The rational design of high-performance and cheap nanomaterials for multiple sustainable energy storage applications is extremely urgent but remains challenging. Herein, a facile commercial melamine-sponge-directed multicomponent surface self-assembly strategy has been reported to synthesize N-doped carbon aerogels (NCAs) with low density (0.01 g cm(-3)), large open pores, and high surface area (1626 m2 g(-1)). The commercial melamine sponge simultaneously serves as a green N source for N-doping and a 3D scaffold to buffer electrolytes for reducing ion transport resistance and minimizing ion diffusion distance. With their tailored architecture characteristics, the NCAs-based supercapacitor and oxygen reduction electrocatalyst show excellent performance.

A new approach to the computation of correlation functions involving two determinant operators as well as one non-protected single trace operator has recently been developed by Jiang, Komatsu and Vescovi. This correlation function provides the holographic description of the absorption of a closed string by a giant graviton. The analysis has a natural interpretation in the framework of group representation theory, which admits a generalization to general Schur polynomials and restricted Schur polynomials. This generalizes the holographic description to any giant or dual giant gravitons which carry more than one angular momentum on the sphere. For a restricted Schur polynomial labeled by a column with N boxes (dual to a maximal giant graviton) we find evidence in favor of integrability.

Investigation of photoexcited charge transfer mechanism has always been one of the hotspots of the photocatalysis field. In our recent studies, the relative p–n junction was proposed as a new concept, and the built-in electric field formed in the heterojunction is the inner impetus for driving photoexcited charge transfer. Here, a series of g-C3N4/TiO2 samples with different mass percentage contents were synthesized and further characterized by physical and chemical techniques for the investigation of the charge transfer mechanism and internal natural law. The results state clearly that the migration of photoexcited charges belongs to Z-scheme mechanism, which is suitable for as-synthesized g-C3N4/TiO2 samples, whether the main part of the g-C3N4/TiO2 is TiO2 or g-C3N4. The photoexcited electrons enriched in g-C3N4 with a higher negative conduction band (CB) potential have reduction ability to convert O2 into superoxide radicals (•O2 –). Meanwhile, the photoexcited holes in TiO2 with a higher positive valence band (VB) potential have oxidation ability to activate H2O or hydroxyl ions (OH–) to hydroxyl radicals (•OH). Furthermore, the g-C3N4/TiO2 photocatalyst exhibits better photocatalytic performance than TiO2 and g-C3N4. It is encouraging that the abovementioned Z-scheme mechanism of photoexcited charge transfer can also be explained and confirmed by the relative p–n junction theory. The built-in electric field promotes the migration of the photoexcited charges in the heterojunction, and its migration direction is opposite to that of the photoexcited charge in the CB and VB of g-C3N4 and TiO2. Therefore, the relative p–n junction theory not only is used to explicate the migration mechanism and internal natural law of the photoexcited charge in the heterojunction photocatalysts but also has crucial guiding significance for the theoretical design and practical construction of composite photocatalysts.

The transfer mechanism of photogenerated charges (e − and h + ) has always been a research hotspot of the photocatalysis field. Here, a series of WO 3 /ZnO composite photocatalysts with different ratios were synthesized, and importantly, the transfer mechanism of photoexcited charges was systematically studied. By performing various characterizations, the direct Z-scheme of WO 3 /ZnO was proposed, and the results verified that the immanent electric field formed between WO 3 and ZnO semiconductors is the inner impetus of charge transfer. This work distinguished the transfer mechanism of photogenerated charges in the heterojunction photocatalyst by the relative p−n junction theory and can also provide guidance for the construction and application of novel heterojunction photocatalysts in theory and practice.