@article{PhilippEfthimiouPaganoetal.2022, author = {Philipp, Mohr and Efthimiou, Nikos and Pagano, Fiammetta and Kratochwil, Nicolaus and Pizzichemi, Marco and Tsoumpas, Charalampos and Auffray, Etiennette and Ziemons, Karl}, title = {Image reconstruction analysis for positron emission tomography with heterostructured scintillators}, series = {IEEE Transactions on Radiation and Plasma Medical Sciences}, volume = {7}, journal = {IEEE Transactions on Radiation and Plasma Medical Sciences}, number = {1}, publisher = {IEEE}, address = {New York, NY}, issn = {2469-7311}, doi = {10.1109/TRPMS.2022.3208615}, pages = {41 -- 51}, year = {2022}, abstract = {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.}, language = {en} } @article{PichlerGeorgeSeileretal.2009, author = {Pichler, A. and George, A. and Seiler, F. and Srulijes, J. and Havermann, Marc}, title = {Doppler Picture Velocimetry (DPV) applied to hypersonics}, series = {Shock Waves [Elektronische Ressource] : 26th International Symposium on Shock Waves, Volume 1 / edited by Klaus Hannemann, Friedrich Seiler}, journal = {Shock Waves [Elektronische Ressource] : 26th International Symposium on Shock Waves, Volume 1 / edited by Klaus Hannemann, Friedrich Seiler}, publisher = {Springer}, address = {Berlin}, isbn = {978-3-540-85168-4}, pages = {503 -- 508}, year = {2009}, language = {en} } @article{Pieper2009, author = {Pieper, Martin}, title = {Vector hyperinterpolation on the sphere}, series = {Journal of approximation theory. 156 (2009), H. 2}, journal = {Journal of approximation theory. 156 (2009), H. 2}, isbn = {0021-9045}, pages = {173 -- 186}, year = {2009}, language = {en} } @article{Pieper2008, author = {Pieper, Martin}, title = {Nonlinear integral equations for an inverse electromagnetic scattering problem}, series = {Journal of Physics Conference Series. 124 (2008)}, journal = {Journal of Physics Conference Series. 124 (2008)}, isbn = {1742-6596}, year = {2008}, language = {en} } @article{Pieper2011, author = {Pieper, Martin}, title = {Multiobjective optimization with expensive objectives applied to a thermodynamic material design problem}, series = {Proceedings in applied mathematics and mechanics : PAMM. 11 (2011), H. 1}, journal = {Proceedings in applied mathematics and mechanics : PAMM. 11 (2011), H. 1}, publisher = {Wiley}, address = {Weinheim}, isbn = {1617-7061}, pages = {733 -- 734}, year = {2011}, language = {en} } @book{Pieper2021, author = {Pieper, Martin}, title = {Quantum mechanics: Introduction to mathematical formulation}, publisher = {Springer}, address = {Wiesbaden}, isbn = {978-3-658-32644-9}, doi = {10.1007/978-3-658-32645-6}, pages = {XIII, 33}, year = {2021}, abstract = {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 Schr{\"o}dinger'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.}, language = {en} } @article{PieperIvanyshyn2008, author = {Pieper, Martin and Ivanyshyn, Olha}, title = {Nonlinear integral equations for a 3D inverse acoustic scattering problem : abstract / O. Ivanyshyn and M. Pieper}, year = {2008}, language = {en} } @article{PieperKlein2011, author = {Pieper, Martin and Klein, Peter}, title = {A simple and accurate numerical network flow model for bionic micro heat exchangers}, series = {Heat mass transfer}, volume = {47}, journal = {Heat mass transfer}, number = {5}, publisher = {Springer}, address = {Berlin}, isbn = {0947-7411}, pages = {491 -- 503}, year = {2011}, language = {en} } @article{PieperKlein2012, author = {Pieper, Martin and Klein, Peter}, title = {Application of simple, periodic homogenization techniques to non-linear heat conduction problems in non-periodic, porous media}, series = {Heat mass transfer}, volume = {48}, journal = {Heat mass transfer}, number = {2}, publisher = {Springer}, address = {Berlin}, issn = {0947-7411}, doi = {10.1007/s00231-011-0879-4}, pages = {291 -- 300}, year = {2012}, abstract = {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.}, language = {en} } @article{PieperKlein2010, author = {Pieper, Martin and Klein, Peter}, title = {Numerical solution of the heat equation with non-linear, time derivative-dependent source term}, series = {International Journal for Numerical Methods in Engineering}, volume = {84}, journal = {International Journal for Numerical Methods in Engineering}, number = {10}, publisher = {Wiley}, address = {Chichester}, issn = {0029-5981}, doi = {10.1002/nme.2937}, pages = {1205 -- 1221}, year = {2010}, abstract = {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.}, language = {en} }