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Electrochemical cycling stabilities were compared for undoped and Al/Co dual-doped spinel LiMn2O4 synthesized by solid state reactions. We observed the suppression of particle fracture in Al/Co dual-doped LiMn2O4 during charge/discharge cycling and its distinguishable particle morphology with respect to the undoped material. Systematic first-principles calculations were performed on undoped, Al or Co single-doped, and Al/Co dual-doped LiMn2O4 to investigate their structural differences at the atomistic level. We reveal that while Jahn-Teller distortion associated with the Mn(3+)O6 octahedron is the origin of the lattice strain, the networking -i.e. the distribution of mixed valence Mn ions - is much more important to release the lattice strain, and thus to alleviating particle cracking. The calculations showed that the lattice mismatching between Li(+) intercalation and deintercalation of LiMn2O4 can be significantly reduced by dual-doping, and therefore also the volumetric shrinkage during delithiation. This may account for the near disappearance of cracks on the surface of Al/Co-LiMn2O4 after 350 cycles, while some obvious cracks have developed in undoped LiMn2O4 at similar particle size even after 50 cycles. Correspondingly, Al/Co dual-doped LiMn2O4 showed a good cycling stability with a capacity retention of 84.1% after 350 cycles at a rate of 1C, 8% higher than the undoped phase.

Recently, one type of mesoscale structure called core-periphery (CP) structure has received much attention in complex networks, as the algorithmic detection of such structures makes it possible to discover network features that are not apparent either at the local scale of nodes and edges or at the global scale of summary statistics. The core-periphery structure refers to that core nodes are densely interconnected, while periphery nodes are connected to core nodes to different extents, and periphery nodes are sparsely interconnected. Core-periphery structure containing a single core or multiple cores has been identified in various networks. However, investigation of the detection problems of the core-periphery has not been summarized in the literature. In this paper, we first introduce the definition of the core-periphery structure. The core-periphery structure has been paid more and more attention by researchers in various fields since its introduction, and it has been proved to be a powerful tool to analyze the theory of various topologies in our society, we briefly expounded the application of core-periphery structure in economics, sociology, medicine and other fields, and revealed the huge development potential of this theory. Then, we give a detailed overview of classical detection algorithms since the core-periphery structure theory was proposed. Finally, we give the development characteristics and the possible research directions of the core-periphery detection algorithm.

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