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  1. Abstract

    The stable reduction theorem says that a family of curves of genus$$g\ge 2$$g2over a punctured curve can be uniquely completed (after possible base change) by inserting certain stable curves at the punctures. We give a new this result for curves defined over$${\mathbb {C}}$$C, using the Kähler–Einstein metrics on the fibers to obtain the limiting stable curves at the punctures.

     
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  2. We prove two new results on the K K -polystability of Q \mathbb {Q} -Fano varieties based on purely algebro-geometric arguments. The first one says that any K K -semistable log Fano cone has a special degeneration to a uniquely determined K K -polystable log Fano cone. As a corollary, we combine it with the differential-geometric results to complete the proof of Donaldson-Sun’s conjecture which says that the metric tangent cone of any point appearing on a Gromov-Hausdorff limit of Kähler-Einstein Fano manifolds depends only on the algebraic structure of the singularity. The second result says that for any log Fano variety with the torus action, K K -polystability is equivalent to equivariant K K -polystability, that is, to check K K -polystability, it is sufficient to check special test configurations which are equivariant under the torus action. 
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  3. Living organisms have evolved, over billions of years, to develop specialized biostructures with switchable adhesion for various purposes including climbing, perching, preying, sensing, and protecting. According to adhesion mechanisms, switchable adhesives can be divided into four categories: mechanically-based adhesion, liquid-mediated adhesion, physically-actuated adhesion and chemically-enhanced adhesion. Mimicking these biostructures could create smart materials with switchable adhesion, appealing for many engineering applications in robotics, sensors, advanced drug-delivery, protein separation, etc. Progress has been made in developing bioinspired materials with switchable adhesion modulated by external stimuli such as electrical signal, magnetic field, light, temperature, pH value, etc. This review will be focused on new advance in biomimetic design and synthesis of the materials and devices with switchable adhesion. The underlying mechanisms, design principles, and future directions are discussed for the development of high-performance smart surfaces with switchable adhesion.

     
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    Abstract The origins of an observed weakly sheared nonturbulent (laminar) layer (WSL), and a strongly sheared turbulent layer above the Equatorial Undercurrent core (UCL) in the eastern equatorial Pacific are studied, based mainly on the data from the Tropical Atmosphere and Ocean mooring array. Multiple-time-scale (from 3 to 25 days) equatorial waves were manifested primarily as zonal velocity oscillations with the maximum amplitudes (from 10 to 30 cm s −1 ) occurring at different depths (from the surface to 85-m depths) above the seasonal thermocline. The subsurface-intensified waves led to vertically out-of-phase shear variations in the upper thermocline via destructive interference with the seasonal zonal flow, opposing the tendency for shear instability. These waves were also associated with depth-dependent, multiple-vertical-scale stratification variations, with phase lags of π /2 or π , further altering stability of the zonal current system to vertical shear. The WSL and UCL were consequently formed by coupling of multiple equatorial waves with differing phases, particularly of the previously identified equatorial mode and subsurface mode tropical instability waves (with central period of 17 and 20 days, respectively, in this study), and subsurface-intensified waves with central periods of 6, 5, and 12 days and velocity maxima at 45-, 87-, and 40-m depths, respectively. In addition, a wave-like feature with periods of 50–90 days enhanced the shear throughout the entire UCL. WSLs and UCLs seem to emerge without a preference for particular tropical instability wave phases. The generation mechanisms of the equatorial waves and their joint impacts on thermocline mixing remain to be elucidated. 
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  7. Electrochemical conversion of carbon dioxide (CO 2 ) to chemicals or fuels can effectively promote carbon capture and utilization, and reduce greenhouse gas emission but a serious impediment to the process is to find highly active electrocatalysts that can selectively produce desired products. Herein, we have established the design principles based on the density functional theory calculations to screen the most promising catalysts from the family of coordinately unsaturated/saturated transition metal (TM) embedded into covalent organic frameworks (TM-COFs). An intrinsic descriptor has been discovered to correlate the molecular structures of the active centers with both the activity and selectivity of the catalysts. Among all the catalysts, the coordinately unsaturated Ni-doped covalent triazine framework (Ni-CTF) is identified as one of the best electrocatalysts with the lowest overpotential (0.34 V) for CO 2 reduction toward CO while inhibiting the formation of the side products, H 2 and formic acid. Compared with coordinately saturated TM-COFs and noble metals ( e.g. Au and Ag), TM-CTFs exhibit higher catalytic activity and stronger inhibition of side products. The predictions are supported by previous experimental results. This study provides an effective strategy and predictive tool for developing desired catalysts with high activity and selectivity. 
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