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Abstract As the United States phases out traditional fossil fuels in favor of renewable energy sources, it is important to capitalize on all available avenues to increase renewable penetration. In the last decade, the costs associated with residential solar photovoltaic (PV) installations have decreased significantly, providing more homeowners with the opportunity to generate their own clean electricity. Research has found that the decision to invest in a residential solar PV system is guided by economic, social, and personal factors. Accounting for such complexities, the joint power of agent-based modeling and social network analysis is leveraged in this study to evaluate the effect of social influence on solar PV adoption. Featuring residential consumer agents with data-driven attributes, a logistic regression function to predict solar adoption, and random and small-world social network implementations, this work simulates residential solar PV adoption in New Jersey. Results indicate that including social influence in an agent-based electricity system model leads to increased installed residential solar capacity, but not necessarily higher adoption rates. These findings suggest that, with an understanding of the intricacies of consumer social networks, there are potential opportunities to bolster residential solar installations through low-cost social campaigns that motivate individuals to adopt home solar through their social ties. 

The relativistic Vlasov-Maxwell-Landau (r-VML) system and the relativistic Landau (r-LAN) equation are fundamental models that describe the dynamics of an electron gas. In this paper, we introduce a novel weighted energy method and establish the validity of the Hilbert expansion for the one-species r-VML system and r-LAN equation. As the Knudsen number shrinks to zero, we rigorously demonstrate the relativistic Euler-Maxwell limit and relativistic Euler limit, respectively. This successfully resolves the long-standing open problem regarding the hydrodynamic limits of Landau-type equations.