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In nature, high-speed rain drops often impact and spread on curved surfaces, e.g., leaves and animal bodies. Although a drop's impact on a surface is a traditional topic for industrial applications, drop-impact dynamics on curved surfaces are less known. In the present study, we examine the time-dependent spreading dynamics of a drop onto a curved hydrophobic surface. We also observed that a drop on a curved surface spreads farther than one on a flat surface. To further understand the spreading dynamics, a new analytical model is developed based on volume conservation and temporal energy balance. This model converges to previous models at the early stage and the final stage of droplet impact. We compared the new model with measured spreading lengths on various curved surfaces and impact speeds, which resulted in good agreement. 

Abstract Optimizing group performance is one of the principal objectives that underlie human collaboration and prompts humans to share resources with each other. Connectivity between individuals determines how resources can be accessed and shared by the group members, yet, empirical knowledge on the relationship between the topology of the interconnecting network and group performance is scarce. To improve our understanding of this relationship, we created a game in virtual reality where small teams collaborated toward a shared goal. We conducted a series of experiments on 30 groups of three players, who played three rounds of the game, with different network topologies in each round. We hypothesized that higher network connectivity would enhance group performance due to two main factors: individuals’ ability to share resources and their arousal. We found that group performance was positively associated with the overall network connectivity, although registering a plateau effect that might be associated with topological features at the node level. Deeper analysis of the group dynamics revealed that group performance was modulated by the connectivity of high and low performers in the group. Our findings provide insight into the intricacies of group structures, toward the design of effective human teams. 

Social groups such as schools of fish or flocks of birds display collective dynamics that can be modulated by group leaders, which facilitate decision-making toward a consensus state beneficial to the entire group. For instance, leaders could alert the group about attacking predators or the presence of food sources. Motivated by biological insight on social groups, we examine a stochastic leader–follower consensus problem where information sharing among agents is affected by perceptual constraints and each individual has a different tendency to form social connections. Leveraging tools from stochastic stability and eigenvalue perturbation theories, we study the consensus protocol in a mean-square sense, offering necessary-and-sufficient conditions for asymptotic stability and closed-form estimates of the convergence rate. Surprisingly, the prediction of our minimalistic model share similarities with observed traits of animal and human groups. Our analysis anticipates the counterintuitive result that heterogeneity can be beneficial to group decision-making by improving the convergence rate of the consensus protocol. This observation finds support in theoretical and empirical studies on social insects such as spider or honeybee colonies, as well as human teams, where inter-individual variability enhances the group performance. 

Abstract Amid the ongoing COVID‐19 pandemic, public health authorities and the general population are striving to achieve a balance between safety and normalcy. Ever changing conditions call for the development of theory and simulation tools to finely describe multiple strata of society while supporting the evaluation of “what‐if” scenarios. Particularly important is to assess the effectiveness of potential testing approaches and vaccination strategies. Here, an agent‐based modeling platform is proposed to simulate the spreading of COVID‐19 in small towns and cities, with a single‐individual resolution. The platform is validated on real data from New Rochelle, NY—one of the first outbreaks registered in the United States. Supported by expert knowledge and informed by reported data, the model incorporates detailed elements of the spreading within a statistically realistic population. Along with pertinent functionality such as testing, treatment, and vaccination options, the model accounts for the burden of other illnesses with symptoms similar to COVID‐19. Unique to the model is the possibility to explore different testing approaches—in hospitals or drive‐through facilities—and vaccination strategies that could prioritize vulnerable groups. Decision‐making by public authorities could benefit from the model, for its fine‐grain resolution, open‐source nature, and wide range of features.