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We present the production of 58mCo on a small, 13 MeV medical cyclotron utilizing a siphon style liquid target system. Different concentrated iron(III)-nitrate solutions of natural isotopic distribution were irradiated at varying initial pressures and subsequently separated by solid phase extraction chromatography. The radio cobalt (58m/gCo and 56Co) was successfully produced with saturation activities of (0.35 ± 0.03) MBq μA−1 for 58mCo with a separation recovery of (75 ± 2) % of cobalt after one separation step utilizing LN-resin.
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.
An alternative method is presented to numerically compute interior elastic transmission eigenvalues for various domains in two dimensions. This is achieved by discretizing the resulting system of boundary integral equations in combination with a nonlinear eigenvalue solver. Numerical results are given to show that this new approach can provide better results than the finite element method when dealing with general domains.
The hot spots conjecture is only known to be true for special geometries. This paper shows numerically that the hot spots conjecture can fail to be true for easy to construct bounded domains with one hole. The underlying eigenvalue problem for the Laplace equation with Neumann boundary condition is solved with boundary integral equations yielding a non-linear eigenvalue problem. Its discretization via the boundary element collocation method in combination with the algorithm by Beyn yields highly accurate results both for the first non-zero eigenvalue and its corresponding eigenfunction which is due to superconvergence. Additionally, it can be shown numerically that the ratio between the maximal/minimal value inside the domain and its maximal/minimal value on the boundary can be larger than 1 + 10− 3. Finally, numerical examples for easy to construct domains with up to five holes are provided which fail the hot spots conjecture as well.
There is a very large number of very important situations which can be modeled with nonlinear parabolic partial differential equations (PDEs) in several dimensions. In general, these PDEs can be solved by discretizing in the spatial variables and transforming them into huge systems of ordinary differential equations (ODEs), which are very stiff. Therefore, standard explicit methods require a large number of iterations to solve stiff problems. But implicit schemes are computationally very expensive when solving huge systems of nonlinear ODEs. Several families of Extrapolated Stabilized Explicit Runge-Kutta schemes (ESERK) with different order of accuracy (3 to 6) are derived and analyzed in this work. They are explicit methods, with stability regions extended, along the negative real semi-axis, quadratically with respect to the number of stages s, hence they can be considered to solve stiff problems much faster than traditional explicit schemes. Additionally, they allow the adaptation of the step length easily with a very small cost.
Two new families of ESERK schemes (ESERK3 and ESERK6) are derived, and analyzed, in this work. Each family has more than 50 new schemes, with up to 84.000 stages in the case of ESERK6. For the first time, we also parallelized all these new variable step length and variable number of stages algorithms (ESERK3, ESERK4, ESERK5, and ESERK6). These parallelized strategies allow to decrease times significantly, as it is discussed and also shown numerically in two problems. Thus, the new codes provide very good results compared to other well-known ODE solvers. Finally, a new strategy is proposed to increase the efficiency of these schemes, and it is discussed the idea of combining ESERK families in one code, because typically, stiff problems have different zones and according to them and the requested tolerance the optimum order of convergence is different.
A second-order L-stable exponential time-differencing (ETD) method is developed by combining an ETD scheme with approximating the matrix exponentials by rational functions having real distinct poles (RDP), together with a dimensional splitting integrating factor technique. A variety of non-linear reaction-diffusion equations in two and three dimensions with either Dirichlet, Neumann, or periodic boundary conditions are solved with this scheme and shown to outperform a variety of other second-order implicit-explicit schemes. An additional performance boost is gained through further use of basic parallelization techniques.
In this article, a concept of implicit methods for scalar conservation laws in one or more spatial dimensions allowing also for source terms of various types is presented. This material is a significant extension of previous work of the first author (Breuß SIAM J. Numer. Anal. 43(3), 970–986 2005). Implicit notions are developed that are centered around a monotonicity criterion. We demonstrate a connection between a numerical scheme and a discrete entropy inequality, which is based on a classical approach by Crandall and Majda. Additionally, three implicit methods are investigated using the developed notions. Next, we conduct a convergence proof which is not based on a classical compactness argument. Finally, the theoretical results are confirmed by various numerical tests.
The inverse scattering problem for a conductive boundary condition and transmission eigenvalues
(2018)
In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. In particular, we are interested in two problems that arise from this inverse problem: the inverse conductivity problem and the corresponding interior transmission eigenvalue problem. The inverse conductivity problem is to recover the conductive boundary parameter from the measured scattering data. We prove that the measured scatted data uniquely determine the conductivity parameter as well as describe a direct algorithm to recover the conductivity. The interior transmission eigenvalue problem is an eigenvalue problem associated with the inverse scattering of such materials. We investigate the convergence of the eigenvalues as the conductivity parameter tends to zero as well as prove existence and discreteness for the case of an absorbing media. Lastly, several numerical and analytical results support the theory and we show that the inside–outside duality method can be used to reconstruct the interior conductive eigenvalues.
The aim of the current study was to investigate the performance of integrated RF
transmit arrays with high channel count consisting of meander microstrip antennas
for body imaging at 7 T and to optimize the position and number of transmit ele-
ments. RF simulations using multiring antenna arrays placed behind the bore liner
were performed for realistic exposure conditions for body imaging. Simulations were
performed for arrays with as few as eight elements and for arrays with high channel
counts of up to 48 elements. The B1+ field was evaluated regarding the degrees of
freedom for RF shimming in the abdomen. Worst-case specific absorption rate
(SARwc ), SAR overestimation in the matrix compression, the number of virtual obser-
vation points (VOPs) and SAR efficiency were evaluated. Constrained RF shimming
was performed in differently oriented regions of interest in the body, and the devia-
tion from a target B1+ field was evaluated. Results show that integrated multiring
arrays are able to generate homogeneous B1+ field distributions for large FOVs, espe-
cially for coronal/sagittal slices, and thus enable body imaging at 7 T with a clinical
workflow; however, a low duty cycle or a high SAR is required to achieve homoge-
neous B1+ distributions and to exploit the full potential. In conclusion, integrated
arrays allow for high element counts that have high degrees of freedom for the pulse
optimization but also produce high SARwc , which reduces the SAR accuracy in the
VOP compression for low-SAR protocols, leading to a potential reduction in array
performance. Smaller SAR overestimations can increase SAR accuracy, but lead to a
high number of VOPs, which increases the computational cost for VOP evaluation
and makes online SAR monitoring or pulse optimization challenging. Arrays with
interleaved rings showed the best results in the study.
Im Verfahren gegen die Österreichische Post AG (Rs. C-300/21) befasste sich der EuGH erstmals mit dem in Art. 82 DS-GVO geregelten datenschutzrechtlichen Schadensersatzanspruch. Mit den Klarstellungen des EuGH verschieben sich die Probleme nun stärker zu den „klassischen“ Fragen des Schadensersatzrechts im Zivilprozess. Relevant sind dabei vor allem Aspekte der Darlegungs- und Beweislast und deren Besonderheiten mit Blick auf den Ersatz immaterieller Schäden. Der Beitrag fokussiert sich auf die Voraussetzungen und den dabei zu führenden Tatsachenbeweis bei der Klage des Betroffenen gegen den Verantwortlichen auf Ersatz immaterieller Schäden.