The rod-structure formalism has played an important role in the study of black holes in D = 4 and 5 dimensions with R × U(1) D−3 isometry. In this paper, we apply this formalism to the study of four-dimensional gravitational instantons with U(1) × U(1) isometry, which could serve as spatial backgrounds for five-dimensional black holes. We first introduce a stronger version of the rod structure with the rod directions appropriately normalised, and show how the regularity conditions can be read off from it. Requiring the absence of conical and orbifold singularities will in general impose periodicity conditions on the coordinates, and we illustrate this by considering known gravitational instantons in this class. Some previous results regarding certain gravitational instantons are clarified in the process. Finally, we show how the rod-structure formalism is able to provide a classification of gravitational instantons, and speculate on the existence of possible new gravitational instantons.
Robust composite structures consisting of Fe3O4 nanoparticles (∼5 nm) embedded in mesoporous carbon spheres with an average size of about 70 nm (IONP@mC) are synthesized by a facile two‐step method: uniform Fe3O4 nanoparticles are first synthesized followed by a post‐synthetic low‐temperature hydrothermal step to encapsulate them in mesoporous carbon spheres. Instead of graphene which has been extensively reported for use in high‐rate battery applications as a carbonaceous material combined with metal oxides mesoporous carbon is chosen to enhance the overall performances. The interconnecting pores facilitate the penetration of electrolyte leading to direct contact between electrochemically active Fe3O4 and lithium ion‐carrying electrolyte greatly facilitating lithium ion transportation. The interconnecting carbon framework provides continuous 3D electron transportation routes. The anodes fabricated from IONP@mC are cycled under high current densities ranging from 500 to 10 000 mA g−1. A high reversible capacity of 271 mAh g−1 is reached at 10 000 mAh g−1 demonstrating its superior high rate performance.
Carbon‐based materials are considered to be one of the most promising materials for negative electrodes of the future, because of their good chemical stability, high electrical conductivity, and environmental benignity. However, to date, the underlying principles of K‐ion storage in carbonaceous anodes remain elusive, which greatly hinders the development of such a category of anodes. Herein, the ultrastable K‐ion storage of carbonaceous anode through systematic analyses, including comprehensive electrochemical characterizations, kinetics calculations, and structural/compositional evolution mechanism studies, is theoretically elucidated and experimentally verified. Specifically, it is found that the uniquely envelope‐like nitrogen‐doped carbon nanosheets with high pseudocapacitive could bring ultrastable storage of potassium ions, delivering a high initial reversible capacity of 367 mAh g−1 at a current density of 50 mA g−1 and retain 70.5 and 75.6% at current densities of 500 and 1000 mA g−1 after 1000th cycle, respectively. This study could enlighten researchers on further progress in the field of carbonaceous K‐ion battery negative electrode with a long cycle life.
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