Spread‐out percolation in ℝd

Fix d ≥ 2, and let X be either ℤ^d or the points of a Poisson process in ℝ^d of intensity 1. Given parameters r and p, join each pair of points of X within distance r independently with probability p. This is the simplest case of a “spread‐out” percolation model studied by Penrose [Ann Appl Probab 3 (1993) 253–276], who showed that, as r → ∞, the average degree of the corresponding random graph at the percolation threshold tends to 1, i.e., the percolation threshold and the threshold for criticality of the naturally associated branching process approach one another. Here we show that this result follows immediately from of a general result of [3] on inhomogeneous random graphs. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007     

Fast ortho-para conversion of H2 adsorbed at copper surface step atoms

Ortho-para conversion of H2 adsorbed at the step atoms of a Cu(510) surface proceeds with a short conversion time constant around 1 s as observed in electron-energy-loss measurements of rotational populations. We suggest that this rapid conversion is related to the special character of the adsorption state, which involves a short H2-Cu bond length of 1.8 A. On the flat Cu(100) surface, conversion is found to occur at active sites, most likely step atoms.     

Constructive cooperative coevolution for large-scale global optimisation

This paper presents the Constructive Cooperative Coevolutionary (\(\mathrm {C}^3\)) algorithm, applied to continuous large-scale global optimisation problems. The novelty of \(\mathrm {C}^3\) is that it utilises a multi-start architecture and incorporates the Cooperative Coevolutionary algorithm. The considered optimisation problem is decomposed into subproblems. An embedded optimisation algorithm optimises the subproblems separately while exchanging information to co-adapt the solutions for the subproblems. Further, \(\mathrm {C}^3\) includes a novel constructive heuristic that generates different feasible solutions for the entire problem and thereby expedites the search. In this work, two different versions of \(\mathrm {C}^3\) are evaluated on high-dimensional benchmark problems, including the CEC’2013 test suite for large-scale global optimisation. \(\mathrm {C}^3\) is compared with several state-of-the-art algorithms, which shows that \(\mathrm {C}^3\) is among the most competitive algorithms. \(\mathrm {C}^3\) outperforms the other algorithms for most partially separable functions and overlapping functions. This shows that \(\mathrm {C}^3\) is an effective algorithm for large-scale global optimisation. This paper demonstrates the enhanced performance by using constructive heuristics for generating initial feasible solutions for Cooperative Coevolutionary algorithms in a multi-start framework.     

Ionic-charge dependence of the intermolecular coulombic decay time scale for aqueous ions probed by the core-hole clock

Auger electron spectroscopy combined with theoretical calculations has been applied to investigate the decay of the Ca 2p core hole of aqueous Ca(2+). Beyond the localized two-hole final states on the calcium ion, originating from a normal Auger process, we have further identified the final states delocalized between the calcium ion and its water surroundings and produced by core level intermolecular Coulombic decay (ICD) processes. By applying the core-hole clock method, the time scale of the core level ICD was determined to be 33 ± 1 fs for the 2p core hole of the aqueous Ca(2+). The comparison of this time constant to those associated with the aqueous K(+), Na(+), Mg(2+), and Al(3+) ions reveals differences of 1 and up to 2 orders of magnitude. Such large variations in the characteristic time scales of the core level ICD processes is qualitatively explained by different internal decay mechanisms in different ions as well as by different ion-solvent distances and interactions.     

Upper tails for counting objects in randomly induced subhypergraphs and rooted random graphs

General upper tail estimates are given for counting edges in a random induced subhypergraph of a fixed hypergraph ℋ, with an easy proof by estimating the moments. As an application we consider the numbers of arithmetic progressions and Schur triples in random subsets of integers. In the second part of the paper we return to the subgraph counts in random graphs and provide upper tail estimates in the rooted case.     

Quantum Mechanical Calculations of Redox Potentials of the Metal Clusters in Nitrogenase

We have calculated redox potentials of the two metal clusters in Mo-nitrogenase with quantum mechanical (QM) calculations. We employ an approach calibrated for iron–sulfur clusters with 1–4 Fe ions, involving QM-cluster calculations in continuum solvent and large QM systems (400–500 atoms), based on structures from combined QM and molecular mechanics (QM/MM) geometry optimisations. Calculations on the P-cluster show that we can reproduce the experimental redox potentials within 0.33 V. This is similar to the accuracy obtained for the smaller clusters, although two of the redox reactions involve also proton transfer. The calculated P¹⁺/P^N redox potential is nearly the same independently of whether P¹⁺ is protonated or deprotonated, explaining why redox titrations do not show any pH dependence. For the FeMo cluster, the calculations clearly show that the formal oxidation state of the cluster in the resting E₀ state is MoIIIFe3IIFe4III , in agreement with previous experimental studies and QM calculations. Moreover, the redox potentials of the first five E₀–E₄ states are nearly constant, as is expected if the electrons are delivered by the same site (the P-cluster). However, the redox potentials are insensitive to the formal oxidation states of the Fe ion (i.e., whether the added protons bind to sulfide or Fe ions). Finally, we show that the later (E₄–E₈) states of the reaction mechanism have redox potential that are more positive (i.e., more exothermic) than that of the E₀/E₁ couple.     

Über den Stark-Effekt einiger Singulettlinien in Erdalkalienspektren

Zeitschrift für Physik A Hadrons and nuclei - Es wird über eine experimentelle Untersuchung des Stark-Effektes einiger Singulettlinien des Cadmiums λ 4663 Å und λ 6439...