Random networks are intensively used as null models to investigate properties of complex networks. We describe an efficient and accurate algorithm to generate arbitrarily two-point degree-degree correlated undirected random networks without self-edges or multiple edges among vertices. With the goal to systematically investigate the influence of two-point correlations, we furthermore develop a formalism to construct a joint degree distribution P(j,k) , which allows one to fix an arbitrary degree distribution P(k) and an arbitrary average nearest neighbor function k_{nn}(k) simultaneously. Using the presented algorithm, this formalism is demonstrated with scale-free networks [P(k) proportional, variantk;{-gamma}] and empirical complex networks [ P(k) taken from network] as examples. Finally, we generalize our algorithm to annealed networks which allows networks to be represented in a mean-field-like manner.

No abstract

The way cooperation organizes dynamically strongly depends on the topology of the underlying interaction network. We study this dependence using heterogeneous scale-free networks with different levels of (a) degree-degree correlations and (b) enhanced clustering, where the number of neighbors of connected nodes are correlated and the number of closed triangles are enhanced, respectively. Using these networks, we analyze a finite population analog of the evolutionary replicator dynamics of the prisoner's dilemma, the latter being a two-player game with two strategies, defection and cooperation, whose payoff matrix favors defection. Both topological features significantly change the dynamics with respect to the one observed for fully randomized scale-free networks and can strongly facilitate cooperation even for a large temptation to defect, and should hence be considered as important factors in the evolution and sustainment of cooperation.

No abstract

Lead halide perovskite solar cells afford high power conversion efficiencies, even though the photoactive layer is formed in a solution process. At the same time, solution processing may impose some severe dewetting issues, especially if organic, hydrophobic charge transport layers are considered. Ultimately, very narrow processing windows with a relatively large spread in device performance and a considerable lab-to-lab variation result. Here, we unambiguously identify dimethylsulfoxide (DMSO), which is commonly used as a co-solvent and complexing agent, to be the main reason for dewetting of the precursor solution on hydrophobic hole transport layers, such as polytriarylamine, in a gas-quenching-assisted deposition process. In striking contrast, we will show that N-methyl-2-pyrrolidon (NMP), which has a lower hydrophilic–lipophilic-balance, can be favorably used instead of DMSO to strongly mitigate these dewetting issues. The resulting high-quality perovskite layers are extremely tolerant with respect to the mixing ratio (NMP/dimethylformamide) and other process parameters. Thus, our findings afford an outstandingly robust, easy to use, and fail-safe deposition technique, yielding single (MAPbI3) and double (FA0.94Cs0.06PbI3) cation perovskite solar cells with high efficiencies (∼18.5%). Most notably, the statistical variation of the devices is significantly reduced, even if the deposition process is performed by different persons. We foresee that our results will further the reliable preparation of perovskite thin films and mitigate process-to-process variations that still hinder the prospects of upscaling perovskite solar technology.

No abstract

No abstract

No abstract