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107 records · Page 6

Time and wavelength domain algorithms for chemical analysis by laser radar

Laser-induced fluorescence (LIF) is a promising technique for laser radar applications. Laser radar using LIF has already been applied to algae blooms and oil slicks. Laser radar using LIF has great potential for remote chemical analysis because LIF spectra are extremely sensitive to chemical composition. However, most samples in the real world contain mixtures of fluorescing components, not merely individual components. Multicomponent analysis of laser radar returns from mixtures is often difficult because LIF spectra from solids and liquids are very broad and devoid of line structure. Therefore, algorithms for interpreting LIF spectra from laser radar returns must be able to analyze spectra that overlap in multicomponent systems. This paper analyzes the possibility of using factor analysis-rank annihilation (FARA) to analyze emission-time matrices (ETM) from laser radar returns instead of excitation-emission matrices (EEM). The authors here define ETM as matrices where the rows (or columns) are emission spectra at fixed times and the columns (or rows) are temporal profiles for fixed emission wavelengths. Laser radar usually uses pulsed lasers for ranging purposes, which are suitable for measuring temporal profiles. Laser radar targets are hard instead of diffuse; that is, a definite surface emits the fluorescence instead of an extended volume. A hard target would not broaden the temporal profiles as would a diffuse target. Both fluorescence lifetimes and emission spectra are sensitive to chemical composition. Therefore, temporal profiles can be used instead of excitation spectra in FARA analysis of laser radar returns. The resulting laser radar returns would be ETM instead of EEM.

Rosen, David L.↗

Plane Smoothers for Multiblock Grids: Computational Aspects

Standard multigrid methods are not well suited for problems with anisotropic discrete operators, which can occur, for example, on grids that are stretched in order to resolve a boundary layer. One of the most efficient approaches to yield robust methods is the combination of standard coarsening with alternating-direction plane relaxation in the three dimensions. However, this approach may be difficult to implement in codes with multiblock structured grids because there may be no natural definition of global lines or planes. This inherent obstacle limits the range of an implicit smoother to only the portion of the computational domain in the current block. This report studies in detail, both numerically and analytically, the behavior of blockwise plane smoothers in order to provide guidance to engineers who use block-structured grids. The results obtained so far show alternating-direction plane smoothers to be very robust, even on multiblock grids. In common computational fluid dynamics multiblock simulations, where the number of subdomains crossed by the line of a strong anisotropy is low (up to four), textbook multigrid convergence rates can be obtained with a small overlap of cells between neighboring blocks.

Llorente, Ignacio M.↗

Calmodulin activation of an endoplasmic reticulum-located calcium pump involves an interaction with the N-terminal autoinhibitory domain

To investigate how calmodulin regulates a unique subfamily of Ca(2+) pumps found in plants, we examined the kinetic properties of isoform ACA2 identified in Arabidopsis. A recombinant ACA2 was expressed in a yeast K616 mutant deficient in two endogenous Ca(2+) pumps. Orthovanadate-sensitive (45)Ca(2+) transport into vesicles isolated from transformants demonstrated that ACA2 is a Ca(2+) pump. Ca(2+) pumping by the full-length protein (ACA2-1) was 4- to 10-fold lower than that of the N-terminal truncated ACA2-2 (Delta2-80), indicating that the N-terminal domain normally acts to inhibit the pump. An inhibitory sequence (IC(50) = 4 microM) was localized to a region within valine-20 to leucine-44, because a peptide corresponding to this sequence lowered the V(max) and increased the K(m) for Ca(2+) of the constitutively active ACA2-2 to values comparable to the full-length pump. The peptide also blocked the activity (IC(50) = 7 microM) of a Ca(2+) pump (AtECA1) belonging to a second family of Ca(2+) pumps. This inhibitory sequence appears to overlap with a calmodulin-binding site in ACA2, previously mapped between aspartate-19 and arginine-36 (J.F. Harper, B. Hong, I. Hwang, H.Q. Guo, R. Stoddard, J.F. Huang, M.G. Palmgren, H. Sze inverted question mark1998 J Biol Chem 273: 1099-1106). These results support a model in which the pump is kept "unactivated" by an intramolecular interaction between an autoinhibitory sequence located between residues 20 and 44 and a site in the Ca(2+) pump core that is highly conserved between different Ca(2+) pump families. Results further support a model in which activation occurs as a result of Ca(2+)-induced binding of calmodulin to a site overlapping or immediately adjacent to the autoinhibitory sequence.

NASA Program Fundamental Space Biology↗

Application of homomorphic signal processing to stress wave factor analysis

The stress wave factor (SWF) signal, which is the output of an ultrasonic testing system where the transmitting and receiving transducers are coupled to the same face of the test structure, is analyzed in the frequency domain. The SWF signal generated in an isotropic elastic plate is modelled as the superposition of successive reflections. The reflection which is generated by the stress waves which travel p times as a longitudinal (P) wave and s times as a shear (S) wave through the plate while reflecting back and forth between the bottom and top faces of the plate is designated as the reflection with p, s. Short-time portions of the SWF signal are considered for obtaining spectral information on individual reflections. If the significant reflections are not overlapped, the short-time Fourier analysis is used. A summary of the elevant points of homomorphic signal processing, which is also called cepstrum analysis, is given. Homomorphic signal processing is applied to short-time SWF signals to obtain estimates of the log spectra of individual reflections for cases in which the reflections are overlapped. Two typical SWF signals generated in aluminum plates (overlapping and non-overlapping reflections) are analyzed.

Karagulle, H.↗

Application of homomorphic signal processing to stress wave factor analysis

The stress wave factor (SWF) signal, which is the output of an ultrasonic testing system where the transmitting and receiving transducers are coupled to the same face of the test structure, is analyzed in the frequency domain. The SWF signal generated in an isotropic elastic plate is modelled as the superposition of successive reflections. The reflection which is generated by the stress waves which travel P times as a longitudinal (P) wave and s times as a shear (S) wave through the plate while reflecting back and forth between the bottom and top faces of the plate is designated as the reflection with P, s. Short-time portions of the SWF signal are considered for obtaining spectral information on individual reflections. If the significant reflections are not overlapped, the short-time Fourier analysis is used. A summary of the elevant points of homomorphic signal processing, which is also called cepstrum analysis, is given. Homomorphic signal processing is applied to short-time SWF signals to obtain estimates of the log spectra of individual reflections for cases in which the reflections are overlapped. Two typical SWF signals generated in aluminum plates (overlapping and non-overlapping reflections) are analyzed.

Williams, J. H., Jr.↗

Scope and Abstraction: Two Criteria for Localized Planning

Localization is a general-purpose representational technique for partitioning problem requirements into subproblems. Localized search utilizes a partitioning by breaking the overall search space into several smaller search spaces, one for each subproblem. Unlike most methods of partitioning, localization allows for subproblems that overlap -- i.e., multiple search spaces may be involved in constructing shared pieces of the overall plan. In this paper we focus on two criteria for forming localizations: abstraction and scope. Abstraction-based localizations are motivated by activation relationships between problem requirements. In contrast, scope-based localizations are motivated by the relevance of problem requirements to specific portions of the overall plan. This paper also describes a method for automatically generating scope and abstraction-based localizations. Empirical results are provided that contrast their use in an office-building construction planning domain.

Lansky, Amy L.↗

Modal Q Factor and Modal Overlap of Electrically Small Avionics Box

Estimating the electromagnetic field strength in avionics boxes and other small enclosures at the design stage requires an estimate of the Q factor of the cavity modes. When the enclosure is small, it is typically under-moded so that Q measurement techniques which are standard practice in over-moded reverberation chambers may not be a robust measure. Furthermore, practical antenna used to measure Q in a small cavity may have a strong influence on the result obtained, as reported by Tait et al, IEEE Trans. EMC 55 2 2012. This paper reports the results of testing to determine the Q factor of a small aperture enclosure, used in a statistical power balance model to predict the electric field strength. The contributors to the total Q are identified. A novel S(sub 11) curve fitting method to measure modal Q is introduced and compared with the time domain method for measuring Q.

Statistical Electromagnetics↗

An object-oriented approach for parallel self adaptive mesh refinement on block structured grids

Self-adaptive mesh refinement dynamically matches the computational demands of a solver for partial differential equations to the activity in the application's domain. In this paper we present two C++ class libraries, P++ and AMR++, which significantly simplify the development of sophisticated adaptive mesh refinement codes on (massively) parallel distributed memory architectures. The development is based on our previous research in this area. The C++ class libraries provide abstractions to separate the issues of developing parallel adaptive mesh refinement applications into those of parallelism, abstracted by P++, and adaptive mesh refinement, abstracted by AMR++. P++ is a parallel array class library to permit efficient development of architecture independent codes for structured grid applications, and AMR++ provides support for self-adaptive mesh refinement on block-structured grids of rectangular non-overlapping blocks. Using these libraries, the application programmers' work is greatly simplified to primarily specifying the serial single grid application and obtaining the parallel and self-adaptive mesh refinement code with minimal effort. Initial results for simple singular perturbation problems solved by self-adaptive multilevel techniques (FAC, AFAC), being implemented on the basis of prototypes of the P++/AMR++ environment, are presented. Singular perturbation problems frequently arise in large applications, e.g. in the area of computational fluid dynamics. They usually have solutions with layers which require adaptive mesh refinement and fast basic solvers in order to be resolved efficiently.

Lemke, Max↗

Large Modal Survey Testing Using the Ibrahim Time Domain Identification Technique

The ability of the ITD identification algorithm in identifying a complete set of structural modal parameters using a large number of free-response time histories simultaneously in one analysis, assuming a math model with a high number of degrees-of-freedom, has been studied. Identification results using simulated free responses of a uniform rectangular plate, with 225 measurement stations, and experimental responses from a ground vibration test of the Long Duration Exposure Facility (LDEF) Space Shuttle payload, with 142 measurement stations, are presented. As many as 300 degrees-of-freedom were allowed in analyzing these data. In general, the use of a significantly oversized math model in the identification process was found to maintain or increase identification accuracy and to identify modes of low response level that are not identified with smaller math model sizes. The concept of a Mode Shape Correlation Constant is introduced for use when more than one identification analysis of the same structure are conducted. This constant quantifies the degree of correlation between any two sets of complex mode shapes identified using different excitation conditions, different user-selectable algorithm constants, or overlapping sets of measurements.

Ibrahim, S. R.↗

Large modal survey testing using the Ibrahim time domain /ITD/ identification technique

The ability of the ITD identification algorithm in identifying a complete set of structural modal parameters using a large number of free-response time histories simultaneously in one analysis, assuming a math model with a high number of degrees-of-freedom, has been studied. Identification results using simulated free responses of a uniform rectangular plate, with 225 measurement stations, and experimental responses from a ground vibration test of the Long Duration Exposure Facility (LDEF) Space Shuttle payload, with 142 measurement stations, are presented. As many as 300 degrees-of-freedom were allowed in analyzing these data. In general, the use of a significantly oversized math model in the identification process was found to maintain or increase identification accuracy and to identify modes of low response level that are not identified with smaller math model sizes. The concept of a Mode Shape Correlation Constant is introduced for use when more than one identification analysis of the same structure are conducted. This constant quantifies the degree of correlation between any two sets of complex mode shapes identified using different excitation conditions, different user-selectable algorithm constants, or overlapping sets of measurements.

Ibrahim, S. R.↗

Physics of Hard Spheres Experiment: Significant and Quantitative Findings Made

Direct examination of atomic interactions is difficult. One powerful approach to visualizing atomic interactions is to study near-index-matched colloidal dispersions of microscopic plastic spheres, which can be probed by visible light. Such spheres interact through hydrodynamic and Brownian forces, but they feel no direct force before an infinite repulsion at contact. Through the microgravity flight of the Physics of Hard Spheres Experiment (PHaSE), researchers have sought a more complete understanding of the entropically driven disorder-order transition in hard-sphere colloidal dispersions. The experiment was conceived by Professors Paul M. Chaikin and William B. Russel of Princeton University. Microgravity was required because, on Earth, index-matched colloidal dispersions often cannot be density matched, resulting in significant settling over the crystallization period. This settling makes them a poor model of the equilibrium atomic system, where the effect of gravity is truly negligible. For this purpose, a customized light-scattering instrument was designed, built, and flown by the NASA Glenn Research Center at Lewis Field on the space shuttle (shuttle missions STS 83 and STS 94). This instrument performed both static and dynamic light scattering, with sample oscillation for determining rheological properties. Scattered light from a 532- nm laser was recorded either by a 10-bit charge-coupled discharge (CCD) camera from a concentric screen covering angles of 0 to 60 or by sensitive avalanche photodiode detectors, which convert the photons into binary data from which two correlators compute autocorrelation functions. The sample cell was driven by a direct-current servomotor to allow sinusoidal oscillation for the measurement of rheological properties. Significant microgravity research findings include the observation of beautiful dendritic crystals, the crystallization of a "glassy phase" sample in microgravity that did not crystallize for over 1 year in 1g (Earth's gravity), and the emergence of face-centered-cubic (FCC) crystals late in the coarsening process (as small crystallites lost particles to the slow ripening of large crystallites). Significant quantitative findings from the microgravity experiments have been developed describing complex interactions among crystallites during the growth process, as concentration fields overlap in the surrounding disordered phase. Time-resolved Bragg scattering under microgravity captures one effect of these interactions quite conclusively for the sample at a volume fraction of 0.528. From the earliest time until the sample is almost fully crystalline, the size and overall crystallinity grow monotonically, but the number of crystallites per unit volume (number density) falls. Apparently nucleation is slower than the loss of crystallites because of the transfer of particles from small to large crystals. Thus, coarsening occurs simultaneously with growth, rather than following the completion of nucleation and growth as is generally assumed. In the same sample, an interesting signature appears in the apparent number density of crystallites and the volume fraction within the crystallites shortly before full crystallinity is reached. A brief upturn in both indicates the creation of more domains of the size of the average crystallite simultaneous with the compression of the crystallites. Only the emergence of dendritic arms offers a reasonable explanation. The arms would be "seen" by the light scattering as separate domains whose smaller radii of curvature would compress the interior phase. In fiscal year 1999, numerous papers, a doctoral dissertation, and the PHaSE final report were produced. Although this flight project has been completed, plans are in place for a follow-on colloid experiment by Chaikin and Russel that employs a light microscope within Glenn's Fluids and Combustion Facility on the International Space Station. PHaSE is providing us with a deeper understanding of the nure of phase transitions. The knowledge derived has added to the understanding of condensed matter. In addition, the burgeoning study of the dynamics of colloidal self-assembly may lead to the development of a range of photonic materials that control the desirable properties of light. Thus, applications of ordered colloidal structures include not only ultrastructure ceramics, but also photonic crystals and photothermal nanosecond light-switching devices. Industries dealing with semiconductors, electro-optics, ceramics, and composites stand to benefit from such advancements.

Doherty, Michael P.↗

Computation of Domain-Averaged Shortwave Irradiance by a One-Dimensional Algorithm Incorporating Correlations between Optical Thickness and Direct Incident Radiation

A one-dimensional radiative transfer algorithm that accounts for correlations between the optical thickness and the incident direct solar radiation is developed to compute the domain-averaged shortwave irradiance profile. It divides the direct irradiance into four components and treats the direct irradiance in two separate, clear and cloudy columns to account for the fact that clouds attenuate the direct irradiance more than clear-sky. The horizontal inhomogeneity of clouds in the cloudy column is treated by the gamma weighted two-stream approximation, which assumes that the optical thickness of clouds follows a gamma distribution. The algorithm inputs the cloud fraction, cumulative cloud fraction as a function of height, and a parameter expressing the shape of the probability density function of the cloud optical thickness distribution in addition to inputs required for a two-stream radiative transfer model. These cloud property inputs can be obtained using ground- and satellite-based instruments. Therefore, the algorithm can treat realistic cloud overlap features and horizontal inhomogeneity of clouds in a framework of one- dimensional radiative transfer. Heating rates computed by the algorithm using cloud fields generated by cloud resolving models agree with those computed with a Monte Carlo model. If optical properties in computational layers that divide a vertically extensive cloud are correlated, the irradiance profile computed by the algorithm further improves.

Kato, S.↗

Quasi-Optimal Schwarz Methods for the Conforming Spectral Element Discretization

Fast methods are proposed for solving the system K(sub N)x = b resulting from the discretization of self-adjoint elliptic equations in three dimensional domains by the spectral element method. The domain is decomposed into hexahedral elements, and in each of these elements the discretization space is formed by polynomials of degree N in each variable. Gauss-Lobatto-Legendre (GLL) quadrature rules replace the integrals in the Galerkin formulation. This system is solved by the preconditioned conjugate gradients method. The conforming finite element space on the GLL mesh consisting of piecewise Q(sub 1) elements produces a stiffness matrix K(sub h) that is spectrally equivalent to the spectral element stiffness matrix K(sub N). The action of the inverse of K(sub h) is expensive for large problems, and is therefore replaced by a Schwarz preconditioner B(sub h) of this finite element stiffness matrix. The preconditioned operator then becomes B(sub h)(exp -l)K(sub N). The technical difficulties stem from the nonregularity of the mesh. Tools to estimate the convergence of a large class of new iterative substructuring and overlapping Schwarz preconditioners are developed. This technique also provides a new analysis for an iterative substructuring method proposed by Pavarino and Widlund for the spectral element discretization.

Casarin, Mario↗

Advancing the Standards for Unmanned Air System Communications, Navigation and Surveillance

Under NASA program NNA16BD84C, new architectures were identified and developed for supporting reliable and secure Communications, Navigation and Surveillance (CNS) needs for Unmanned Air Systems (UAS) operating in both controlled and uncontrolled airspace. An analysis of architectures for the two categories of airspace and an implementation technology readiness analysis were performed. These studies produced NASA reports that have been made available in the public domain and have been briefed in previous conferences. We now consider how the products of the study are influencing emerging directions in the aviation standards communities. The International Civil Aviation Organization (ICAO) Communications Panel (CP), Working Group I (WG-I) is currently developing a communications network architecture known as the Aeronautical Telecommunications Network with Internet Protocol Services (ATN/IPS). The target use case for this service is secure and reliable Air Traffic Management (ATM) for manned aircraft operating in controlled airspace. However, the work is more and more also considering the emerging class of airspace users known as Remotely Piloted Aircraft Systems (RPAS), which refers to certain UAS classes. In addition, two Special Committees (SCs) in the Radio Technical Commission for Aeronautics (RTCA) are developing Minimum Aviation System Performance Standards (MASPS) and Minimum Operational Performance Standards (MOPS) for UAS. RTCA SC-223 is investigating an Internet Protocol Suite (IPS) and AeroMACS aviation data link for interoperable (INTEROP) UAS communications. Meanwhile, RTCA SC-228 is working to develop Detect And Avoid (DAA) equipment and a Command and Control (C2) Data Link MOPS establishing LBand and C-Band solutions. These RTCA Special Committees along with ICAO CP WG/I are therefore overlapping in terms of the Communication, Navigation and Surveillance (CNS) alternatives they are seeking to provide for an integrated manned- and unmanned air traffic management service as well as remote pilot command and control. This paper presents UAS CNS architecture concepts developed under the NASA program that apply to all three of the aforementioned committees. It discusses the similarities and differences in the problem spaces under consideration in each committee, and considers the application of a common set of CNS alternatives that can be widely applied. As the works of these committees progress, it is clear that the overlap will need to be addressed to ensure a consistent and safe framework for worldwide aviation. In this study, we discuss similarities and differences in the various operational models and show how the CNS architectures developed under the NASA program apply.

Ponchak, Denise S.↗

Novel Approach to Simulating Diagnostic Capabilities in Medical Resource Risk Assessment

Diagnostics represent a key subset of medical resources considered for helping mitigate and control spaceflight medical risk. Historically, when modeling the medical risk domain for spaceflight, diagnostic resources have been handled like any other medical resource used for treatment. That is to say, the resource being unavailable will result in the related condition having suboptimal treatment outcomes. However in the real world, should a diagnostic resource be unavailable, a more analogous effect would be that the condition might be misdiagnosed, and thus inappropriate treatment applied. This talk presents an alternative means of representing diagnostic resources within the Medical Extensible Dynamic Probabilistic Risk Assessment Tool (MEDPRAT) that can simulate the effect both in risk, resource consumption, and competition for resources of a missing or depleted diagnostic. The scenario where a differential diagnosis may not be possible for abdominal conditions that use an ultrasound machine as a diagnostic tool is considered. Two approaches for modeling the effect of not having a diagnostic capability on the medical system are demonstrated. In the “simple” approach, it is assumed that any abdominal condition requiring the ultrasound machine for diagnosis is mis-diagnosed and treated as an appendicitis. This is represented by replacing the treatment for the affected conditions with the treatment for appendicitis, thereby changing the optimized medical set available for treatment for the remainder of the mission. In the “complex” approach, MEDPRAT treatment clusters are utilized to capture and represent overlapping treatment between the misdiagnosed condition and appendicitis. This elicits both the effect that inappropriate treatment is applied, resulting in wasted resource consumption, and that treatment which was truly needed for the misdiagnosed condition was not applied, which reduces the treatment effectiveness. In this talk, results comparing the simple and complex diagnostic capability approach to a baseline where the diagnostic is treated as a traditional resource is presented. Either approach provides an option for a more analogous representation of diagnostic resources and provides insight into how the modeled spaceflight medical resources and outcomes change when that diagnostic is unavailable.

C. M. Gasiewski↗

Creating A Consistent Historical NASA POWER Solar Radiation Dataset to Support Renewable Energy, Building Energy Efficiency and Agro-Climatology Decisions

Prediction of Worldwide Energy Resources (POWER) project provides irradiance dataset to support renewable energy, building energy efficiency and agricultural needs. These datasets are derived from Global Energy and Water Cycle Experiment Surface Radiation Budget (GEWEX SRB) and Clouds and the Earth’s Radiant Energy System (CERES SYN1Deg). A systematic bias has been reported between these two datasets for the years with overlapping observations. For obtaining a consistent climate data record spanning the entire time record of observations, it is crucial to understand and remove the bias in the irradiance dataset. Inconsistency in solar radiation data can lead to inaccurate conclusions about solar energy potential and obscure real trends in solar radiation patterns that would impact energy availability assessments. In this study, we adapt quantile mapping approach to remove the systematic bias and to improve reliability of shortwave and longwave irradiance data. We present a validation of the bias corrected data against ground truth. For each 1° latitude and 1° longitude grid box across the globe, we match the CDFs of the reference dataset (CERES SYN1Deg) to that of the SRB dataset, thereby, adjusting the irradiance values to match the empirical distribution of two different measurements. The performance of quantile mapping is evaluated by using the metrics such as Mean Absolute Deviation (MAD). The results indicate that the quantile mapping significantly improves the accuracy and reliability of solar irradiance dataset especially for the weather conditions associated with high cloud cover and extreme irradiance values. The initial range of MAD for the studied sites for daily data was 4 to 19 Wm-2. After correction these reduced to 3 to 7 Wm-2. The findings from this study have important implications for solar energy system design, agricultural planning, and climate modeling community. Reducing the inconsistency and biases in solar irradiance dataset can enable better planning and operation of solar energy systems, leading to increased efficiency and cost-effectiveness. Additionally, this work also contributes to the statistical post-processing techniques in the renewable energy domain and highlights the potential of historical and near-real-time NASA POWER dataset as a valuable resource for solar energy research and applications.

POWER↗

Thermodynamic and Diffusion Model Estimates on Metamorphic Temperatures and Timescales for Basaltic Eucrite GRA 98098

Introduction: HED meteorites are thought to rep-resent igneous rocks from Vesta’s basaltic crust and preserve evidence of early crustal metamorphism. Determining the temperatures and timescales of thermal metamorphism is important for reconstructing crustal evolution in the early solar system. Here, we study basaltic eucrite Graves Nunataks (GRA) 98098, which has been identified as a highly metamorphosed eucrite [1]. We present new estimates on metamorphic temperatures determined via thermodynamic modeling as well as the initial results from diffusion models constraining timescales of thermal metamorphism. Sample Description: GRA 98098 is an unbrecciated eucrite with a granoblastic plagioclase and pyroxene mineralogy. Millimeter to cm-long lathes of tridymite cross-cut and poikilitically enclose plagioclase and pyroxene [1,this work]. Pyroxene grains have exsolved into Ca-rich (~Wo38En29Fs33) and Ca-poor (~Wo4.5En36Fs59.5) lamellae. Both unzoned and zoned plagioclase grains are observed. Unzoned plagioclase grains are found solely with tridymite laths. These grains have ~An92 compositions. The cores of the zoned plagioclase grains have the same composition and thin, relatively sodic rims (~An67), (Fig. 1). The bulk sample is unusually enriched in highly in-compatible elements and has one of the most fractionated REE patterns reported [1]. Maximum metamorphic temperatures of 985±78°C have been estimated using two-pyroxene thermometry [2]. Methods: Thermodynamic modeling. Thermodynamic models were constructed using the software Perple_X, which employs a Gibbs free energy minimization in order to determine the most stable phase assemblage for a given bulk rock composition [3]. Bulk composition was calculated using mineral com-positions acquired via EMPA (this study) and the observed abundancies present in the thin section. Two bulk compositions were estimated; 1) includes all phases present in the thin section, (assumes that all phases are present during metamorphism), 2) excludes tridymite from the bulk calculation (assumes that tridymite was not present during metamorphism). In order to determine whether metamorphic equilibria was achieved and estimate temperatures of metamorphism, we compared measured pyroxene compositions with thermodynamically predicted compositions [4, Fig. 2]. Diffusion Modeling. Several time-temperature de-pendent diffusion profiles were calculated in order to determine the best match for XAn chemical profiles observed at the edges of the zoned plagioclase (Fig. 3). We assumed that the start condition was a stepwise gradient at the plagioclase/pyroxene interface. We also assumed an average diffusion coefficient (D) and a constant temperature using the equation in [5]. D was determined for two temperatures (T = 1060ºC; near eucrite solidus [6] and T = 985ºC; metamorphism reported in [4]) and then XAn was calculated as a function of distance from plagioclase core to rim using an error function solution to Fick’s second law. Results: Thermodynamic model results are summarized in Fig. 2. For a bulk composition that includes all phases in the thin section, pyroxene endmember compositions plot in the following temperature ranges: Fs ~660-860ºC, En~1000ºC & 1150ºC, and Wo~760-900ºC (Fig. 2a). For a bulk composition that excludes tridymite from the peak metamorphic assemblage (i.e., the bulk composition minus the contribution from tridymite), a temperature range could not be determined for the Fs component of pyroxene. For Wo, T~760-900ºC and En, T~1000ºC & 1150ºC (Fig. 2b). Fig. 3 summarizes the diffusion model results. For T = 1060°C & 985°C, the most appropriate time interval was estimated based on which diffusion curve most matched (solid lines, Fig. 3) the EMPA data. For T = 1060°C, the best looking match was t = 500 ka. For T = 985°C, the best match was t = 7 Ma. Discussion and future work: Temperature estimates from thermodynamic models are not conclusive because the temperature ranges determined for pyroxene endmember stability do not overlap (colored fields in Fig. 2), thus implying that there is disequilibrium between pyroxene crystals and the bulk composition considered [4]. Thus, additional exploration is needed to define a metamorphically equilibrated do-main that accurately records peak temperature. The utility of defining metamorphically equilibrated do-mains to improve the accuracy and level of detail elucidated regarding the petrogenetic history of metamorphose samples has been demonstrated previously [4,7]. We suggest that in the case of Fig. 2a, the thin section composition is not representative of the length scales over which metamorphic equilibrium was achieve and in the case of Fig. 2b, the assumption that tridymite was not present during metamorphism was incorrect. However, results from thermodynamic models can provide insight into the relative timing of mineral and compositional textures. For example from texture alone, it is unclear whether tridymite was igneous in origin and represents the last bits of melt in a crystallizing magma chamber, or if it formed during (and possibly initiated) open system thermal metamorphism. The latter could be consistent with a partial melt hypothesis [8,9] while the former implies that simple fractional crystallization can yield the textures present in GRA 98098. The lack of coincidence be-tween pyroxene endmember compositions in Fig. 2b suggest that the bulk composition minus tridymite was not the assemblage in equilibrium with the pyroxene, suggesting that tridymite was present during metamorphism and formed during igneous crystallization. We conclude that the development of the Na-rich plagioclase rims likely occurred during or immediately after peak thermal metamorphism, because eucrites of similar metamorphic grade and texture have unzoned plagioclase (~An92) [2,4,8], and Na zoning is only observed in the plagioclase not included in the tridymite. This suggests that the zoning formed after tridymite formation, and therefore after igneous crystallization. Thus, the timescales calculated via diffusion modeling possibly represent the time interval over which thermal metamorphism occurred. Cooling rates approximated for the Vestan crust predict that the crust cooled below 300°C around 35-40 Ma after formation[10]. This is consistent with our modeling results that predict formation of the Na rich plagioclase rims occurring at higher temperatures over a period of 0.5 to 7 Ma years. Future work. Additional thermodynamic modeling work will focus on selecting an equilibrated bulk rock domain in which to elucidate metamorphic conditions. Diffusion models currently provide a minimum time-scale, since diffusion slows down as the system cools. Future work with will focus on integrating cooling into the diffusion models and constraining the depth at which thermal metamorphism occurs because it could be used to determine whether the range of time-scales calculated for thermal metamorphism are consistent with the geologic environment.

J S Gorce↗