Social exclusion, keeping free riders from benefit sharing, plays an important role in sustaining cooperation in our world. Here we propose two different exclusion regimes, namely, peer exclusion and pool exclusion, to investigate the evolution of social exclusion in finite populations. In the peer exclusion regime, each excluder expels all the defectors independently, and thus bears the total cost on his own, while in the pool exclusion regime, excluders spontaneously form an institution to carry out rejection of the free riders, and each excluder shares the cost equally. In a public goods game containing only excluders and defectors, it is found that peer excluders outperform pool excluders if the exclusion costs are small, and the situation is converse once the exclusion costs exceed some critical points, which holds true for all the selection intensities and different update rules. Moreover, excluders can dominate the whole population under a suitable parameters range in the presence of second-order free riders (cooperators), showing that exclusion has prominent advantages over common costly punishment. More importantly, our finding indicates that the group exclusion mechanism helps the cooperative union to survive under unfavorable conditions. Our results may give some insights into better understanding the prevalence of such a strategy in the real world and its significance in sustaining cooperation.

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Rockfalls and rockslides often occur in mountainous areas, and they may develop into rock avalanches because of fragmentation. A series of laboratory experiments were conducted to study the contributions of rock mass structure to the emplacement of fragmenting rockfalls and rockslides. In these experiments, we considered the process of breakable analog blocks with different structures sliding along an inclined plane, impacting at the kink point with a horizontal plane where deposition occurs. The results show that the initial geometrical subdivision (i.e., the rock mass structure) of the source rock can greatly influence the impact of the fragmentation process and total runout, while the degree of fragmentation controls the travel distance of the center of mass. The occurrence of transversal discontinuities enhances the momentum transfer efficiency from the rear to the front part of the rock mass. A negative correlation between the apparent friction coefficient (linked to the total runout) and equivalent friction coefficient (linked to the center of mass runout) was found, which appears to be induced by fragmentation. We proposed a new fragmentation-spreading model to describe this negative correlation. This simple physical model supports the importance of fragmentation in rock fragment trajectories and the runout of rockfalls and rockslides. Fragmentation is an energy-sinking process that will shorten the runout of the center of mass. Thus, we suggest that impact fragmentation does not fully account for the long runout of large rockfalls and rockslides.

In this work, a series of Cu/ZnO/ZnAl 2 O 4 catalysts with different metal molar fractions (Cu : Zn : Al) were successfully prepared using a one-pot method via the evaporation-induced self-assembly (EISA) of Pluronic P123 and the corresponding metal precursors. The catalysts were characterized using N 2 adsorption, H 2 temperatureprogrammed reduction (H 2 -TPR), X-ray diffraction (XRD), transmission electron microscopy (TEM) and X-ray photoelectron spectra (XPS). The catalytic properties of the resulting Cu/ZnO/ZnAl 2 O 4 with different molar fractions of metals were investigated for the selective hydrogenolysis of glycerol to 1,2-propanediol (1,2-PDO). It was observed that the ZnAl 2 O 4 support exerts a strong positive effect on the catalytic activity of the copper-based catalysts, and the presence of ZnO further improves the catalytic activity of the Cu/ZnAl 2 O 4 catalysts. The Cu/ZnO/ZnAl 2 O 4 catalyst (Cu 10 Zn 30 Al 60 , Cu/Zn/Al molar ratio is 10 : 30 : 60), which was the best catalyst, exhibited the highest yield (79%) of 1,2-PDO with 85.8% glycerol conversion and 92.1% 1,2-PDO selectivity at 180 °C reaction temperature in 80 wt% glycerol aqueous solution over 10 h reaction time. The high catalytic activity was attributed to the presence of the ZnAl 2 O 4 support, the strong interaction between ZnO and Cu nanoparticles and the small particle size of ZnO and Cu. Moreover, the Cu/ZnO/ZnAl 2 O 4 catalysts exhibited higher stability than Cu/ZnO and Cu/ZnO/Al 2 O 3 catalysts prepared by a co-precipitation method during consecutive cycling experiments, which is due to the high chemical and thermal stability of crystalline ZnAl 2 O 4 under harsh reaction conditions.

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