On a Chebychev matrix operator method for ordinary linear differential equations with non-constant coefficients

Summary A spectral method based on the -method is developed to solve initial and boundary value problems. The usual problem of setting up the system of algebraic equations by sophisticated terms of the series coefficients is overcome by the use of operator matrices for derivation and multiplication with non-constant coefficients. The applicability is also given for eigenvalue problems as is demonstrated by the Orr-Sommerfeld equation.     

Inducing imperfections in germanium nanowires

Nanowires with inhomogeneous heterostructures such as polytypes and periodic twin boundaries are interesting due to their potential use as components for optical,electrical,and thermophysical applications.Additionally,the incorporation of metal impurities in semiconductor nanowires could substantially alter their electronic and optical properties.In this highlight article,we review our recent progress and understanding in the deliberate induction of imperfections,in terms of both twin boundaries and additional impurities in germanium nanowires for new/enhanced functionalities.The role of catalysts and catalyst-nanowire interfaces for the growth of engineered nanowires via a three-phase paradigm is explored.Three-phase bottom-up growth is a feasible way to incorporate and engineer imperfections such as crystal defects and impurities in semiconductor nanowires via catalyst and/or interfacial manipulation."Epitaxial defect transfer"process and catalyst-nanowire interfacial engineering are employed to induce twin defects parallel and perpendicular to the nanowire growth axis.By inducing and manipulating twin boundaries in the metal catalysts,twin formation and density are controlled in Ge nanowires.The formation of Ge polytypes is also observed in nanowires for the growth of highly dense lateral twin boundaries.Additionally,metal impurity in the form of Sn is injected and engineered via third-party metal catalysts resulting in above-equilibrium incorporation of Sn adatoms in Ge nanowires.Sn impurities are precipitated into Ge bi-layers during Ge nanowire growth,where the impurity Sn atoms become trapped with the deposition of successive layers,thus giving an extraordinary Sn content (＞6 at.％) in Ge nanowires.A larger amount of Sn impingement (＞9 at.％) is further encouraged by utilizing the eutectic solubility of Sn in Ge along with impurity trapping.     

Characterization of weld seam properties of extruded magnesium hollow profiles

Extrusions of hollow profiles with weld seams were conducted using the magnesium alloy ME21 applying various extrusion ratios. Subsequent analysis of the profiles’ microstructure was performed comparing weld free with weld seam containing material using (polarized) light optical microscopy (LOM). Additionally, the local texture and microstructure in the weld-free material as well as in the weld seam region has been examined with a scanning electron microscope coupled with electron backscatter diffraction technique (SEM-EBSD). The weld-free material and the weld seam are characterized by recrystallized microstructures, whereas few residual cast grains were identified. The local texture distinctively changes from the weld-free material to the weld seam. The texture of the weld-free material is comparable with the typical ME21 sheet texture. In the weld seam area, a pole density is found, which is distributed towards the transverse direction (TD) combined with a split and broadening of the pole density in the extrusion direction (ED). This texture influences the mechanical anisotropy due to the dependence of the activation of basal 〈a〉-slip and \( \{ 10\bar{1}2\} \;\langle 10\bar{1}1\rangle \)-extension twinning on the loading direction in favorably oriented grains.     

Ultralow Expansion Glass as Material for Advanced Micromechanical Systems

Ultralow expansion (ULE) glasses are of special interest for temperature stabilized systems for example in precision metrology. Nowadays, ULE materials are mainly used in macroscopic and less in micromechanical systems. Reasons for this are a lack of technologies for parallel fabricating high-quality released microstructures with a high accuracy. As a result, there is a high demand in transferring these materials into miniaturized application examples, realistic system modeling, and the investigation of microscopic material properties. Herein, a technological base for fabricating released micromechanical structures and systems with a structure height above 100 μm in ULE 7972 glass is established. Herein, the main fabrication parameters that are important for the system design and contribute thus to the introduction of titanium silicate as material for glass-based micromechanical systems are discussed. To study the mechanical properties in combination with respective simulation models, microcantilevers are used as basic mechanical elements to evaluate technological parameters and other impact factors. The implemented models allow to predict the micromechanical system properties with a deviation of only ±5% and can thus effectively support the micromechanical system design in an early stage of development.     

An algebraic foundation for automatic feature-based program synthesis

Feature-Oriented Software Development provides a multitude of formalisms, methods, languages, and tools for building variable, customizable, and extensible software. Along different lines of research, different notions of a feature have been developed. Although these notions have similar goals, no common basis for evaluation, comparison, and integration exists. We present a feature algebra that captures the key ideas of feature orientation and that provides a common ground for current and future research in this field, on which also alternative options can be explored. Furthermore, our algebraic framework is meant to serve as a basis for the development of the technology of automatic feature-based program synthesis and architectural metaprogramming.     

Temporal kernel CCA and its application in multimodal neuronal data analysis

Data recorded from multiple sources sometimes exhibit non-instantaneous couplings. For simple data sets, cross-correlograms may reveal the coupling dynamics. But when dealing with high-dimensional multivariate data there is no such measure as the cross-correlogram. We propose a simple algorithm based on Kernel Canonical Correlation Analysis (kCCA) that computes a multivariate temporal filter which links one data modality to another one. The filters can be used to compute a multivariate extension of the cross-correlogram, the canonical correlogram, between data sources that have different dimensionalities and temporal resolutions. The canonical correlogram reflects the coupling dynamics between the two sources. The temporal filter reveals which features in the data give rise to these couplings and when they do so. We present results from simulations and neuroscientific experiments showing that tkCCA yields easily interpretable temporal filters and correlograms. In the experiments, we simultaneously performed electrode recordings and functional magnetic resonance imaging (fMRI) in primary visual cortex of the non-human primate. While electrode recordings reflect brain activity directly, fMRI provides only an indirect view of neural activity via the Blood Oxygen Level Dependent (BOLD) response. Thus it is crucial for our understanding and the interpretation of fMRI signals in general to relate them to direct measures of neural activity acquired with electrodes. The results computed by tkCCA confirm recent models of the hemodynamic response to neural activity and allow for a more detailed analysis of neurovascular coupling dynamics.     

Process and learning outcomes from remotely-operated,simulated, and hands-on student laboratories

A large-scale, multi-year, randomized study compared learning activities and outcomes for hands-on, remotely-operated, and simulation-based educational laboratories in an undergraduate engineering course. Students (N = 458) worked in small-group lab teams to perform two experiments involving stress on a cantilever beam. Each team conducted the experiments in one of three lab formats (hands-on, remotely-operated, or simulation-based), collecting data either individually or as a team. Lab format and data-collection mode showed an interaction, such that for the hands-on lab format learning outcomes were higher when the lab team collected data sets working as a group rather than individually collecting data sets to be combined later, while for remotely-operated labs individual data collection was best. The pattern of time spent on various lab-related activities suggests that working with real instead of simulated data may induce higher levels of motivation. The results also suggest that learning with computer-mediated technologies can be improved by careful design and coordination of group and individual activities.     

Optimizing the execution of XSLT stylesheets for querying transformed XML data

We have to deal with different data formats whenever data formats evolve or data must be integrated from heterogeneous systems. These data when implemented in XML for data exchange cannot be shared freely among applications without data transformation. A common approach to solve this problem is to convert the entire XML data from their source format to the applications’ target formats using the transformations rules specified in XSLT stylesheets. However, in many cases, not all XML data are required to be transformed except for a smaller part described by a user’s query (application). In this paper, we present an approach that optimizes the execution time of an XSLT stylesheet for answering a given XPath query by modifying the XSLT stylesheet in such a way that it would (a) capture only the parts in the XML data that are relevant to the query and (b) process only those XSLT instructions that are relevant to the query. We prove the correctness of our optimization approach, analyze its complexity and present experimental results. The experimental results show that our approach performs the best in terms of execution time, especially when many cost-intensive XSLT instructions can be excluded in the XSLT stylesheet.