Erratum to ``On a conjecture of Koike on identities between Thompson series and Rogers-Ramanujan functions'

This note gives a correction to formula (A.18) of Appendix A.

     

IR and SFM study of PTCDA thin films on different substrates

FT-IR spectroscopy and SFM were used to investigate the growth of thin films of the organic semiconductor 3,4,9,10-perylenetetracarboxylicdianhydride (PTCDA) deposited by vacuum sublimation onto various substrates, i.e. Ag(111) layers on mica, KBr(100), mica, oxidized Si, and TiO₂ nanoparticles on Si. Layer thicknesses of PTCDA varied from 10 to 1500 nm.The anhydride vibrations of PTCDA differ for the used substrates, which can be connected to the orientation of the molecules relative to the substrate surface and the film morphology as detected in the SFM pictures.     

Tuning the limiting thickness of a thin oxide layer on Al(111) with oxygen gas pressure

We report an x-ray photoelectron spectroscopy study of the oxidation of Al(111) surfaces at room temperature, which reveals that the limiting thickness of an aluminum oxide film can be tuned by using oxygen pressure. This behavior is attributed to a strong dependence of the kinetic potential on the oxygen gas pressure. The coverage of oxygen anions on the surface of the oxide film depends on the gas pressure leading to a pressure dependence of the kinetic potential. Our results indicate that a significantly large oxygen pressure (>1 Torr) is required to develop the saturated surface coverage of oxygen ions, which results in the maximum kinetic potential and therefore the saturated limiting thickness of the oxide film.     

Studying Dynamical Principles of Human Locomotion using Inverse Optimal Control

Human movement, as for example human gait, can be considered as an optimal realization of some given task. However, the criterion for which the naturally performed human motion is optimal, is generally not known. In this article we formulate an inverse optimal control problem to study the relevance of four different optimization criteria in human locomotion. As a walking model we use an actuated three dimensional spring loaded inverted pendulum (3D-SLIP), which is able to mirror the typical shape of the center of mass trajectory in human gait. Using a direct all-at-once approach, the weighting of the optimization criteria and the position of the footsteps are optimized in such a way, that the center of mass trajectory of the resulting optimal state fits real motion capture data as good as possible. Numerical experiments show, that whereas the so called capture point seems to have a great impact on human walking, minimization of the vertical center of mass movement does not show any relevance at all. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Shintani lifts and fractional derivatives for harmonic weak Maass forms

In this paper, we construct Shintani lifts from integral weight weakly holomorphic modular forms to half-integral weight weakly holomorphic modular forms. Although defined by different methods, these coincide with the classical Shintani lifts when restricted to the space of cusp forms. As a side effect, this gives the coefficients of the classical Shintani lifts as new cycle integrals. This yields new formulas for the L-values of Hecke eigenforms. When restricted to the space of weakly holomorphic modular forms orthogonal to cusp forms, the Shintani lifts introduce a definition of weakly holomorphic Hecke eigenforms. Along the way, auxiliary lifts are constructed from the space of harmonic weak Maass forms which yield a “fractional derivative” from the space of half-integral weight harmonic weak Maass forms to half-integral weight weakly holomorphic modular forms. This fractional derivative complements the usual ξ-operator introduced by Bruinier and Funke.     

Simulation of oscillatory flow in an aortic bifurcation using FVM and FEM: A comparative study of implementation strategies

Cardiovascular diseases are one of the major causes of long‐term morbidity and mortality in human beings. The nearly epidemic increase in prevalence of such diseases poses a serious threat to public health and calls for efficient methods of diagnosis and treatment. Non‐invasive diagnostic procedures such as MRI are often used in this context; however, these are limited in terms of spatial and temporal resolution and do not provide information on time‐dependent pressures and wall shear stresses—key quantities considered to be partially responsible for the formation and development of related pathologies. The present study is concerned with the numerical simulation of oscillatory flow through the abdominal aortic bifurcation. Computational fluid dynamics simulation of oscillatory flow in a branched geometry at high Reynolds numbers poses considerable challenges. The present study reports a detailed comparison of simulations performed with a finite volume and a finite element method, two approaches with significant differences in their discretization strategy, treatment of boundary conditions and other numerical aspects. Both solvers were parallelized, using loop parallelization of the BiCGStab linear solver for the finite volume and domain decomposition based on the Schur complement method for the finite element technique. The experience gained with these two approaches for the solution of flow in a bifurcation forms the focus of this study. Although similar results were obtained for both methods, the computation time required for convergence was found to be significantly smaller for the finite element approach. Copyright © 2010 John Wiley & Sons, Ltd.