On the Lipschitz Continuity of Spectral Bands of Harper-Like and Magnetic Schrödinger Operators

We show for a large class of discrete Harper-like and continuous magnetic Schrödinger operators that their band edges are Lipschitz continuous with respect to the intensity of the external constant magnetic field. We generalize a result obtained by Bellissard (Commun Math Phys 160:599–613, 1994), and give examples in favor of a recent conjecture of G. Nenciu.     

Investigation of a catalyst ink dispersion using both ultra-small-angle X-ray scattering and cryogenic TEM

The dispersion of Nafion ionomer particles and Pt/C catalyst aggregates in liquid media was studied using both ultra-small-angle X-ray scattering (USAXS) and cryogenic TEM. A systematic approach was taken to study first the dispersion of each component (i.e., ionomer particles and Pt/C aggregates), then the combination of the components, and last the catalyst ink. Multiple-level curve fitting was used to extract the particle size, size distribution, and geometry of the Pt/C aggregates and the Nafion particles in liquid media from the scattering data. The results suggest that the particle size, size distribution, and geometry are not uniform throughout the systems but rather vary significantly. It was found that the interaction of each component (i.e., the Nafion ionomer particles and the Pt/C aggregates) occurs in the dispersion. Cryogenic TEM was used to observe the size and geometry of the particles in liquid directly and to validate the scattering results. The TEM results showed excellent agreement.     

On the transfer matrix of a MIMO system

We develop a deterministic ab initio model for the input–output relationship of a multiple‐input multiple‐output (MIMO) wireless channel, starting from the Maxwell equations combined with Ohm's law. The main technical tools are scattering and geometric perturbation theories. The derived relationship can lead us to a deep understanding of how the propagation conditions and the coupling effects between the elements of multiple‐element arrays affect the properties of an MIMO channel, e.g. its capacity and its number of degrees of freedom. Copyright © 2011 John Wiley & Sons, Ltd.     

Very high Reynolds number boundary layers over 3D sparse roughness and obstacles: the mean flow

Hot-wire and oil-film interferometry measurements are taken for 3D rough wall boundary layers at very high Reynolds numbers (61,000 < Re θ < 120,000) with low blockage ratios, 10 < δ/H < 135, and high roughness, 100 < H ⁺ < 4,900. The results cover flows over both rough walls and over obstacles and are compared with and provide extension to recent lower Reynolds number results. The validity of the Townsend ‘wall similarity hypothesis’ in relation to consistently increasing 3D roughness is interrogated. In agreement with recent work, Schultz and Flack (J Fluid Mech 580:381–405, 2007) and Castro (J Fluid Mech 585:469–485, 2007) found that, for relatively low roughness, Townsend’s hypothesis holds for the mean velocity field. With increasing roughness, the equilibrium layer diminishes and gradually vanishes. The viscous component of the wall shear stress decreases, while the turbulent component increases as the roughness effects extend across the boundary layer.     

A topological classification of linear differential equations on Banach spaces

In the present work, we give necessary and sufficient conditions for linear differential non-autonomous equations on a Banach space, that satisfy exponential dichotomy, to be topologically equivalent. We shall also prove that such equations are structurally stable.     

Efficient electrocatalyst utilization: electrochemical deposition of Pt nanoparticles using nafion membrane as a template

We deposit Pt particles electrochemically on an electrode covered with a Nafion membrane. Platinum ions travel through the hydrophilic channels of the membrane, and platinum deposits are formed at the place where the channels make contact with the planar electrode. This procedure deposits the catalyst only at the end of the hydrophilic channels that cross the membrane; no catalyst is placed under the hydrophobic domains, where it would not be in contact with the electrolyte. By performing a series of cyclic voltammograms with this system, we show that deposition of the platinum through the membrane achieves better platinum utilization than deposition of platinum on the naked electrode followed by the placement of the membrane on top.