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Abstract. Earth and other terrestrial and icy planetary bodies deform viscoelastically under various forces. Numerical modeling plays a critical role in understanding the nature of various dynamic deformation processes. This article introduces a newly developed open-source package, CitcomSVE-3.0, which efficiently solves the viscoelastic deformation of planetary bodies. Based on its predecessor, CitcomSVE-2.1, CitcomSVE-3.0 is updated to account for three-dimensional elastic compressibility and depth-dependent density, which are particularly important in modeling horizontal displacement for viscoelastic deformation. We benchmark CitcomSVE-3.0 against a semi-analytical code for two types of loading problems: (1) single harmonic loads on the surface or as a tidal force and (2) the glacial isostatic adjustment (GIA) problem with a realistic ice sheet loading history (ICE-6G_D) and an updated version of sea level equations. The benchmark results presented here demonstrate the accuracy and efficiency of this package. CitcomSVE-3.0 shows second-order accuracy in terms of spatial resolution. For typical GIA modeling with a 122 kyr glaciation–deglaciation history, a surface horizontal resolution of ∼50 km, and a time increment of 125 years, this takes ∼3 h on 384 CPU cores to complete, with displacement rate errors of less than 5 %. 

Abstract Two commonly used ice models that are constructed using glacial isostatic adjustment (GIA) modeling are the ICE‐6G and ANU ice models. In this study, we examined the relationships among mantle viscosity, ice models and relative sea level (RSL) data through an analytic GIA model. In general, almost all the pairs of RSL data sets and ice models we considered appear to be consistent with a mantle viscosity structure with a factor of 10–20 viscosity increase from the upper to lower mantles. By using the GIA model with the viscosity structure that produces a minimum model‐data misfit, we constructed the temporal and spatial distributions of misfit (i.e., misfit maps) to different RSL data sets, for both the ICE‐6G and ANU ice models. While the misfit maps at different times clearly show that more observations are desired to constrain ice models, we propose that the spatial and temporal misfit maps should be used to revise the existing ice models to further improve the fit to RSL data. In our initial proof of concept attempts to modify ICE‐6G by adding more ice to it, the three modified ICE‐6G ice models we considered all significantly improve the fit to the far‐field RSL data, although additional effort is needed to reduce misfit to near field RSL data. Finally, we emphasize that RSL at different far‐field sites may differ by up to ∼25 m at the Last Glacial Maximum (LGM) (∼26 ka), suggesting the need for a sufficiently large number of far‐field RSL data in determining the total melt ice volume since the LGM. 

Mantle viscosity exerts important controls on the long-term (i.e., >106 years) dynamics of the mantle and lithosphere and the short-term (i.e., 10 to 104 years) crustal motion induced by loading forces including ice melting, sea-level changes, and earthquakes. However, mantle viscosity structures inferred from modeling observations associated with mantle dynamic and loading processes may differ significantly and remain a hotly debated topic over recent decades. In this study, we investigate the effects of mantle viscosity structures on observations of the geoid, mantle structures, and present-day crustal motions and time-varying gravity by considering five representative mantle viscosity structures in models of mantle convection and glacial isostatic adjustment (GIA). These five viscosity models fall into two categories: 1) two viscosity models derived from modeling the geoid in mantle convection models with ~100 times more viscous lower mantle than the upper mantle, and 2) the other three with less viscosity increase from the upper to lower mantles that are derived from modeling the late Pleistocene and Holocene relative sea level changes and other observations in GIA models. Our convection models use the plate motion history for the last 130 Myrs as the surface boundary conditions and depth- and temperature-dependent viscosity to predict the present-day convective mantle structure of subducted slabs and the intermediate wavelength (degrees 4–12) geoid. Our GIA models using different ice history models (e.g., ICE-6 G and ANU) compute the GIA-induced present-day crustal motions and time-varying gravity. Our calculations demonstrate that while the viscosity models with a higher viscosity in the lower mantle (~2 × 1022 Pa.s) reproduce the degrees 4–12 geoid and seismic slab structures, they significantly over-predict the geodetic (i. e., GPS and GRACE) observations of crustal motions and time varying gravity. Our calculations also show that while two viscosity models derived from fitting the RSL data with averaged mantle viscosity of ~1021 Pa.s for the top 1200 km of the mantle reproduce well the geodetic observations independent of ice models, they fail to explain the geoid and seismic slab structures. Therefore, our study highlights the persisting conundrum of mantle viscosity structures derived from different observations. We also discuss a number of possible ways including transient, stress-dependent and 3-D viscosity to resolve this important issue in Geodynamics. 

This paper proposes a differential burn-in policy that considers the spatial nonhomogeneous distribution of defects in semiconductor manufacturing. Due to the nonhomogeneous distribution of spatial defects, devices at different locations on a semiconductor wafer may exhibit different probabilities of being defective. Unlike conventional burn-in policies, which subject all devices to the same burn-in test, the differential burn-in policy can take different actions for different devices, i.e., acceptance without burn-in, rejection without burn-in, or burn-in with a certain duration. A mixed integer nonlinear programming model is developed to find the cost-optimal decisions. A numerical example is used to demonstrate the potential application of the proposed burn-in policy. 

The development of anode materials with high-rate capability is critical to high-power lithium batteries. T-Nb 2 O 5 has been widely reported to exhibit pseudocapacitive behavior and fast lithium storage capability. However, the other polymorphs of Nb 2 O 5 prepared at higher temperatures have the potential to achieve even higher specific capacity and tap density than T-Nb 2 O 5 , offering higher volumetric power and energy density. Here, micrometer-sized H-Nb 2 O 5 with rich Wadsley planar defects (denoted as d-H-Nb 2 O 5 ) is designed for fast lithium storage. The performance of H-Nb 2 O 5 with local rearrangements of [NbO 6 ] octahedra blocks surpasses that of T-Nb 2 O 5 in terms of specific capacity, rate capability, and stability. A wide range variation in the valence of niobium ions upon lithiation was observed for defective H-Nb 2 O 5 via operando X-ray absorption spectroscopy. Operando extended X-ray absorption fine structure and ex situ Raman spectroscopy analyses reveal a large and reversible distortion of the structure in the two-phase region. Computation and ex situ X-ray diffraction analysis reveal that the shear structure expands along major lithium diffusion pathways and contracts in the direction perpendicular to the shear plane. Planar defects relieve strain through perpendicular arrangements of blocks, minimizing volume change and enhancing structural stability. In addition, strong Li adsorption on planar defects enlarges intercalation capacity. Different from nanostructure engineering, our strategy to modify the planar defects in the bulk phase can effectively improve the intrinsic properties. The findings in this work offer new insights into the design of fast Li-ion storage materials in micrometer sizes through defect engineering, and the strategy is applicable to the material discovery for other energy-related applications.