach is applied to the governing equation for fluid flow in a cylindrical geometry, and dome relaxation is explored assuming a volume of cryolava has been rapidly emplaced onto the surface. Nonphysical sin- gularities inherent in previous models for dome relaxation have been eliminated, and cryolava cooling is represented by a time-variable viscosity. We find that at the onset of relaxation, bulk kinematic viscosities may lie in the range between 10(exp 3) and 10(exp 6) sq m/s, while the actual fluid lava viscosity may be much lower. Plausible relaxation times to form the domes, which are linked to bulk cryolava rheology, are found to range from 3.6 days to 7.5 years. We find that cooling of the cryolava, while dominated by conduction through an icy skin, should not prevent fluids from advancing and relaxing to form domes within the timescales considered. Determining the range of emplacement conditions for putative cryolava domes will shed light on Europa's resurfacing history. In addition, the rheologies and compositions of erupted cryolavas have implications for subsurface cryomagma ascent and local surface stress conditions on Europa.

volcanism↗

NASA NTRSDate not supplied

In Vitro Selections with RNAs of Variable Length Converge on a Robust Catalytic Core

In vitro selection is a powerful tool that can be used to understand basic principles of molecular evolution. We used in vitro selection to understand how changes in length and the accumulation of point mutations enable the evolution of functional RNAs. Using RNA populations of various lengths, we performed a series of in vitro experiments to select for ribozymes with RNA ligase activity. We identified a core ribozyme structure that was robust to changes in RNA length, high levels of mutagenesis, and increased selection pressure. Elaboration on this core structure resulted in improved activity which we show is consistent with a larger trend among functional RNAs in which increasing motif size can lead to an exponential improvement in fitness. We conclude that elaboration on conserved core structures is a preferred mechanism in RNA evolution. This conclusion, drawn from selections of RNAs from random sequences, is consistent with proposed evolutionary histories of specific biological RNAs. More generally, our results indicate that modern RNA structures can be used to infer ancestral structures. Our observations also suggest a mechanism by which structural outcomes of early RNA evolution would be largely reproducible even though RNA fitness landscapes consist of disconnected clusters of functional sequences.

In vitro evolution↗

DOE OSTI2022

Occurrences of REE and CM in volcanic ash beds associated with coals in SW Wyoming & NW Colorado

Rare earth elements (REEs) and critical minerals (CMs) are vital components in the nation’s economy, national security, and the further strengthening of our renewable energy capabilities and infrastructure. Recent work has revealed more insight into previously unknown modes of occurrence for REEs, particularly in coal seams and adjacent noncoal sediments, but many data gaps persist. Temporal relationships between coal beds and adjacent tonstiens, ash beds, or other partings are widely recognized but not fully understood. Variations in REE concentration and their direct or indirect association with coal beds are not predictable. This study presents findings from examining lateral and potentially stratigraphic variation of REE and CM occurrences in coals of late Cretaceous and Paleocene age. In this study we collected and examined samples of differing ages both core and coal mine exposures for qualitative x-ray fluorescence (XRF), and multi-element geochemistry. Preliminary XRF data indicates variable levels of light REEs in a core from the Yampa coalfield of Moffat County in northwest Colorado. An absence of similar enrichments in slightly older coals in the Adaville Formation of the Fold and Thrust belt in southwest Wyoming is described from XRF and ICP-MS evaluation. Previous work has shown an association with the Yampa Bed and REE enrichment in coals of the Upper Cretaceous Williams Fork Formation. While not common and widespread, this association suggests that leaching or reworking of the ash bed could lead to elevated REEs in the adjacent coal. We investigate differences between the two data occurringas geologic compositions and post-depositional histories. In-depth petrography and precise geochemistry should reveal data that at the very least will help improve some aspects of the geologic models of coal basins and the effect of an influx of non-coal sediments.

REE, CM, ash, volcanic ash, coal↗

DOE OSTI2024

Laser-induced quenching of metastability at the Mott insulator to metal transition

There is growing interest in strongly correlated insulator thin films because the intricate interplay of their intrinsic and extrinsic state variables causes memristive behavior that might be used for biomimetic devices in the emerging field of neuromorphic computing. Here, in this study, we find that laser irradiation tends to drive V 2 ⁢O 3 from supercooled/superheated metastable states toward thermodynamic equilibrium, most likely in a nonthermal way. We study thin films of the prototypical Mott-insulator V2⁢O3, which show spontaneous phase separation into metal-insulator herringbone domains during the Mott transition. Here, we use low-temperature microscopy to investigate how these metal-insulator domains can be modified by scanning a focused laser beam across the thin film surface. We find that the response depends on the thermal history: When the thin film is heated from below the Mott transition temperature, the laser beam predominantly induces metallic domains. On the contrary, when the thin film is cooled from a temperature above the transition, the laser beam predominantly induces insulating domains. Very likely, the V 2 ⁢O 3 thin film is in a superheated or supercooled state, respectively, during the first-order phase transition, and the perturbation by a laser beam drives these metastable states into stable ones. This way, the thermal history is locally erased. Our findings are supported by a phenomenological model with a laser-induced lowering of the energy barrier between the metastable and equilibrium states.

Materials Science↗

DOE OSTI2024

Perturbations of Gibbons-Maeda black holes in Einstein-Maxwell-dilaton theories

The study of perturbations around black hole backgrounds in general relativity and Einstein-Maxwell theory has a long history, going back to the work of Regge and Wheeler in the 1950s. As part of a broader investigation of perturbations around black holes in supergravity, we describe here our results for the perturbations around the Gibbons-Maeda static charged black holes in a class of Einstein-Maxwell-Dilaton theories. Our analysis follows the general strategy developed by Chandrasekhar and Xanthopoulos for the perturbations of the Reissner-Nordström black hole. Here, the analysis is considerably more involved, because of the presence of the dilaton field, which couples to the other polar modes. We nonetheless find that the problem is completely solvable, in the sense that one can separate variables and eventually describe all the perturbations in terms of diagonalised second-order radial equations. We are able to prove the mode stability of all the Gibbons-Maeda black hole solutions. Published by the American Physical Society 2024

Pope, C. N. (ORCID:0000000284012564)↗

DOE OSTI2022

Capturing the interactions between ice sheets, sea level and the solid Earth on a range of timescales: a new “time window” algorithm

Retreat and advance of ice sheets perturb the gravitational field, solid surface and rotation of the Earth, leading to spatially variable sea-level changes over a range of timescales $\textit{O}$ (10 0–6 years), which in turn feed back onto ice-sheet dynamics. Coupled ice-sheet–sea-level models have been developed to capture the interactive processes between ice sheets, sea level and the solid Earth, but it is computationally challenging to capture short-term interactions $\textit{O}$ (10 0–2 years) precisely within longer $\textit{O}$ (10 3–6 years) simulations. The standard forward sea-level modelling algorithm assigns a uniform temporal resolution in the sea-level model, causing a quadratic increase in total CPU time with the total number of input ice history steps, which increases with either the length or temporal resolution of the simulation. In this study, we introduce a new “time window” algorithm for 1D pseudo-spectral sea-level models based on the normal mode method that enables users to define the temporal resolution at which the ice loading history is captured during different time intervals before the current simulation time. Utilizing the time window, we assign a fine temporal resolution $\textit{O}$ (10 0–2 years) for the period of ongoing and recent history of surface ice and ocean loading changes and a coarser temporal resolution $\textit{O}$ (10 3–6 years) for earlier periods in the simulation. This reduces the total CPU time and memory required per model time step while maintaining the precision of the model results. We explore the sensitivity of sea-level model results to the model temporal resolution and show how this sensitivity feeds back onto ice-sheet dynamics in coupled modelling. We apply the new algorithm to simulate sea-level changes in response to global ice-sheet evolution over two glacial cycles and the rapid collapse of marine sectors of the West Antarctic Ice Sheet in the coming centuries and provide appropriate time window profiles for each application. The time window algorithm reduces the total CPU time by ~ 50 % in each of these examples and changes the trend of the total CPU time increase from quadratic to linear. This improvement would increase with longer simulations than those considered here. Our algorithm also allows for coupling time intervals of annual temporal scale for coupled ice-sheet–sea-level modelling of regions such as West Antarctica that are characterized by rapid solid Earth response to ice changes due to the thin lithosphere and low mantle viscosities.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS1984

Review of the Effects of Microstructure on Fatigue in Aluminum Alloys

Literature survey was conducted to determine the effects of different microstructural features and different load histories on fatigue crack initiation and propagation of aluminum alloys. Comparison of microstructure and monotonic and cyclic properties between powder metallurgy (P/M) and ingot metallurgy (I/M) alloys is presented. The two alloys that are representative of each process on which the comparison is focused are X7091 and 7050. Included is a detailed description of the microstructure produced through the P/M and I/M proesses. The effect of each pertinent microstructural feature on monotonic and cyclic properties, such as yield strength, toughness, crack initiation and propagation is discussed. Also discussed are the proposed mechanisms for crack initiation and propagation, as well as the effects of aggressive environments on these cyclic properties. The effects of variable amplitude loadin on fatigue crack propagation and the various models proposed to predict load interaction effects are discussed.

Telesman, J.↗

NASA NTRS1999

A Study of Short-Term Variations in Jupiter's Synchrotron Emission

Earth-based observations of the flux density and polarization of Jupiter's microwave emission provide useful data to test and constrain computational models of synchrotron radio emission from the inner regions of the Jovian magnetosphere. Stimulated by the sudden brightening of the synchrotron emission caused by the impacts of comet Shoemaker-Levy 9 in 1994, the observational techniques of the NASA-JPL Jupiter Patrol were modified to search for other short-term variations unrelated to the SL-9 event. The characteristics of the improved data base are described and the results of the search for variability on timescales of 5 to 100 days are reported. The first results of Jupiter observations from the Goldstone-Apple Valley Radio Telescope (GAVRT) project are reported and included in the data base. GAVRT is a new project in science education that engages middle- and high school students in science research. The paper also includes new observations of Jupiter's rotational beamed emission, commonly known as the "beaming curve", that describes the observed flux density as a function of System III longitude. The shape of the "beaming curve" is known to change with the parameter D(sub E), the declination of the earth relative to Jupiter's rotational equator. While the history of Jupiter's beaming curve exhibits remarkable stability and repeatability as a function of D(sub E), there may be evidence for short term departures from the nominal curves. Data supporting this tentative conclusion are presented. Preliminary results of a study comparing the observations and computer simulations of the synchrotron beaming curve will also be presented and discussed (see companion paper, "Modeling Jupiter's Synchrotron Emission", by Bolton et. al.). The research reported in this paper was performed by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

Klein, M.J.↗

NASA NTRS2017

On the Magnetic Protection of the Atmosphere of Proxima Centauri b

The discovery of exoplanets orbiting red dwarfs, such as Proxima Centauri b, has led to questions of their habitability and capacity to retain liquid surface water. While Proxima b is in a ''temperate orbit,'' i.e., an Earth at that location would not freeze or boil its oceans, its proximity to a parent star with quite high magnetic activity is likely to influence its atmospheric evolution and habitability. Planetary magnetic fields can prevent direct stripping away of the planetary atmosphere by the stellar wind, but ion escape can still occur at the magnetic poles. This process, the polar wind, is well known to occur at Earth and may have contributed to the habitability of Earth's early atmosphere. The polar wind is highly variable and sensitive to both ionizing radiation and geomagnetic activity. The higher ionizing radiation levels of M dwarfs at habitable zone distances are expected to increase the polar wind by orders of magnitude and, instead of helping create a habitable atmosphere, may strip away enough volatiles to render the planet inhospitable. Here, we compute the ionospheric outflow of an Earth-twin subject to the enhanced stellar EUV flux of Proxima b, and the effect on atmospheric escape timescales. We show that an Earth-like planet would not survive the escape of its atmosphere at that location, and therefore the pathway to habitability for Proxima b requires a very different atmospheric history than that of Earth.

planets and satellites↗

DOE OSTI2021

Volatile Element Evidence of Local MORB Mantle Heterogeneity Beneath the Southwest Indian Ridge, 48°–51°E

Abstract The mantle source beneath the Southwest Indian Ridge (SWIR) reflects a complex history of contamination. Magmatic volatile contents are vital tracers of these kinds of heterogeneities, which may fractionate otherwise constant volatile/non‐volatile elemental ratios, such as the H 2 O/Ce ratio. Although several studies have recently used trace element and isotopic data to address mantle source heterogeneity and magmatic processes at SWIR 48°–51°E region, volatile element constraints provide a valuable test of models for the origins of mantle heterogeneities in this region. Here, we present new data for nine rare basaltic glass samples from the 48°–51°E region, which enable careful assessment of the effects of primary versus secondary processes on the glass volatile contents. These samples are strongly affected by variable extents of carbon degassing, and shallow assimilation of Cl‐rich fluid, but also reveal consistently high H 2 O/Ce ratios (458.8 ± 14.9), among the highest in MORBs, that cannot be explained by late‐stage secondary processes, crustal assimilation, or simple melting of peridotite mantle at variable depths. Instead, the high H 2 O/Ce ratios are features of the mantle source composition. The 48°–51°E region is notably more depleted in highly incompatible trace elements relative to other regions of the SWIR, although this depletion is not apparent in H 2 O, which is similarly abundant throughout the SWIR. We link the high H 2 O/Ce ratios in these glasses with other trace element characteristics diagnostic of subduction and fluid addition, suggesting that the mantle source reflects signatures of a refractory mantle residue that previously melted within a subduction zone.

Wang, Wei↗

NASA NTRS1982

Reconstruction of the 1st Space Shuttle (STS-1) entry trajectory

A discussion of the generation of the best estimate trajectory (BET) of the first Space Shuttle Orbiter entry flight is presented. The BET defines a time history of the state, attitude, and atmospheric relative parameters throughout the Shuttle entry from an altitude of approximately 183 km to rollout. The inertial parameters were estimated utilizing a weighted least squares batch filter algorithm. Spacecraft angular rate and acceleration data derived from the Inertial Measurement Unit were utilized to predict the state and attitude which was constrained in a weighted least squares process to fit external tracking data consisting of ground based S-band and C-band data. Refined spacecraft altitude and velocity during and post rollout were obtained by processing artificial altimeter and Doppler data. The BET generation process is discussed. Software and data interface discussions are included. The variables and coordinate systems utilized are defined. STS-1 mission peculiar inputs are summarized. A listing of the contents of the actual BET is provided.

Findlay, J. T.↗

NASA NTRS2002

Effects of Thermomechanical History on the Tensile Behavior of Nitinol Ribbon

Shape memory alloys (SMAs) have enormous potential for a wide variety of applications. A large body of work exists on the characterization of the microstructure and stress-strain behavior of these alloys, Nitinol (NiTi) in particular. However, many attributes of these materials are yet to be fully understood. Previous work at NASA Langley Research Center (LaRC) has included fabrication of hybrid composite specimens with embedded Nitinol actuators and modeling of their thermomechanical behavior. An intensive characterization effort has been undertaken to facilitate fundamental understanding of this alloy and to promote implementation of Nitinol in aerospace applications. Previous work revealed attributes of the Nitinol ribbon that were not easily rationalized with existing data in the literature. In particular, tensile behavior at ambient temperature showed significant dependence on the thermomechanical history prior to testing. The present work is focused on characterizing differences in the microstructure of Nitinol ribbons exposed to four different thermomechanical histories and correlation of the microstructure with tensile properties. Differential scanning calorimetry (DSC) and x-ray diffraction (XRD) analysis were employed to rationalize the microstructures present after exposure to various thermomechanical histories. Three of the Nitinol ribbon conditions were reversible upon heating (in the DSC) through the reverse transformation temperature (A(sub f) to transform the microstructure to austenite. However, the prior thermomechanical conditioning for the Nitinol ribbon that reflected the entire fabrication procedure (4% thermal cycle condition) was found to have an irreversible effect on the microstructure, as it remained unchanged after repeated complete thermal cycles. Tensile tests were conducted to determine the effect of prior thermomechancal conditioning on both the tensile behavior of the Nitinol ribbons and the stress state of the microstructure. The stress-strain behavior of the Nitinol actuators appears to be governed by the interplay between two major variables: namely, microstructural constituents such as the R-phase and the martensite; and the stress state of these constituents (whether twinned with low residual stresses, or detwinned with high residual stresses). The most significant difference in the stress-strain behavior of the four conditions, the critical stress required to achieve an initial stress plateau, was found to depend on both the amount and stress state (twinned or detwinned) of R-phase present in the initial microstructure. Thus, the effect of prior thermomechanical processing is critical to the resulting tensile behavior of the Nitinol actuator. For numerical modeling inputs one must take into account the entire fabrication process on the Nitinol actuator.

Lach, Cynthia L.↗

NASA NTRS2014

Irrigation as an Historical Climate Forcing

Irrigation is the single largest anthropogenic water use, a modification of the land surface that significantly affects surface energy budgets, the water cycle, and climate. Irrigation, however, is typically not included in standard historical general circulation model (GCM) simulations along with other anthropogenic and natural forcings. To investigate the importance of irrigation as an anthropogenic climate forcing, we conduct two 5-member ensemble GCM experiments. Both are setup identical to the historical forced (anthropogenic plus natural) scenario used in version 5 of the Coupled Model Intercomparison Project, but in one experiment we also add water to the land surface using a dataset of historically estimated irrigation rates. Irrigation has a negligible effect on the global average radiative balance at the top of the atmosphere, but causes significant cooling of global average surface air temperatures over land and dampens regional warming trends. This cooling is regionally focused and is especially strong in Western North America, the Mediterranean, the Middle East, and Asia. Irrigation enhances cloud cover and precipitation in these same regions, except for summer in parts of Monsoon Asia, where irrigation causes a reduction in monsoon season precipitation. Irrigation cools the surface, reducing upward fluxes of longwave radiation (increasing net longwave), and increases cloud cover, enhancing shortwave reflection (reducing net shortwave). The relative magnitude of these two processes causes regional increases (northern India) or decreases (Central Asia, China) in energy availability at the surface and top of the atmosphere. Despite these changes in net radiation, however, climate responses are due primarily to larger magnitude shifts in the Bowen ratio from sensible to latent heating. Irrigation impacts on temperature, precipitation, and other climate variables are regionally significant, even while other anthropogenic forcings (anthropogenic aerosols, greenhouse gases, etc.) dominate the long term climate evolution in the simulations. To better constrain the magnitude and uncertainties of irrigation-forced climate anomalies, irrigation should therefore be considered as another important anthropogenic climate forcing in the next generation of historical climate simulations and multimodel assessments.

simulation↗

NASA NTRS2018

Considerations for Implementing Voice-Controlled Spacecraft Systems Through a Human-Centered Design Approach

As computational power and speech recognition algorithms improve, the consumer market will see better-performing speech recognition applications. The cell phone and Internet-related service industry have further enhanced speech recognition applications using artificial intelligence and statistical data-mining techniques. These improvements to speech recognition technology (SRT) may one day help astronauts on future deep space human missions that require control of complex spacecraft systems or spacesuit applications by voice. Though SRT and more advanced speech recognition techniques show promise, use of this technology for a space application such as vehicle/habitat/spacesuit requires careful considerations. There are still recognition challenges to overcome such as background noise, human speech variability, and task loading. However, implemented correctly, a voice-controlled spacecraft system (VCSS) can provide a useful, natural and efficient form of human-machine communications during complex tasks such as when the hands and eyes are busy or as an aid for vehicle situational awareness inquiries or collaborative human-robot tasks. This document provides considerations and guidance for the use of SRT in VCSS applications for space missions, specifically in command-and-control (C2) applications where the commanding is user-initiated. First, current SRT limitations as known at the time of this report are given. Then, highlights of SRT used in the space program provide the reader with a history of some of the human spaceflight applications and research. Next, an overview of the speech production process and the intrinsic variations of speech are provided. Finally, general guidance and considerations are given for development of a VCSS using a human-centered design approach for space applications that includes vocabulary selection and performance testing, as well as VCSS considerations for C2 dialogue management design, feedback, error handling, and evaluation/usability testing. Available from

Salazar, George A.↗

DOE OSTI2024

A Multiphysics Thermoelastoviscoplastic Damage Internal State Variable Constitutive Model including Magnetism

We present a macroscale constitutive model that couples magnetism with thermal, elastic, plastic, and damage effects in an Internal State Variable (ISV) theory. Previous constitutive models did not include an interdependence between the internal magnetic (magnetostriction and magnetic flux) and mechanical fields. Although constitutive models explaining the mechanisms behind mechanical deformations caused by magnetization changes have been presented in the literature, they mainly focus on nanoscale structure–property relations. A fully coupled multiphysics macroscale ISV model presented herein admits lower length scale information from the nanoscale and microscale descriptions of the multiphysics behavior, thus capturing the effects of magnetic field forces with isotropic and anisotropic magnetization terms and moments under thermomechanical deformations. For the first time, this ISV modeling framework internally coheres to the kinematic, thermodynamic, and kinetic relationships of deformation using the evolving ISV histories. For the kinematics, a multiplicative decomposition of deformation gradient is employed including a magnetization term; hence, the Jacobian represents the conservation of mass and conservation of momentum including magnetism. The first and second laws of thermodynamics are used to constrain the appropriate constitutive relations through the Clausius–Duhem inequality. The kinetic framework employs a stress–strain relationship with a flow rule that couples the thermal, mechanical, and magnetic terms. Experimental data from the literature for three different materials (iron, nickel, and cobalt) are used to compare with the model’s results showing good correlations.

36 MATERIALS SCIENCE↗

DOE OSTI2024

A Multiphysics Thermoelastoviscoplastic Damage Internal State Variable Constitutive Model including Magnetism

36 MATERIALS SCIENCE↗

NASA NTRS1995

Starspot evolution, differential rotation, and magnetic cycles in the chromospherically active binaries lambda andromedae, sigma Geminorum, II Pegasi, and V711 Tauri

We have analyzed 15-19 yr of photoelectric photometry, obtained manually and with automated telescopes, of the chromospherically active binaries lambda And, sigma Gem, II Peg, and V711 Tau. These observations let us identify individual dark starspots on the stellar surfaces from periodic dimming of the starlight, follow the evolution of these spots, and search for long-term cyclic changes in the properties of these starspots that might reveal magnetic cycles analogous to the Sun's 11 yr sunspot cycle. We developed a computer code to fit a simple two-spot model to our observed light curves that allows us to extract the most easily determinable and most reliable spot parameters from the light curves, i.e., spot longitudes and radii. We then used these measured properties to identify individual spots and to chart their life histories by constructing migration and amplitude curves. We identified and followed 11 spots in lambda And, 16 in sigma Gem, 12 in II Peg, and 15 in V711 Tau. Lifetimes of individual spots ranged from a few months to longer than 6 yr. Differential rotation coefficients, estimated from the observed range of spot rotation periods for each star and defined by equation (2), were 0.04 for lambda And, 0.038 for sigma Gem, 0.005 for II Peg, and 0.006 for V711 Tau, versus 0.19 for the Sun. We searched for cyclic changes in mean brightness, B-V color index, and spot rotation period as evidence for long-term cycles. Of these, long-term variability in mean brightness appears to offer the best evidence for such cycles in these four stars. Cycles of 11.1 yr for lambda And, 8.5 yr for sigma Gem, 11 yr for II Peg, and 16 yr V711 Tau are implied by these mean brightness changes. Cyclic changes in spot rotation period were found in lambda And and possibly II Peg. Errors in B-V were too large for any long-term changes to be detectable.

Henry, Gregory W.↗

NASA NTRS1997

Thermal History and Mantle Dynamics of Venus

One objective of this research proposal is to develop a 3-D thermal history model for Venus. The basis of our study is a finite-element computer model to simulate thermal convection of fluids with highly temperature- and pressure-dependent viscosities in a three-dimensional spherical shell. A three-dimensional model for thermal history studies is necessary for the following reasons. To study planetary thermal evolution, one needs to consider global heat budgets of a planet throughout its evolution history. Hence, three-dimensional models are necessary. This is in contrasts to studies of some local phenomena or local structures where models of lower dimensions may be sufficient. There are different approaches to treat three-dimensional thermal convection problems. Each approach has its own advantages and disadvantages. Therefore, the choice of the various approaches is subjective and dependent on the problem addressed. In our case, we are interested in the effects of viscosities that are highly temperature dependent and that their magnitudes within the computing domain can vary over many orders of magnitude. In order to resolve the rapid change of viscosities, small grid spacings are often necessary. To optimize the amount of computing, variable grids become desirable. Thus, the finite-element numerical approach is chosen for its ability to place grid elements of different sizes over the complete computational domain. For this research proposal, we did not start from scratch and develop the finite element codes from the beginning. Instead, we adopted a finite-element model developed by Baumgardner, a collaborator of this research proposal, for three-dimensional thermal convection with constant viscosity. Over the duration supported by this research proposal, a significant amount of advancements have been accomplished.

Hsui, Albert T.↗