Modeling and Simulation of Damage Processes based on a Gradient-Enhanced Free Energy Function

Taking into account softening effects in connection with conventional inelastic material models can cause ill-posed boundary value problems. These problems can be established by obtaining no unique solution for the resulting algebraic system or by having a strong mesh dependence of the numerical results. This is the consequence of losing ellipticity of the governing field equations. A possible approach to solve these problems is to introduce a non-local field function in the model which includes an internal material length scale. For this purpose a gradient-enhanced free energy function is used for the current continuum damage model from which two variational equations are resulting. Calculations with less effort can be achieved due to the enhancement of the free energy function in comparison to other approaches. The mentioned model is applied to a material with locally varying damage properties (yield limits). Furthermore, the model is able to describe crack propagation in cases of completely damaged material. Therewith, a matrix material including precipitates, such as carbides, is modeled. This allows to investigate ship screws, which usually exhibit the mentioned composition, with regard to the influence of cavitation. Cavitation describes the implosion of risen vapor bubbles, whereby the impact on screws causes heavy damages which can lead to a complete destruction. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rigidity of flat surfaces under the boundary measure

Consider a closed marked flat surface S of genus g ≥ 2 and its universal cover ~S endowed with the pulled back metric. We show that the measure class induced by the Hausdorff measure of the Gromov boundary of ~S uniquely determines S up to rescaling.     

Efficient adaptive regression spline algorithms based on mapping approach with a case study on finance

Multivariate adaptive regression splines (MARS) has become a popular data mining (DM) tool due to its flexible model building strategy for high dimensional data. Compared to well-known others, it performs better in many areas such as finance, informatics, technology and science. Many studies have been conducted on improving its performance. For this purpose, an alternative backward stepwise algorithm is proposed through Conic-MARS (CMARS) method which uses a penalized residual sum of squares for MARS as a Tikhonov regularization problem. Additionally, by modifying the forward step of MARS via mapping approach, a time efficient procedure has been introduced by S-FMARS. Inspiring from the advantages of MARS, CMARS and S-FMARS, two hybrid methods are proposed in this study, aiming to produce time efficient DM tools without degrading their performances especially for large datasets. The resulting methods, called SMARS and SCMARS, are tested in terms of several performance criteria such as accuracy, complexity, stability and robustness via simulated and real life datasets. As a DM application, the hybrid methods are also applied to an important field of finance for predicting interest rates offered by a Turkish bank to its customers. The results show that the proposed hybrid methods, being the most time efficient with competing performances, can be considered as powerful choices particularly for large datasets.     

Novel spectrophotometer for the measurement of color and appearance

A new spectrophotometer design permits simultaneous measurement of color and surface appearance attributes of reflecting specimens. The new design provides a multi-channel spectrometer that is simple, compact, light, and inexpensive, while having a unique combination of features and performance. Novel d/8° geometry provides new capabilities. With a single quick measurement, the instrument measures color and several other appearance attributes. A concentric optical configuration used for the spectrometer eliminates third-order optical aberrations. The optical design and unique features are described and performance data are presented.     

Modified cyclodextrines as mass-sensitive coatings for solvent vapour detection

Advances in robustness, selectivity and sensitivity in organic solvent vapour detection can be achieved by the application of β-cyclodextrines as coatings for mass sensitive chemical sensors. Linking the cyclodextrines with e.g. diiodooctane combines the molecular recognition capabilities of host-guest chemistry with the high stability of polymeric layers. Special increase in selectivity is achieved with anhydro cyclodextrines, since their flattened conus is adapted to benzene derivatives as can also be shown by computer modelling. Furthermore methylation elongates the cavity, guaranteeing an optimised engulfing of the analytes. In this way even a differentiation between p- and m-xylene vapours and a QMB detection limit of some μL/L is possible.     

Local stability analysis of a stochastic evolutionary financial market model with a risk-free asset

This paper introduces and analyzes an evolutionary model of a financial market with a risk-free asset. Focus is on the study of local stability of the wealth dynamics through the application of recent results on the linearization and stability of random dynamical systems (Evstigneev et al. Proc Am Math Soc 139:1061–1072, 2011). Conditions are derived for the linearization of the model at an equilibrium state which ensure local convergence of sample paths to this equilibrium. The paper also shows that the concept of local stability is closely related to the notion of evolutionary stability. A locally evolutionarily stable investment strategy in the evolutionary model with a risk-free asset is derived, extending previous research. The method illustrated here is applicable for the analysis of manifold economic and financial dynamic models involving randomness.