Neighbor selection and hitting probability in small-world graphs

Small-world graphs, which combine randomized and structured elements, are seen as prevalent in nature. Jon Kleinberg showed that in some graphs of this type it is possible to route, or navigate, between vertices in few steps even with very little knowledge of the graph itself. In an attempt to understand how such graphs arise we introduce a different criterion for graphs to be navigable in this sense, relating the neighbor selection of a vertex to the hitting probability of routed walks. In several models starting from both discrete and continuous settings, this can be shown to lead to graphs with the desired properties. It also leads directly to an evolutionary model for the creation of similar graphs by the stepwise rewiring of the edges, and we conjecture, supported by simulations, that these too are navigable.Comment: Published in at http://dx.doi.org/10.1214/07-AAP499 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Extraction Current Transients for Selective Charge-Carrier Mobility Determination in Non-Fullerene and Ternary Bulk Heterojunction Organic Solar Cells

The field of organic solar cells has recently gained broad research interest due to the introduction of non-fullerene small-molecule acceptors. The rapid improvement in solar cell efficiency put increased demand on moving toward scalable device architectures. An essential step toward this is enabling thicker active layers for which the hole and electron mobilities and their ratio become increasingly important. In this work, we demonstrate selective charge-carrier mobility determination using the charge extraction by a linearly increasing voltage (CELIV) method. By tuning the contact properties of the solar cell diodes, the hole and electron mobilities are determined separately using the recently developed metal–intrinsic semiconductor–metal-CELIV (MIM-CELIV) technique. Balanced mobility is measured both in non-fullerene and in ternary blends with the recently published PBBF11 polymer. The mobility results are confirmed using the well-established metal–insulator–semiconductor (MIS) and photo-CELIV techniques

Decentralized Search with Random Costs

A decentralized search algorithm is a method of routing on a random graph that uses only limited, local, information about the realization of the graph. In some random graph models it is possible to define such algorithms which produce short paths when routing from any vertex to any other, while for others it is not. We consider random graphs with random costs assigned to the edges. In this situation, we use the methods of stochastic dynamic programming to create a decentralized search method which attempts to minimize the total cost, rather than the number of steps, of each path. We show that it succeeds in doing so among all decentralized search algorithms which monotonically approach the destination. Our algorithm depends on knowing the expected cost of routing from every vertex to any other, but we show that this may be calculated iteratively, and in practice can be easily estimated from the cost of previous routes and compressed into a small routing table. The methods applied here can also be applied directly in other situations, such as efficient searching in graphs with varying vertex degrees

Adaptive Dynamics of Realistic Small-World Networks

Continuing in the steps of Jon Kleinberg's and others celebrated work on decentralized search in small-world networks, we conduct an experimental analysis of a dynamic algorithm that produces small-world networks. We find that the algorithm adapts robustly to a wide variety of situations in realistic geographic networks with synthetic test data and with real world data, even when vertices are uneven and non-homogeneously distributed. We investigate the same algorithm in the case where some vertices are more popular destinations for searches than others, for example obeying power-laws. We find that the algorithm adapts and adjusts the networks according to the distributions, leading to improved performance. The ability of the dynamic process to adapt and create small worlds in such diverse settings suggests a possible mechanism by which such networks appear in nature

Energetics and Kinetics Requirements for Organic Solar Cells to Break the 20% Power Conversion Efficiency Barrier

The thermodynamic limit for the efficiency of solar cells is predominantly defined by the energy bandgap of the used semiconductor. In case of organic solar cells both energetics and kinetics of three different species play role: excitons, charge transfer states and charge separated states. In this work, we clarify the effect of the relative energetics and kinetics of these species on the recombination and generation dynamics. Making use of detailed balance, we develop an analytical framework describing how the intricate interplay between the different species influence the photocurrent generation, the recombination, and the open-circuit voltage in organic solar cells. Furthermore, we clarify the essential requirements for equilibrium between excitons, CT states and charge carriers to occur. Finally, we find that the photovoltaic parameters are not only determined by the relative energy level between the different states but also by the kinetic rate constants. These findings provide vital insights into the operation of state-of-art non-fullerene organic solar cells with low offsets