TY - JOUR A1 - Pieper, Martin T1 - Vector hyperinterpolation on the sphere JF - Journal of approximation theory. 156 (2009), H. 2 Y1 - 2009 SN - 0021-9045 SP - 173 EP - 186 ER - TY - CHAP A1 - Pieper, Martin A1 - Konopka, Mahnaz T1 - Umgestaltung der Mathematik Anfängervorlesungen im Fachbereich Energietechnik T2 - Mathematik im Übergang Schule/Hochschule und im ersten Studienjahr : extended abstracts zur 2. khdm-Arbeitstagung 20.02. - 23.02.2013. (khdm-Report ; 13-01) Y1 - 2013 SP - 115 EP - 116 ER - TY - JOUR A1 - Kahmann, Stephanie L. A1 - Rausch, Valentin A1 - Plümer, Jonathan A1 - Müller, Lars P. A1 - Pieper, Martin A1 - Wegmann, Kilian T1 - The automized fracture edge detection and generation of three-dimensional fracture probability heat maps JF - Medical Engineering & Physics N2 - With proven impact of statistical fracture analysis on fracture classifications, it is desirable to minimize the manual work and to maximize repeatability of this approach. We address this with an algorithm that reduces the manual effort to segmentation, fragment identification and reduction. The fracture edge detection and heat map generation are performed automatically. With the same input, the algorithm always delivers the same output. The tool transforms one intact template consecutively onto each fractured specimen by linear least square optimization, detects the fragment edges in the template and then superimposes them to generate a fracture probability heat map. We hypothesized that the algorithm runs faster than the manual evaluation and with low (< 5 mm) deviation. We tested the hypothesis in 10 fractured proximal humeri and found that it performs with good accuracy (2.5 mm ± 2.4 mm averaged Euclidean distance) and speed (23 times faster). When applied to a distal humerus, a tibia plateau, and a scaphoid fracture, the run times were low (1–2 min), and the detected edges correct by visual judgement. In the geometrically complex acetabulum, at a run time of 78 min some outliers were considered acceptable. An automatically generated fracture probability heat map based on 50 proximal humerus fractures matches the areas of high risk of fracture reported in medical literature. Such automation of the fracture analysis method is advantageous and could be extended to reduce the manual effort even further. KW - Fracture classification KW - Shoulder KW - Probability distribution mapping KW - Morphing KW - Imaging Y1 - 2022 SN - 1350-4533 VL - 2022 IS - 110 PB - Elsevier CY - Amsterdam ER - TY - CHAP A1 - Pieper, Martin A1 - Schulz, Silvia T1 - Teaching Simulation Methods with COMSOL Multiphysics N2 - This paper describes two courses on simulation methods for graduate students: “Simulation Methods” and “Simulation and Optimization in Virtual Engineering” The courses were planned to teach young engineers how to work with simulation software as well as to understand the necessary mathematical background. As simulation software COMSOL is used. The main philosophy was to combine theory and praxis in a way that motivates the students. In addition “soft skills” should be improved. This was achieved by project work as final examination. As underlying didactical principle the ideas of Bloom’s revised taxonomy were followed. The paper basically focusses on educational aspects, e.g. how to structure the course, plan the exercises, organize the project work and include practical COMSOL examples. KW - COMSOL Multiphysics KW - Optimization module KW - LiveLink for MATLAB KW - Bloom Taxonomy KW - education Y1 - 2014 ER - TY - BOOK A1 - Pieper, Martin T1 - Spektralrandintegralmethoden zur Maxwell-Gleichung Y1 - 2007 SN - 978-3-89959-635-9 N1 - Zugl.: Göttingen, Univ., Diss., 2007 PB - Der Andere Verl. CY - Tönning [u.a.] ER - TY - JOUR A1 - Jildeh, Zaid B. A1 - Wagner, Torsten A1 - Schöning, Michael Josef A1 - Pieper, Martin T1 - Simulating the electromagnetic‐thermal treatment of thin aluminium layers for adhesion improvement JF - Physica status solidi (a) N2 - A composite layer material used in packaging industry is made from joining layers of different materials using an adhesive. An important processing step in the production of aluminium-containing composites is the surface treatment and consequent coating of adhesive material on the aluminium surface. To increase adhesion strength between aluminium layer and the adhesive material, the foil is heat treated. For efficient heating, induction heating was considered as state-of-the-art treatment process. Due to the complexity of the heating process and the unpredictable nature of the heating source, the control of the process is not yet optimised. In this work, a finite element analysis of the process was established and various process parameters were studied. The process was simplified and modelled in 3D. The numerical model contains an air domain, an aluminium layer and a copper coil fitted with a magnetic field concentrating material. The effect of changing the speed of the aluminium foil (or rolling speed) was studied with the change of the coil current. Statistical analysis was used for generating a general control equation of coil current with changing rolling speed. Y1 - 2015 U6 - http://dx.doi.org/10.1002/pssa.201431893 SN - 1862-6319 VL - Vol. 212 IS - 6 SP - 1234 EP - 1241 PB - Wiley CY - Weinheim ER - TY - BOOK A1 - Pieper, Martin T1 - Quantum mechanics: Introduction to mathematical formulation N2 - Anyone who has always wanted to understand the hieroglyphs on Sheldon's blackboard in the TV series The Big Bang Theory or who wanted to know exactly what the fate of Schrödinger's cat is all about will find a short, descriptive introduction to the world of quantum mechanics in this essential. The text particularly focuses on the mathematical description in the Hilbert space. The content goes beyond popular scientific presentations, but is nevertheless suitable for readers without special prior knowledge thanks to the clear examples. KW - Quantenmechanik KW - Hilbert Room KW - Postulates KW - Schrödingers cat KW - Operators Y1 - 2021 SN - 978-3-658-32644-9 SN - 978-3-658-32645-6 U6 - http://dx.doi.org/10.1007/978-3-658-32645-6 PB - Springer CY - Wiesbaden ER - TY - BOOK A1 - Pieper, Martin T1 - Quantenmechanik: Einführung in die mathematische Formulierung Y1 - 2019 SN - 978-3-658-28328-5 U6 - http://dx.doi.org/10.1007/978-3-658-28329-2 PB - Springer Spektrum CY - Wiesbaden ER - TY - BOOK A1 - Pieper, Martin T1 - Quantenmechanik : Einführung in die mathematische Formulierung Y1 - 2019 SN - 978-3-658-28329-2 U6 - http://dx.doi.org/10.1007/978-3-658-28329-2 N1 - auch gedruckt in der Bereichbibliothek Jülich unter der Signatur 61 UHH 41 PB - Springer Spektrum CY - Wiesbaden ER - TY - CHAP A1 - Jordan, Frank A1 - Katz, Christiane A1 - Pieper, Martin T1 - Online-Kollaboration in der Mathematik: Ein Design-Based-Research-Projekt T2 - Forschungsimpulse für hybrides Lehren und Lernen an Hochschulen N2 - Die Studie erörtert anhand eines Fallbeispiels aus der Mathematik für Ingenieur*innen, wie didaktische Gestaltungsprinzipien für Soziale Präsenz, Kollaboration und das Lösen von praxisnahen Problemen mit mathematischem Denken in einer Online-Umgebung aussehen können. Hierfür zieht der Beitrag den forschungsmethodologischen Rahmen Design-Based Research (DBR) hinzu und berichtet über Zwischenergebnisse. DBR wird an dieser Stelle als eine systematische Herangehensweise an kurzfristige Lehrveränderungen und als Chance auf dem Weg zu einer neuen Hochschullehre nach der COVID-19-Pandemie dargestellt, die theoretische und empirische Erkenntnisse mit Praxisverknüpfung und -relevanz vereint. Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:hbz:832-cos4-9465 SP - 245 EP - 261 PB - TH Köln CY - Köln ER -