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Hypernetworks are ubiquitous in real-world systems. They provide a powerful means of accurately depicting networks of different types of entity and will attract more attention from researchers in the future. Most previous hypernetwork research has been focused on the application and modeling of uniform hypernetworks, which are based on uniform hypergraphs. However, random hypernetworks are generally more common, therefore, it is useful to investigate the evolution mechanisms of random hypernetworks. In this paper, we construct three dynamic evolutional models of hypernetworks, namely the equal-probability random hypernetwork model, the Poisson-probability random hypernetwork model and the certain-probability random hypernetwork model. Furthermore, we analyze the hyperdegree distributions of the three models with mean-field theory, and we simulate each model numerically with different parameter values. The simulation results agree well with the results of our theoretical analysis, and the findings indicate that our models could help understand the structure and evolution mechanisms of real systems.

The study on the evolution of natural ferroan brucite (MgFe(OH)${}_2)$ was beneficial to discovering the function of brucite in the geologic cycle and directing the reasonable utilization of brucite resources. In this study, natural MgFe(OH)₂ was characterized in detail and Rietveld refinement was employed to determine the precise content and existing environment of Fe${}^{2+}$. The reaction products of MgFe(OH)₂ under various atmospheric conditions, including CO₂, O₂ and a mixed atmosphere of CO₂ and O₂ were innovatively investigated to gain insights into the evolution process and the crucial role played by Fe${}^{2+}$. Accordingly, the evolution mechanism of MgFe(OH)₂ under different atmospheres was afforded based on the characterization and molecular simulations like electron transfer and binding energy. Fe${}^{2+}$ in MgFe(OH)₂ layers could be oxidized by O₂ easily and give positive layers, CO${}_3^{2-}$ produced by CO₂ dissolving in water simultaneously was attracted to finally produce CO${}_3^{2-}$ intercalated MgFe- layered double hydroxides (MgFe-CO${}_3^{2-}$-LDHs) which could be used as adsorbents, catalysts and so on. This process was supported by thermodynamics and also the dominant evolution route due to the dynamic reason. The existence of Fe${}^{2+}$ in MgFe(OH)₂ resulted in the diversity of the evolution products. This work highlighted the composition and structure of evolution products of natural MgFe(OH)₂ under different environment as well as its possible application field.