Influence of Charge Carrier Mobility on the Performance of Organic Solar Cells

The power conversion efficiency of organic solar cells based on donor--acceptor blends is governed by an interplay of polaron pair dissociation and bimolecular polaron recombination. Both processes are strongly dependent on the charge carrier mobility, the dissociation increasing with faster charge transport, with raised recombination losses at the same time. Using a macroscopic effective medium simulation, we calculate the optimum charge carrier mobility for the highest power conversion efficiency, for the first time accounting for injection barriers and a reduced Langevin-type recombination. An enhancement of the charge carrier mobility from $10^{-8}$m$^2$/Vs for state of the art polymer:fullerene solar cells to about $10^{-6}$m$^2$/Vs, which yields the maximum efficiency, corresponds to an improvement of only about 20% for the given parameter set.Comment: 3 pages, 4 figure

Online and quasi-online colorings of wedges and intervals

We consider proper online colorings of hypergraphs defined by geometric regions. We prove that there is an online coloring algorithm that colors $N$ intervals of the real line using $\Theta(\log N/k)$ colors such that for every point $p$, contained in at least $k$ intervals, not all the intervals containing $p$ have the same color. We also prove the corresponding result about online coloring a family of wedges (quadrants) in the plane that are the translates of a given fixed wedge. These results contrast the results of the first and third author showing that in the quasi-online setting 12 colors are enough to color wedges (independent of $N$ and $k$). We also consider quasi-online coloring of intervals. In all cases we present efficient coloring algorithms

Hyperbolicity, degeneracy, and expansion of random intersection graphs

We establish the conditions under which several algorithmically exploitable structural features hold for random intersection graphs, a natural model for many real-world networks where edges correspond to shared attributes. Specifically, we fully characterize the degeneracy of random intersection graphs, and prove that the model asymptotically almost surely produces graphs with hyperbolicity at least $\log{n}$. Further, we prove that in the parametric regime where random intersection graphs are degenerate an even stronger notion of sparseness, so called bounded expansion, holds with high probability. We supplement our theoretical findings with experimental evaluations of the relevant statistics.Comment: Updating license to CC-B

Scaling Exponents for Ordered Maxima

We study extreme value statistics of multiple sequences of random variables. For each sequence with N variables, independently drawn from the same distribution, the running maximum is defined as the largest variable to date. We compare the running maxima of m independent sequences, and investigate the probability S_N that the maxima are perfectly ordered, that is, the running maximum of the first sequence is always larger than that of the second sequence, which is always larger than the running maximum of the third sequence, and so on. The probability S_N is universal: it does not depend on the distribution from which the random variables are drawn. For two sequences, S_N ~ N^(-1/2), and in general, the decay is algebraic, S_N ~ N^(-\sigma_m), for large N. We analytically obtain the exponent sigma_3= 1.302931 as root of a transcendental equation. Furthermore, the exponents sigma_m grow with m, and we show that sigma_m ~ m for large m.Comment: 10 pages, 6 figure