Minimal kernels of Dirac operators along maps

Let M be a closed spin manifold and let N be a closed manifold. For maps and Riemannian metrics g on M and h on N, we consider the Dirac operator of the twisted Dirac bundle . To this Dirac operator one can associate an index in . If M is 2‐dimensional, one gets a lower bound for the dimension of the kernel of out of this index. We investigate the question whether this lower bound is obtained for generic tupels .     

Generalized sensitivity analysis of nonlinear programs using a sequence of quadratic programs

ABSTRACT

Local sensitivity information is obtained for KKT points of parametric NLPs that may exhibit active set changes under parametric perturbations; under appropriate regularity conditions, computationally relevant generalized derivatives of primal and dual variable solutions of parametric NLPs are calculated. Ralph and Dempe obtained directional derivatives of solutions of parametric NLPs exhibiting active set changes from the unique solution of an auxiliary quadratic program. This article uses lexicographic directional derivatives, a newly developed tool in nonsmooth analysis, to generalize the classical NLP sensitivity analysis theory of Ralph and Dempe. By viewing said auxiliary quadratic program as a parametric NLP, the results of Ralph and Dempe are applied to furnish a sequence of coupled QPs, whose unique solutions yield generalized derivative information for the NLP. A practically implementable algorithm is provided. The theory developed here is motivated by widespread applications of nonlinear programming sensitivity analysis, such as in dynamic control and optimization problems.     

Top-down synthesis of polyoxometalate-like sub-nanometer molybdenum-oxo clusters as high-performance electrocatalysts

The top-down fabrication of catalytically active molecular metal oxide anions, or polyoxometalates, is virtually unexplored, although these materials offer unique possibilities, for catalysis, energy conversion and storage. Here, we report a novel top-down route, which enables the scalable synthesis and deposition of sub-nanometer molybdenum-oxo clusters on electrically conductive mesoporous carbon. The new approach uses a unique redox-cycling process to convert crystalline Mo^IVO₂ particles into sub-nanometer molecular molybdenum-oxo clusters with a nuclearity of ∼1–20. The resulting molybdenum-oxo cluster/carbon composite shows outstanding, stable electrocatalytic performance for the oxygen reduction reaction with catalyst characteristics comparable to those of commercial Pt/C. This new material design could give access to a new class of highly reactive polyoxometalate-like metal oxo clusters as high-performance, earth abundant (electro-)catalysts.

The top-down synthesis and deposition of polyoxometalate-like clusters on porous carbon is reported together with the high electrocatalytic oxygen reduction reactivity of the composite.     

Experimental-based material parameter identification of oocytes

In comparison to other eukaryotic cells, mammalian oocytes are characterised by a relative high diameter allowing in turn a straightforward micromechanical testing to study their mechanical properties. The structure of mammalian oocytes is characterised by the so-called zona pellucida (ZP), a thick glycoprotein layer, surrounding the cells interior, the ooplasm. In contrast to other cells, where the load is mainly carried by inner cell structures, in case of oocytes a huge amount of external loads is carried by the ZP. Aim of this work is the determination of the mechanical properties of oocytes. Therefore, a micromechanical setup has been developed and installed on a microscope. Beside the determination of the force-strain relation during loading, the deformation of the oocytes has been recorded optically, too. Both, the force-strain curves and the optical recordings build the basis for a proper parameter identification technique based on the inverse finite element method. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Instrumental neutron absorption activation analysis

We present and discuss a modification of instrumental neutron activation analysis (INAA) that is sensitive for nuclides that do not yield (suitable) activation products but have high cross sections for neutron absorption. Their presence in a sample may thwart INAA by neutron flux suppression inside the sample, but they remain undetected and thus unnoticed by the analyst. In particular, this refers to Li, B, Cd and Gd. The proposed method—instrumental neutron absorption activation analysis (INAAA)—takes advantage of the flux depression inside the sample caused by the neutron absorbers. It is made visible by addition of an activatable nuclide (indicator). The concentration of the neutron absorber (analyte) causes a decrease in activity of the indicator. The activity difference between a mixed sample (sample plus indicator) and the pure indicator carries the analytical information. The calibration curve hence follows a reciprocal exponential function. In a proof-of-principle experiment, the applicability for the quantification of boron was exemplified. In presence of only one neutron absorber (whose nature is known), INAAA can be applied easily for quantification of the analyte in powdered or liquid samples. Although INAAA is no trace sensitive method, it has the potential to increase the reliability of INAA analyses by fast and straightforward quality control (even in presence of two or more neutron absorbing nuclides). It is especially suited for research reactors that do not operate a prompt gamma neutron activation analysis (PGNAA) station.     

Macroscopic damage modeling for silicon nitride

Modeling the damage of brittle materials is of great importance considering a variety of structural components. Prominent examples are high strength engineering ceramics. The present work is concerned with silicon nitride, a material with increasing relevance in industrial applications. In the sense of a hierarchical model structure, effective properties of micromechanical simulations were applied to macroscopic, phenomenological damage models for monotonous and cyclic loading. In the following, both models are introduced and the application of the cyclic damage model to a four point bending test is discussed. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Small-scale fracture toughness of ceramic thin films: the effects of specimen geometry,ion beam notching and high temperature on chromium nitride toughness evaluation

For the implementation of thin ceramic hard coatings into intensive application environments, the fracture toughness is a particularly important material design parameter. Characterisation of the fracture toughness of small-scale specimens has been a topic of great debate, due to size effects, plasticity, residual stress effects and the influence of ion penetration from the sample fabrication process. In this work, several different small-scale fracture toughness geometries (single-beam cantilever, double-beam cantilever and micro-pillar splitting) were compared, fabricated from a thin physical vapour-deposited ceramic film using a focused ion beam source, and then the effect of the gallium-milled notch on mode I toughness quantification investigated. It was found that notching using a focused gallium source influences small-scale toughness measurements and can lead to an overestimation of the fracture toughness values for chromium nitride (CrN) thin films. The effects of gallium ion irradiation were further studied by performing the first small-scale high-temperature toughness measurements within the scanning electron microscope, with the consequence that annealing at high temperatures allows for diffusion of the gallium to grain boundaries promoting embrittlement in small-scale CrN samples. This work highlights the sensitivity of some materials to gallium ion penetration effects, and the profound effect that it can have on fracture toughness evaluation.