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Image reconstruction analysis for positron emission tomography with heterostructured scintillators
(2022)
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.
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.
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.
Numerical solution of the heat equation with non-linear, time derivative-dependent source term
(2010)
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.
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.
Surgical clip applicator
(1996)
The method of fundamental solutions is applied to the approximate computation of interior transmission eigenvalues for a special class of inhomogeneous media in two dimensions. We give a short approximation analysis accompanied with numerical results that clearly prove practical convenience of our alternative approach.
This paper investigates the interior transmission problem for homogeneous media via eigenvalue trajectories parameterized by the magnitude of the refractive index. In the case that the scatterer is the unit disk, we prove that there is a one-to-one correspondence between complex-valued interior transmission eigenvalue trajectories and Dirichlet eigenvalues of the Laplacian which turn out to be exactly the trajectorial limit points as the refractive index tends to infinity. For general simply-connected scatterers in two or three dimensions, a corresponding relation is still open, but further theoretical results and numerical studies indicate a similar connection.
IT Service Deployment
(2007)
IT Products are viewed and managed differently depending on the perspectives and the stage within the life cycle. A model is presented that integrates different perspectives and stages serving as an aid for the analysis of business models and focused positioning of IT-products. Four generic business models are analysed with regard to the product management function in general and the positioning field for IT-products specifically: off-the-shelf (license), license plus service, project, and system service (incl. cloud computing).