TY - JOUR A1 - Philipp, Mohr A1 - Efthimiou, Nikos A1 - Pagano, Fiammetta A1 - Kratochwil, Nicolaus A1 - Pizzichemi, Marco A1 - Tsoumpas, Charalampos A1 - Auffray, Etiennette A1 - Ziemons, Karl T1 - Image reconstruction analysis for positron emission tomography with heterostructured scintillators JF - IEEE Transactions on Radiation and Plasma Medical Sciences N2 - The concept of structure engineering has been proposed for exploring the next generation of radiation detectors with improved performance. A TOF-PET geometry with heterostructured scintillators with a pixel size of 3.0×3.1×15 mm3 was simulated using Monte Carlo. The heterostructures consisted of alternating layers of BGO as a dense material with high stopping power and plastic (EJ232) as a fast light emitter. The detector time resolution was calculated as a function of the deposited and shared energy in both materials on an event-by-event basis. While sensitivity was reduced to 32% for 100 μm thick plastic layers and 52% for 50 μm, the CTR distribution improved to 204±49 ps and 220±41 ps respectively, compared to 276 ps that we considered for bulk BGO. The complex distribution of timing resolutions was accounted for in the reconstruction. We divided the events into three groups based on their CTR and modeled them with different Gaussian TOF kernels. On a NEMA IQ phantom, the heterostructures had better contrast recovery in early iterations. On the other hand, BGO achieved a better contrast to noise ratio (CNR) after the 15th iteration due to the higher sensitivity. The developed simulation and reconstruction methods constitute new tools for evaluating different detector designs with complex time responses. KW - TOF PET KW - Heterostructure KW - Metascintillator KW - Multiple TOF kernels KW - Image Reconstruction Y1 - 2022 U6 - https://doi.org/10.1109/TRPMS.2022.3208615 SN - 2469-7311 SN - 2469-7303 VL - 7 IS - 1 SP - 41 EP - 51 PB - IEEE CY - New York, NY ER - TY - JOUR A1 - Pichler, A. A1 - George, A. A1 - Seiler, F. A1 - Srulijes, J. A1 - Havermann, Marc T1 - Doppler Picture Velocimetry (DPV) applied to hypersonics JF - Shock Waves [Elektronische Ressource] : 26th International Symposium on Shock Waves, Volume 1 / edited by Klaus Hannemann, Friedrich Seiler Y1 - 2009 SN - 978-3-540-85168-4 N1 - International Symposium on Shock Waves ; (26 ; 2007.07.15-20 ; Göttingen) ; ISSW ; (26 ; 2007.07.15-20 ; Göttingen) SP - 503 EP - 508 PB - Springer CY - Berlin ER - 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 - JOUR A1 - Pieper, Martin T1 - Nonlinear integral equations for an inverse electromagnetic scattering problem JF - Journal of Physics Conference Series. 124 (2008) Y1 - 2008 SN - 1742-6596 ER - TY - JOUR A1 - Pieper, Martin T1 - Multiobjective optimization with expensive objectives applied to a thermodynamic material design problem JF - Proceedings in applied mathematics and mechanics : PAMM. 11 (2011), H. 1 Y1 - 2011 SN - 1617-7061 SP - 733 EP - 734 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 - https://doi.org/10.1007/978-3-658-32645-6 PB - Springer CY - Wiesbaden ER - TY - JOUR A1 - Pieper, Martin A1 - Ivanyshyn, Olha T1 - Nonlinear integral equations for a 3D inverse acoustic scattering problem : abstract / O. Ivanyshyn and M. Pieper Y1 - 2008 N1 - World Congress on Computational Mechanics <8, 2008, Venedig> ; European Congress on Computational Methods in Applied Sciences and Engineering <5, 2008, Venedig> ER - TY - JOUR A1 - Pieper, Martin A1 - Klein, Peter T1 - A simple and accurate numerical network flow model for bionic micro heat exchangers JF - Heat mass transfer Y1 - 2011 SN - 0947-7411 VL - 47 IS - 5 SP - 491 EP - 503 PB - Springer CY - Berlin ER - TY - JOUR A1 - Pieper, Martin A1 - Klein, Peter T1 - Application of simple, periodic homogenization techniques to non-linear heat conduction problems in non-periodic, porous media JF - Heat mass transfer N2 - Often, detailed simulations of heat conduction in complicated, porous media have large runtimes. Then homogenization is a powerful tool to speed up the calculations by preserving accurate solutions at the same time. Unfortunately real structures are generally non-periodic, which requires unpractical, complicated homogenization techniques. We demonstrate in this paper, that the application of simple, periodic techniques to realistic media, that are just close to periodic, gives accurate, approximative solutions. In order to obtain effective parameters for the homogenized heat equation, we have to solve a so called “cell problem”. In contrast to periodic structures it is not trivial to determine a suitable unit cell, which represents a non-periodic media. To overcome this problem, we give a rule of thumb on how to choose a good cell. Finally we demonstrate the efficiency of our method for virtually generated foams as well as real foams and compare these results to periodic structures. Y1 - 2012 U6 - https://doi.org/10.1007/s00231-011-0879-4 SN - 0947-7411 VL - 48 IS - 2 SP - 291 EP - 300 PB - Springer CY - Berlin ER - TY - JOUR A1 - Pieper, Martin A1 - Klein, Peter T1 - Numerical solution of the heat equation with non-linear, time derivative-dependent source term JF - International Journal for Numerical Methods in Engineering N2 - The mathematical modeling of heat conduction with adsorption effects in coated metal structures yields the heat equation with piecewise smooth coefficients and a new kind of source term. This term is special, because it is non-linear and furthermore depends on a time derivative. In our approach we reformulated this as a new problem for the usual heat equation, without source term but with a new non-linear coefficient. We gave an existence and uniqueness proof for the weak solution of the reformulated problem. To obtain a numerical solution, we developed a semi-implicit and a fully implicit finite volume method. We compared these two methods theoretically as well as numerically. Finally, as practical application, we simulated the heat conduction in coated aluminum fibers with adsorption in the zeolite coating. Copyright © 2010 John Wiley & Sons, Ltd. Y1 - 2010 U6 - https://doi.org/10.1002/nme.2937 SN - 0029-5981 VL - 84 IS - 10 SP - 1205 EP - 1221 PB - Wiley CY - Chichester ER -