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Density reduction effects on the production of [11C]CO2 in Nb-body targets on a medical cyclotron
(2023)
Medical isotope production of 11C is commonly performed in gaseous targets. The power deposition of the proton beam during the irradiation decreases the target density due to thermodynamic mixing and can cause an increase of penetration depth and divergence of the proton beam. In order to investigate the difference how the target-body length influences the operation conditions and the production yield, a 12 cm and a 22 cm Nb-target body containing N2/O2 gas were irradiated using a 13 MeV proton cyclotron. It was found that the density reduction has a large influence on the pressure rise during irradiation and the achievable radioactive yield. The saturation activity of [11C]CO2 for the long target (0.083 Ci/μA) is about 10% higher than in the short target geometry (0.075 Ci/μA).
Elastic transmission eigenvalues and their computation via the method of fundamental solutions
(2020)
A stabilized version of the fundamental solution method to catch ill-conditioning effects is investigated with focus on the computation of complex-valued elastic interior transmission eigenvalues in two dimensions for homogeneous and isotropic media. Its algorithm can be implemented very shortly and adopts to many similar partial differential equation-based eigenproblems as long as the underlying fundamental solution function can be easily generated. We develop a corroborative approximation analysis which also implicates new basic results for transmission eigenfunctions and present some numerical examples which together prove successful feasibility of our eigenvalue recovery approach.
In der wasserbaulichen Forschung werden neben klassischen Messinstrumenten zunehmend kamerabasierte Verfahren genutzt. Diese erlauben neben der Bestimmung von Fließgeschwindigkeiten auch die Detektion der freien Wasseroberfläche oder zeitliche Vermessung von Kolken. Durch die hohen räumlichen und zeitlichen Auflösungen, welche neueste Kamerasensoren liefern, können neue Erkenntnisse in turbulenten, komplexen Strömungen gewonnen werden. Auch in der Praxis können diese Verfahren mit geringem Aufwand wichtige Daten liefern.
The low-pressure system Bernd involved extreme rainfalls in the Western part of Germany in July 2021,
resulting in major floods, severe damages and a tremendous number of casualties. Such extreme events
are rare and full flood protection can never be ensured with reasonable financial means. But still, this
event must be starting point to reconsider current design concepts. This article aims at sharing some
thoughts on potential hazards, the selection of return periods and remaining risk with the focus on Germany.
Direct sampling method via Landweber iteration for an absorbing scatterer with a conductive boundary
(2024)
In this paper, we consider the inverse shape problem of recovering isotropic scatterers with a conductive boundary condition. Here, we assume that the measured far-field data is known at a fixed wave number. Motivated by recent work, we study a new direct sampling indicator based on the Landweber iteration and the factorization method. Therefore, we prove the connection between these reconstruction methods. The method studied here falls under the category of qualitative reconstruction methods where an imaging function is used to recover the absorbing scatterer. We prove stability of our new imaging function as well as derive a discrepancy principle for recovering the regularization parameter. The theoretical results are verified with numerical examples to show how the reconstruction performs by the new Landweber direct sampling method.
We consider the numerical approximation of second-order semi-linear parabolic stochastic partial differential equations interpreted in the mild sense which we solve on general two-dimensional domains with a C² boundary with homogeneous Dirichlet boundary conditions. The equations are driven by Gaussian additive noise, and several Lipschitz-like conditions are imposed on the nonlinear function. We discretize in space with a spectral Galerkin method and in time using an explicit Euler-like scheme. For irregular shapes, the necessary Dirichlet eigenvalues and eigenfunctions are obtained from a boundary integral equation method. This yields a nonlinear eigenvalue problem, which is discretized using a boundary element collocation method and is solved with the Beyn contour integral algorithm. We present an error analysis as well as numerical results on an exemplary asymmetric shape, and point out limitations of the approach.
Analysis and computation of the transmission eigenvalues with a conductive boundary condition
(2022)
We provide a new analytical and computational study of the transmission eigenvalues with a conductive boundary condition. These eigenvalues are derived from the scalar inverse scattering problem for an inhomogeneous material with a conductive boundary condition. The goal is to study how these eigenvalues depend on the material parameters in order to estimate the refractive index. The analytical questions we study are: deriving Faber–Krahn type lower bounds, the discreteness and limiting behavior of the transmission eigenvalues as the conductivity tends to infinity for a sign changing contrast. We also provide a numerical study of a new boundary integral equation for computing the eigenvalues. Lastly, using the limiting behavior we will numerically estimate the refractive index from the eigenvalues provided the conductivity is sufficiently large but unknown.