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At least 361 records · Page 20

Comparison of conventional and microasperity elastohydrodynamic lubrication of a ballspinning in a nonconforming groove

An analysis was developed for the microasperity elastohydrodynamic lubrication of a ball spinning in a nonconforming groove. This analysis was compared to the conventional elastohydrodynamic analysis of a ball spinning in a nonconforming groove. Rheological models for a di-2-ethylhexyl sebacate, a super-refined naphthenic mineral oil, and a polyphenyl ether (5P4E) were constructed from spinning torque data by using both analyses. The value of the lubricant pressure-viscosity coefficient that makes the data fit the analyses of the fluids differs somewhat from published data. For all three lubricants, an exponential composite model best described the lubricant rheology. Good agreement existed with the experimental and analytical values of torque for both the conventional and microasperity elastohydrodynamic analysis for a spinning ball in a nonconforming groove.

Allen, C. W.↗

Data-scarce surrogate modeling of shock-induced pore collapse process

Understanding the mechanisms of shock-induced pore collapse is of great interest in various disciplines in sciences and engineering, including materials science, biological sciences, and geophysics. However, numerical modeling of the complex pore collapse processes can be costly. To this end, a strong need exists to develop surrogate models for generating economic predictions of pore collapse processes. Here, in this work, we study the use of a data-driven reduced-order model, namely dynamic mode decomposition, and a deep generative model, namely conditional generative adversarial networks, to resemble the numerical simulations of the pore collapse process at representative training shock pressures. Since the simulations are expensive, the training data are scarce, which makes training an accurate surrogate model challenging. To overcome the difficulties posed by the complex physics phenomena, we make several crucial treatments to the plain original form of the methods to increase the capability of approximating and predicting the dynamics. In particular, physics information is used as indicators or conditional inputs to guide the prediction. In realizing these methods, the training of each dynamic mode composition model takes only around 30 s on CPU. In contrast, training a generative adversarial network model takes 8 h on GPU. Moreover, using dynamic mode decomposition, the final-time relative error is around 0.3% in the reproductive cases. We also demonstrate the predictive power of the methods at unseen testing shock pressures, where the error ranges from 1.3 to 5% in the interpolatory cases and 8 to 9% in extrapolatory cases.

97 MATHEMATICS AND COMPUTING↗

A new titanium-bearing calcium aluminosilicate phase. 1: Meteoritic occurrences and formation in synthetic systems

A new titanium-bearing calcium aluminosilicate mineral has been identified in coarse-grained calcium-aluminum-rich inclusions (CAIs) from carbonaceous chondrites. The formula for this phase, which we have temporarily termed 'UNK,' is Ca3Ti(Al,Ti)2(Si,Al)3O14, and it is present in at least 8 of the 20 coarse-grained CAIs from the Allende CV3 chondrite examined as part of this project. The phase occurs in Types A and B1 inclusions as small tabular crystal oriented along two mutually perpendicular planes in melilite. UNK crystallizes from melts in dynamic crystallization experiments conducted in air from four bulk compositions modeled after Types A, B1, B2 and C inclusions. Cooling rates resulting in crystallization of UNK ranged from 0.5 to 200 C/h from maximum (initial) temperatures of 1375 to 1580 C. Only below 1190 C does UNK itself begin to crystallize. To first order, the presence or absence of UNK from individual experiments can be understood in terms of the compositions of residual melts and nucleation probabilities. Compositions of synthetic and meteoritic UNK are very similar in terms of major oxides, differing only in the small amounts of trivalent Ti(7-13% of total Ti) in meteoritic samples. UNK crystallized from the Type A analog is similar texturally to that found in CAIs, although glass, which is typically associated with synthetic UNK, is not observed in the meteoritic occurrences. A low Ti end-member of UNK ('Si-UNK') with a composition near that of Ca3Al2Si4O14 was produced in a few samples from the Type B1 analog. This phase has not been found in the meteoritic inclusions.

Paque, Julie M.↗

A New Titanium-Bearing Calcium Aluminosilicate Phase: Meteoritic Occurrences and Formation in Synthetic Systems - 1

A new titanium-bearing calcium aluminosilicate mineral has been identified in coarse-grained calcium-aluminum-rich inclusions (CAIs) from carbonaceous chondrites. The formula for this phase, which we have temporarily termed "UNK," is Ca3Ti(AlTi)2(Si,Al)3O14, and it is present in at least 8 of the 20 coarse-grained CAIs from the Allende CV3 chondrite examined as part of this project. The phase occurs in Types A and B1 inclusions as small tabular crystals oriented along two mutually perpendicular planes in melilite. UNK crystallizes from melts in dynamic crystallization experiments conducted in air from four bulk compositions modeled after Types A, B1, B2 and C inclusions. Cooling rates resulting in crystallization of UNK ranged from 0.5 to 200 C/h from maximum (initial) temperatures of 1375 to 1580 C. Only below 1190 C does UNK itself begin to crystallize. To first order, the presence or absence of UNK from individual experiments can be understood in terms of the compositions of residual melts and nucleation probabilities. Compositions of synthetic and meteoritic LINK are very similar in terms of major oxides, differing only in the small amounts of trivalent Ti (7-13% of total Ti) in meteoritic samples. UNK crystallized from the Type A analog is similar texturally to that found in CAls, although glass, which is typically associated with synthetic UN& is not observed in meteoritic occurrences. A low Ti end-member of UNK ("Si-UNK") with a composition new that of Ca3Al2Si4O14 was produced in a few samples from the Type B1 analog. This phase has not been found in the meteoritic inclusions.

Paque, Julie M.↗

Examination of Scanning Electron Microscope and Computed Tomography Images of PICA

Micrographs of PICA (Phenolic Impregnated Carbon Ablator) taken using a Scanning Electron Microscope (SEM) and 3D images taken with a Computed Tomography (CT) system are examined. PICA is a carbon fiber based composite (Fiberform ) with a phenolic polymer matrix. The micrographs are taken at different surface depths and at different magnifications in a sample after arc jet testing and show different levels of oxidative removal of the charred matrix (Figs 1 though 13). CT scans, courtesy of Xradia, Inc. of Concord CA, were captured for samples of virgin PICA, charred PICA and raw Fiberform (Fig. 14). We use these images to calculate the thermal conductivity (TC) of these materials using correlation function (CF) methods. CF methods give a mathematical description of how one material is embedded in another and is thus ideally suited for modeling composites like PICA. We will evaluate how the TC of the materials changes as a function of surface depth. This work is in collaboration with ETH-Zurich, which has expertise in high temperature materials and TC modeling (including CF methods).

Lawson, John W.↗

Processing and mechanical characterization of short carbon fiber-reinforced epoxy composites for material extrusion additive manufacturing

Fiber-reinforced polymer composites have been extensively utilized in recent years as feedstock materials for material extrusion additive manufacturing (AM) processes to improve strength, stiffness, and functionality of printed parts over unfilled printed polymers. However, the widespread adoption of AM of fiber-reinforced polymer composites requires a deeper understanding of the process-structure-property relationships in printed components, and such relationships are not well understood yet. Fiber length is critically important to the mechanical performance of short fiber composites, but very few studies to-date have focused on how the fiber length distribution (FLD) evolves during processing of composite feedstocks and how this evolution affects printing behavior and mechanical properties in 3D-printed composites. Here, FLD is measured for carbon fiber reinforced epoxy composites over a wide range of ink compositions and shear mixing times, and the distributions are fit with a Weibull-type distribution function. The effects of FLD on the tradeoff between ink processability, ink rheology, printing behavior and mechanical properties are investigated. Furthermore, the effects of printing parameters (nozzle size and print speed) on mechanical anisotropy and fiber orientation distribution (FOD) in printed composites are explored. Mechanical properties of printed composites are characterized via 3 pt-flexural testing, and microstructure is investigated using optical and scanning electron microscopy (SEM), and x-ray computed tomography. Finally, the fitted Weibull parameters are fed into a composite model that incorporates FLD and FOD, and model predictions are found to be in excellent agreement with experimental observations.

3D printing↗

Oxidation of Boron Nitride in Composites

Boron nitride (BN) is a prime candidate for fiber coatings in silicon carbide (SiC) fiber-reinforced SiC matrix composites. The properties of BN allow the fiber to impart beneficial composite properties to the matrix, even at elevated temperatures. The problem with BN is that it is readily attacked by oxygen. Although BN is an internal component of the composite, a matrix crack or pore can create a path for hot oxygen to attack the BN. This type of attack is not well understood. A variety of phenomena have been observed. These include borosilicate glass formation, volatilization of the BN, and under some conditions, preservation of the BN. In this study at the NASA Lewis Research Center, a series of BN materials and BN-containing model composites were methodically examined to understand the various issues dealing with the oxidation of BN in composites. Initial studies were done with a series of monolithic BN materials prepared by hot pressing and chemical vapor deposition (CVD). From these studies, we found that BN showed a strong orientation effect in oxidation and was extremely sensitive to the presence of water vapor in the environment. In addition, CVD material deposited at a high temperature showed much better oxidation behavior than CVD material deposited at a lower temperature.

Jacobson, Nathan S.↗

Preliminary IHLW Formulation Algorithm Description

This report documents the initial algorithm that could be used by the Waste Treatment and Immobilization Plant (WTP) in batching high-level waste (HLW) and glass-forming chemicals (GFCs) in the HLW melter feed preparation vessel (MFPV) (HFP-VSL-00001 and -00005). Not all Hanford tank waste can be accommodated by the models developed for this report and significant expansion of the model boundaries could be achievable to reduce the WTP mission life and total canister production count. The immobilized HLW (IHLW) must meet a series of constraints to be acceptable for disposal in the Monitored Geologic Repository, which are contained in the Specification 1 of the Contract (DOE 2000), the Waste Acceptance Product Specifications (WAPS, DOE 1996), and the Waste Acceptance System Requirements Document (WASRD, DOE 2007). The IHLW Waste Form Compliance Plan (WCP, 24590-HLW-PL-RT-07-0001, Rev 3) specifies that the formulation algorithm will be developed and used to comply with the constraints associated with glass composition and properties. This report is not an engineering calculation, does not provide design input, and is not an engineering study. Algorithm inputs include the chemical analyses of the blended HLW in the HLW blend vessel (HBV) (HLP-VSL-00028, the volume and composition of the MFPV heel, the volume and composition of the MFPV after waste addition, the volume and composition of MFPV batch after GFC addition, the compositions of individual GFCs, and the mass of glass in each canister. In addition to these inputs, uncertainties in the HLW composition and processing parameters are included in the algorithm. Using the above inputs, the algorithm calculates the following outputs: 1) the volume of HLW to be transferred from the HBV to the MFPV, 2) the mass of each GFC for addition to the MFPV, 3) the composition of the glass that will be produced along with uncertainties, and 4) the predicted properties, with associated uncertainties, of the resulting IHLW. The algorithm uses the property-composition models to calculate properties with associated uncertainties and compares them with various constraints to ensure that a processable feed is formulated and a compliant IHLW is produced. The GFC additions are determined using an optimization approach to provide high confidence that the HLW glass will meet all product quality requirements and key processing constraints. For most HLW batches there are many possible glass compositions that meet all constraints. In these cases, the glass composition is optimized for a series of target component concentrations and target property values. The algorithm also incorporates process measurement and product quality uncertainties, based on the work of Piepel et al. (2005). Estimates of the various process and measurement uncertainties that affect glass compositions and predicted glass properties have been previously reported (Piepel et al. 2005, 2006) and the impacts of these estimated uncertainties on the IHLW composition envelope that meets product quality and processing-related properties with sufficient confidence were evaluated. The details of work performed to date to develop this initial GFC addition and batching algorithm are summarized in Sections 4 and 5. An example data set is used to illustrate the calculations of the algorithm summarized in Section 6. Finally, in Section 7, there is a statement of the required work to achieve a final operational IHLW formulation control algorithm. This report is not an engineering calculation, does not provide design input, and is not an engineering study.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Interlaminar R-Curve Effects in Thermoplastic Composites: Experiments and Model Correlations

The interlaminar fracture behavior of thermoplastic composites under Mode-I and Mode-II static loading is investigated in this research. The material system under consideration is a carbon fiber reinforced low melt semi-crystalline resin TC1225 LMPAEK T700G (T700/LMPAEK)†. Characterization experiments were conducted to measure the load-displacement response, peak load, and propagation of delamination from a pre-implanted Kapton® insert. The Mode-I response was characterized using a double cantilever beam (DCB) test according to the ASTM D5528-22 standard. It was observed that the propagation exhibited significant resistance to delamination growth, i.e., an R-Curve effect. The test data indicated that the steady-state fracture toughness, G SS I , was approximately twice the mean initiation fracture toughness, G Ic . The Mode-II response of an end notch flexure (ENF) specimen tested according to the ASTM D7905-19 standard exhibited an unexpected stable behavior upon attaining peak load. Prior to attaining peak load, the Mode-II response exhibited some non-linearity, which may be attributed to nonlinear bulk material response, e.g., hyper-elasticity, viscoelasticity, plasticity, etc., and potentially friction at the load/support rollers and R-Curve effects. Finite element models based on the Cohesive Zone Method (CZM) and the Virtual Crack Closure Technique (VCCT) were used to predict the DCB and ENF specimen responses. DCB analysis results obtained using G SS I predicted propagation consistent with experimental data. However, results obtained with the as characterized G Ic were inaccurate in predicting delamination growth onset and peak load. ENF analysis results obtained with the as-characterized Mode-II fracture toughness, G IIc , were inaccurate in predicting the peak load and propagation. Hence, R-Curve effects were included in both DCB and ENF simulations, which enabled improved predictions. The experimentally determined Mode-I R-Curve was used for the DCB simulations, whereas an R-Curve was derived for Mode-II assuming that the change in compliance of the specimen was associated with crack growth only.

Prabhakar M Rao↗

Interlaminar R-Curve Effects in Thermoplastic Composites: Experiments and Model Correlations

The interlaminar fracture behavior of thermoplastic composites under Mode-I and Mode-II static loading is investigated in this research. The material system under consideration is a carbon fiber reinforced low melt semi-crystalline resin TC1225 LMPAEK T700G (T700/LMPAEK)†. Characterization experiments were conducted to measure the load-displacement response, peak load, and propagation of delamination from a pre-implanted Kapton® insert. The Mode-I response was characterized using a double cantilever beam (DCB) test according to the ASTM D5528-22 standard. It was observed that the propagation exhibited significant resistance to delamination growth, i.e., an R-Curve effect. The test data indicated that the steady-state fracture toughness, G SS I , was approximately twice the mean initiation fracture toughness, G Ic . The Mode-II response of an end notch flexure (ENF) specimen tested according to the ASTM D7905-19 standard exhibited an unexpected stable behavior upon attaining peak load. Prior to attaining peak load, the Mode-II response exhibited some non-linearity, which may be attributed to nonlinear bulk material response, e.g., hyper-elasticity, viscoelasticity, plasticity, etc., and potentially friction at the load/support rollers and R-Curve effects. Finite element models based on the Cohesive Zone Method (CZM) and the Virtual Crack Closure Technique (VCCT) were used to predict the DCB and ENF specimen responses. DCB analysis results obtained using G SS I predicted propagation consistent with experimental data. However, results obtained with the as characterized G Ic were inaccurate in predicting delamination growth onset and peak load. ENF analysis results obtained with the as-characterized Mode-II fracture toughness, G IIc , were inaccurate in predicting the peak load and propagation. Hence, R-Curve effects were included in both DCB and ENF simulations, which enabled improved predictions. The experimentally determined Mode-I R-Curve was used for the DCB simulations, whereas an R-Curve was derived for Mode-II assuming that the change in compliance of the specimen was associated with crack growth only.

Prabhakar Rao↗

Micromechanical models for textile structural composites

The objective is to develop micromechanical models for predicting the stiffness and strength properties of textile composite materials. Two models are presented to predict the homogeneous elastic constants and coefficients of thermal expansion of a textile composite. The first model is based on rigorous finite element analysis of the textile composite unit-cell. Periodic boundary conditions are enforced between opposite faces of the unit-cell to simulate deformations accurately. The second model implements the selective averaging method (SAM), which is based on a judicious combination of stiffness and compliance averaging. For thin textile composites, both models can predict the plate stiffness coefficients and plate thermal coefficients. The finite element procedure is extended to compute the thermal residual microstresses, and to estimate the initial failure envelope for textile composites.

Marrey, Ramesh V.↗

Modeling creep behavior of fiber composites

A micromechanical model for the creep behavior of fiber composites is developed based on a typical cell consisting of a fiber and the surrounding matrix. The fiber is assumed to be linearly elastic and the matrix nonlinearly viscous. The creep strain rate in the matrix is assumed to be a function of stress. The nominal stress-strain relations are derived in the form of differential equations which are solved numerically for off-axis specimens under uniaxial loading. A potential function and the associated effective stress and effective creep strain rates are introduced to simplify the orthotropic relations.

Chen, J. L.↗

Nonmethane hydrocarbon chemistry in the remote marine boundary layer

A photochemical model of the remote marine boundary layer (MBL) is presented, with focus placed on the role of reactive nonmethane hydrocarbons (NMHC). A wide range of NMHC air-sea fluxes with various relative distributions of NMHC regions are considered. In particular, the flux magnitude at which NMHC emissions become significant, and then dominant, players in MBL chemistry is identified. Emphasis is placed on diurnal variability, diurnal ozone variations and sensitivity to NMHC emission fluxes, to CO, O3, H2O, and UV light, and to kinetics and isometric composition. Model runs indicate that, in the range consistent with current observations, the NMHCs may either dominate MBL chemistry, or simply be contributors at the 10-percent level. These model runs also show that existing observations of NMHCs in ocean water find them to scarce for fluxes from bulk-flux air-sea gas exchange models to be consistent with the fluxes needed in the proposed model to maintain the lowest observed MBL NMHC.

Donahue, Neil M.↗

Improved interfacial li-ion transport in composite polymer electrolytes via surface modification of LLZO

Composite polymer electrolytes that incorporate ceramic fillers in a polymer matrix offer mechanical strength and flexibility as solid electrolytes for lithium metal batteries. However, fast Li + transport between polymer and Li + -conductive filler phases is not a simple achievement due to high barriers for Li + exchange across the interphase. This study demonstrates how modification of Li 7 La 3 Zr 2 O 12 (LLZO) nanofiller surfaces with silane chemistries influences Li + transport at local and global electrolyte scales. Anhydrous reactions covalently link amine-functionalized silanes [(3-aminopropyl)triethoxysilane (APTES)] to LLZO nanoparticles, which protects LLZO in air. APTES functionalization lowers the poly (ethylene oxide) (PEO)-LLZO interphase resistance to half that of unmodified LLZO and increases effective Li + transference number, while insulating Al 2 O 3 completely blocks ion exchange and lowers transference number and conductivity in PEO-lithium bis(trifluoromethanesulfonyl)imide (LiTFSI)-LLZO composites. Modeling an inner resistive interphase between LLZO and PEO surrounded by an outer conductive interphase explains non-linear conductivity trends. Solid-state 7 Li & 6 Li nuclear magnetic resonance shows Li + only exchanges between PEO-LiTFSI and some LLZO interphase, with no appreciable Li + transport through bulk LLZO. Surface functionalization is a promising path toward lowering the polymer-ceramic interphase resistance. This work demonstrates that local changes in Li + transport affect macroscopic performance, highlighting the intricate relationships between all interfaces in inherently heterogeneous composite polymer electrolytes.

25 ENERGY STORAGE↗

A Shell/3D Modeling Technique for Delaminations in Composite Laminates

A shell/3D modeling technique was developed for which a local solid finite element model is used only in the immediate vicinity of the delamination front. The goal was to combine the accuracy of the full three-dimensional solution with the computational efficiency of a plate or shell finite element model. Multi-point constraints provide a kinematically compatible interface between the local 3D model and the global structural model which has been meshed with plate or shell finite elements. For simple double cantilever beam (DCB), end notched flexure (ENF), and single leg bending (SLB) specimens, mixed mode energy release rate distributions were computed across the width from nonlinear finite element analyses using the virtual crack closure technique. The analyses served to test the accuracy of the shell/3D technique for the pure mode I case (DCB), mode II case (ENF) and a mixed mode I/II case (SLB). Specimens with a unidirectional layup where the delamination is located between two 0 plies, as well as a multidirectional layup where the delamination is located between two non-zero degree plies, were simulated. For a local 3D model extending to a minimum of about three specimen thicknesses in front of and behind the delamination front, the results were in good agreement with mixed mode strain energy release rates obtained from computations where the entire specimen had been modeled with solid elements. For large built-up composite structures modeled with plate elements, the shell/3D modeling technique offers a great potential, since only a relatively small section in the vicinity of the delamination front needs to be modeled with solid elements.

Krueger, Ronald↗

Composite fracture using the normal stress ratio theory

Experiments were performed on center-notched specimens of unidirectional AS4/3501-6 graphite-epoxy subjected to varied far-field loading conditions. Specimens tested include on-axis and off-axis tensile coupons and Iosipescu shear specimens, allowing the study of normal, shear, and combined far-field loading conditions. From the tests, the direction of initial crack extension and the far-field stresses at crack initiation and fracture are obtained. The normal stress ratio theory is subsequently applied within a macroscopic-level homogeneous anisotropic stress solution to predict the direction of crack extension, critical stresses, and other crack growth behavior for the experiments. Comparison between experimental results and theoretical predictions indicates that application of the normal stress ratio theory within a macroscopic-level stress analysis has significant potential as an approach to modeling composite crack growth.

Beuth, J. L., Jr.↗

High Pressure Melting Curve of Fe‐Si: Implication for the Thermal Properties in Mercury's Core

The motion of liquid iron (Fe) alloy materials in the outer core drives the dynamo, which generates Mercury's magnetic field. The assessment of core models requires laboratory measurements of the melting temperature of Fe alloys at high pressure. Here, we experimentally determined the melting curve of Fe9wt%Si and Fe17wt%Si up to 17 GPa using in situ and ex situ measurements of intermetallic fast diffusion that serves as the melting criterion in a large-volume press. Our determined melting slopes are comparable with previous studies up to about 17 GPa. However, when extrapolated, our melting slopes significantly deviate from previous studies at higher pressures. For Mercury's core with a model composition of Fe9wt%Si, the melting temperature-depth profile determined in our study is lower by ∼150–250 K when compared with theoretical calculations. Using the new melting curve of Fe9wt%Si and the electrical resistivity values from a previous study of Fe8.5wt%Si, we estimate that the electronic thermal conductivity of liquid Fe9wt%Si is 30 Wm −1 K −1 at the Mercury's CMB pressure of 5 GPa and 37 Wm −1 K −1 at an assumed ICB of 21 GPa, corresponding to heat flux values of 23 mWm −2 and 32 mWm −2 , respectively. These values provide new constraints on the core models.

58 GEOSCIENCES↗

Global Geodetic Signatures of the Antarctic Ice Sheet

Four scenarios of present day Antarctic ice sheet mass change are developed from comprehensive reviews of the available glaciological and oceanographic evidence. The gridded scenarios predict widely varying contributions to secular sea level change xi ranging from -1.1 to 0.45 mm/yr, and predict polar motion m and time-varying low-degree gravitational coefficients J(sub l) that differ significantly from earlier estimates. A reasonably linear relationship between the rate of sea level change from Antarctica xi(sub A) and the predicted Antarctic J(sub l) is found for the four scenarios. This linearity permits a series of forward models to be constructed that incorporate the effects of ice mass changes in Antarctica, Greenland, and distributed smaller glaciers, as well as postglacial rebound (assuming the ICE-3G deglaciation history), with the goal of obtaining optimum reconciliation between observed constraints on J(sub l) and sea level rise xi. Numerous viable combinations of lower mantle viscosity and hydrologic sources are found that safely "observed" in the range of 1 to 2-2.5 mm/yr and observed J(sub l) for degrees 2, 3, and 4. In contrast, rates of global sea level rise above 2.5 mm/yr are inconsistent with available J(sub l) observations. The successful composite models feature a pair of lower mantle viscosity solutions arising from the sensitivity of J(sub l) to glacial rebound. The paired values are well separated at xi = 1 mm/yr, but move closer together as xi is increased, and, in fact, merge around xi = 2 - 2.5 mm/yr, revealing an intimate relation between xi and preferred lower mantle viscosity. This general pattern is quite robust and persists for different J(sub l) solutions, for variations in source assumptions, and for different styles of lower mantle viscosity stratification. Tighter J(sub l) constraints for l greater than 2 may allow some viscosity stratification schemes and source assumptions to be excluded in the future. For a given total observed xi the sea level rise from Antarctica xi(sub A) is tightly constrained and ranges from 0 to + 1 mr/yr (corresponding to an ablating ice sheet) as estimates of xi are raised from 1 to 2.5 mm/yr. However, when the degree 3 zonal harmonic constraint is removed, the solutions show little sensitivity to Antarctic mass balance, emphasizing the need for a well determined odd-degree secular zonal harmonic for determining polar ice mass balance.

James, Thomas S.↗