Surface modification of highly oriented pyrolytic graphite by reaction with atomic nitrogen at high temperatures

Dry etching of {0 0 0 1} basal planes of highly oriented pyrolytic graphite (HOPG) using active nitridation by nitrogen atoms was investigated at low pressures and high temperatures. The etching process produces channels at grain boundaries and pits whose shapes depend on the reaction temperature. For temperatures below 600 °C, the majority of pits are nearly circular, with a small fraction of hexagonal pits with rounded edges. For temperatures above 600 °C, the pits are almost exclusively hexagonal with straight edges. The Raman spectra of samples etched at 1000 °C show the D mode near 1360 cm⁻¹, which is absent in pristine HOPG. For deep hexagonal pits that penetrate many graphene layers, neither the surface number density of pits nor the width of pit size distribution changes substantially with the nitridation time, suggesting that these pits are initiated at a fixed number of extended defects intersecting {0 0 0 1} planes. Shallow pits that penetrate 1-2 graphene layers have a wide size distribution, which suggests that these pits are initiated on pristine graphene surfaces from lattice vacancies continually formed by N atoms. A similar wide size distribution of shallow hexagonal pits is observed in an n-layer graphene sample after N-atom etching.     

Upper bounds on the sum of powers of the degrees of a simple planar graph

For a simple planar graph G and a positive integer k, we prove the upper bound 2(n ? 1)^k + 4^k(n ? 4) + 2·3^k ? 2((δ + 1)^k ? δ^k)(3n ? 6 ? m) on the sum of the kth powers of the degrees of G, where n, m, and δ are the order, the size, and the minimum degree of G, respectively. The bound is tight for all m with 0?3n ? 6 ? m≤?n/2? ? 2 and δ = 3. We also present upper bounds in terms of order, minimum degree, and maximum degree of G. © 2010 Wiley Periodicals, Inc. J Graph Theory 67:112‐123, 2011     

Multiscale simulation reveals multiple pathways for H2 and O2 transport in a [NiFe]-hydrogenase

Hydrogenases are enzymes that catalyze the reversible conversion of hydrogen molecules to protons and electrons. The mechanism by which the gas molecules reach the active site is important for understanding the function of the enzyme and may play a role in the selectivity for hydrogen over inhibitor molecules. Here, we develop a general multiscale molecular simulation approach for the calculation of diffusion rates and determination of pathways by which substrate or inhibitor gases can reach the protein active site. Combining kinetic data from both equilibrium simulations and enhanced sampling, we construct a master equation describing the movement of gas molecules within the enzyme. We find that the time-dependent gas population of the active site can be fit to the same phenomenological rate law used to interpret experiments, with corresponding diffusion rates in very good agreement with experimental data. However, in contrast to the conventional picture, in which the gases follow a well-defined hydrophobic tunnel, we find that there is a diverse network of accessible pathways by which the gas molecules can reach the active site. The previously identified tunnel accounts for only about 60% of the total flux. Our results suggest that the dramatic decrease in the diffusion rate for mutations involving the residue Val74 could be in part due to the narrowing of the passage Val74-Arg476, immediately adjacent to the binding site, explaining why mutations of Leu122 had only a negligible effect in experiment. Our method is not specific to the [NiFe]-hydrogenase and should be generally applicable to the transport of small molecules in proteins.     

Thermodynamics of electron flow in the bacterial deca-heme cytochrome MtrF

Electron-transporting multi-heme cytochromes are essential to the metabolism of microbes that inhabit soils and carry out important biogeochemical processes. Recently the first crystal structure of a prototype bacterial deca-heme cytochrome (MtrF) has been resolved and its electrochemistry characterized. However, the molecular details of electron transport along heme chains in the cytochrome are difficult to access via experiment due to the nearly identical chemical nature of the heme cofactors. Here we employ large-scale molecular dynamics simulations to compute the redox potentials of the 10 hemes of MtrF in aqueous solution. We find that as a whole they fall within a range of ~0.3 V, in agreement with experiment. Individual redox potentials give rise to a free energy profile for electron transport that is approximately symmetric with respect to the center of the protein. Our calculations indicate that there is no significant potential bias along the orthogonal octa- and tetra-heme chains, suggesting that under aqueous conditions MtrF is a nearly reversible two-dimensional conductor.     

Challenging the curse of dimensionality in multivariate local linear regression

Local polynomial fitting for univariate data has been widely studied and discussed, but up until now the multivariate equivalent has often been deemed impractical, due to the so-called curse of dimensionality. Here, rather than discounting it completely, we use density as a threshold to determine where over a data range reliable multivariate smoothing is possible, whilst accepting that in large areas it is not. The merits of a density threshold derived from the asymptotic influence function are shown using both real and simulated data sets. Further, the challenging issue of multivariate bandwidth selection, which is known to be affected detrimentally by sparse data which inevitably arise in higher dimensions, is considered. In an effort to alleviate this problem, two adaptations to generalized cross-validation are implemented, and a simulation study is presented to support the proposed method. It is also discussed how the density threshold and the adapted generalized cross-validation technique introduced herein work neatly together.     

Numerical and experimental investigation of the turbulent flow through a low-pressure turbine cascade in the endwall region

In the present work, direct numerical simulations (DNS) of the flow through a low-pressure linear turbine cascade T106 with parallel endwalls were conducted to investigate the effects of unsteady passing wakes of the upstream blade row on the secondary flow in the endwall region of the passage. The impact of the wakes on the secondary flow is discussed by means of the time-averaged values. Furthermore, the results of DNS are compared with experimental data. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)