Anodic and Cathodic Platinum Dissolution Processes Involve Different Oxide Species

The degradation of Pt-containing oxygen reduction catalysts for fuel cell applications is strongly linked to the electrochemical surface oxidation and reduction of Pt. Here, we study the surface restructuring and Pt dissolution mechanisms during oxidation/reduction for the case of Pt(100) in 0.1 M HClO₄ by combining operando high-energy surface X-ray diffraction, online mass spectrometry, and density functional theory. Our atomic-scale structural studies reveal that anodic dissolution, detected during oxidation, and cathodic dissolution, observed during the subsequent reduction, are linked to two different oxide phases. Anodic dissolution occurs predominantly during nucleation and growth of the first, stripe-like oxide. Cathodic dissolution is linked to a second, amorphous Pt oxide phase that resembles bulk PtO₂ and starts to grow when the coverage of the stripe-like oxide saturates. In addition, we find the amount of surface restructuring after an oxidation/reduction cycle to be potential-independent after the stripe-like oxide has reached its saturation coverage.     

Wavelet estimation in diffusions with periodicity

We consider a time-inhomogeneous diffusion process, whose drift term contains a deterministic T-periodic signal with known periodicity. This signal is supposed to be contained in a Besov space, we try to estimate it using a non-parametric wavelet estimator. Our estimator is inspired by the thresholded wavelet density estimator constructed by Donoho, Johnstone, Kerkyacharian and Picard in 1996. Under certain ergodicity assumptions to the process, we can give the same asymptotic rate of convergence as for the density estimator.     

On the gonality sequence of an algebraic curve

For any smooth irreducible projective curve X, the gonality sequence ${\{d_r \;| \; r \in \mathbb N\}}$ is a strictly increasing sequence of positive integer invariants of X. In most known cases d _r+1 is not much bigger than d _r . In our terminology this means the numbers d _r satisfy the slope inequality. It is the aim of this paper to study cases when this is not true. We give examples for this of extremal curves in ${{\mathbb P}^r}$ , for curves on a general K3-surface in ${{\mathbb P}^r}$ and for complete intersections in ${{\mathbb P}^3}$ .     

Convergence Analysis of the Implicit Euler-discretization and Sufficient Conditions for Optimal Control Problems Subject to Index-one Differential-algebraic Equations

For optimal control problems subject to index-one differential-algebraic equations in semi-explicit form we discuss second order sufficient conditions in form of a coercivity condition taking into account the two-norm discrepancy. Furthermore we introduce a related Riccati-type and Legendre-Clebsch condition which are sufficient for the validity of the coercivity condition. Using the implicit Euler-discretization we approximate the optimal control problem and analyze the convergence of solutions of the local minimum principle for the discretized optimal control problem by applying the general convergence framework of Stetter, which requires the discretization method to be continuous, consistent, and stable.

     

Credit rating prediction using Ant Colony Optimization

The introduction of the Basel II Capital Accord has encouraged financial institutions to build internal rating systems assessing the credit risk of their various credit portfolios. One of the key outputs of an internal rating system is the probability of default (PD), which reflects the likelihood that a counterparty will default on his/her financial obligation. Since the PD modelling problem basically boils down to a discrimination problem (defaulter or not), one may rely on the myriad of classification techniques that have been suggested in the literature. However, since the credit risk models will be subject to supervisory review and evaluation, they must be easy to understand and transparent. Hence, techniques such as neural networks or support vector machines are less suitable due to their black box nature. Building upon previous research, we will use AntMiner+ to build internal rating systems for credit risk. AntMiner+ allows to infer a propositional rule set from a given data set, hereby using the principles from Ant Colony Optimization. Experiments will be conducted using various types of credit data sets (retail, small- and medium-sized enterprises and banks). It will be shown that the extracted rule sets are both powerful in terms of discriminatory power and comprehensibility. Furthermore, a framework will be presented describing how AntMiner+ fits into a global Basel II credit risk management system.     

On curves on K3 surfaces,II

We study the Clifford index c of a smooth irreducible curve X in the linear series |2H| on a special K3 surface S of degree 2n in \({{\mathbb P}}^{n+1}\), with hyperplane section H, and we look for the complete and base point free linear series of S whose restrictions to X compute c. In a more general context, we discuss the features of such series, for an assigned curve on a K3 surface; this discussion is of some independent interest.     

Newton's method on Riemannian manifolds and a geometric model for the human spine

To study a geometric model of the human spine we are led tofinding a constrained minimum of a real valued function definedon a product of special orthogonal groups. To take advantgeof its Lie group structure we consider Newton's method on thismanifold. Comparisons between measured spines and computed spinesshow the pertinence of this approach.     

Renormalization in the Hénon family,II: the heteroclinic web

We study highly dissipative Hénon maps

$F_{c,b}: (x,y) \mapsto (c-x^2-by, x)$

with zero entropy. They form a region Π in the parameter plane bounded on the left by the curve W of infinitely renormalizable maps. We prove that Morse-Smale maps are dense in Π, but there exist infinitely many different topological types of such maps (even away from W). We also prove that in the infinitely renormalizable case, the average Jacobian b _F on the attracting Cantor set \({\mathcal{O}}_{F}\) is a topological invariant. These results come from the analysis of the heteroclinic web of the saddle periodic points based on the renormalization theory. Along these lines, we show that the unstable manifolds of the periodic points form a lamination outside \({\mathcal{O}}_{F}\) if and only if there are no heteroclinic tangencies.

     

Calculation of probability density functions for nonlinear vibration systems

Technical systems are subjected to a variety of excitations that cannot generally be described in deterministic ways. Random excitations such as road roughness, wind gusts or loads on marine structures are commonly described by stochastic differential equations (SDEs). Given a set of SDEs, the main task is in finding probability density functions (PDFs), which yield statistical information about the system states. Monte-Carlo simulations represent a general way of generating PDFs, however, reliable integration methods can be time-consuming for complex systems. An alternative way of finding PDFs lies in the analysis of the Fokker-Planck equation, a partial differential equation of the PDF. Linear problems under Gaussian excitation can be solved analytically, which is the case only for a small class of nonlinear problems. As a result, there are a number of methods of approximating PDFs for general problems. Most of these are restricted to comparably low dimensions, such as d=4 ("curse of dimensionality"), limiting the relevance to technical applications. This paper presents solutions to problems of dimensions up to d=10, applying a Galerkin-method that expands approximate solutions into orthogonal polynomials. Problems include polynomial nonlinearities in damping and restoring terms, such as classical Duffing-elements, as well as other types of nonlinearities, demonstrated on a typical problem in vehicle dynamics. All results are compared with results from Monte-Carlo simulations or exact solutions, where available. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of spectral phase on cross-polarized wave generation with short femtosecond pulses

In this paper we present the first comprehensive study of the role of spectral phase on cross-polarized wave (XPW) generation using sub-30 femtosecond (fs) laser pulses. XPW generation improves the temporal contrast and shortens the pulse duration of fs chirped pulse amplification (CPA) lasers. For Ti:Sa lasers, compression below 30?fs is non-trivial and therefore never perfect. We therefore systematically analyze the effect of an arbitrary input spectral phase on the output spectrum and efficiency of the XPW process, both theoretically and experimentally. We derive the maximum acceptable value of residual phase for a given initial pulse duration in order to efficiently drive the XPW process for pulse shortening and contrast improvement.