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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 hybrid K+/Ca2+ sensor based on laser scanned silicon transducer for multi-component analysis
(2002)
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.
Humic substances originating from various organic matters can ameliorate soil properties, stimulate plant growth, and improve nutrient uptake. Due to the low calorific heating value, leonardite is rather unsuitable as fuel. However, it may serve as a potential source of humic substances. This study was aimed at characterizing the leonardite-based soil amendments and examining the effect of their application on the soil microbial community, as well as on potato growth and tuber yield. A high yield (71.1%) of humic acid (LHA) from leonardite has been demonstrated. Parental leonardite (PL) and LHA were applied to soil prior to potato cultivation. The 16S rRNA sequencing of soil samples revealed distinct relationships between microbial community composition and the application of leonardite-based soil amendments. Potato tubers were planted in pots in greenhouse conditions. The tubers were harvested at the mature stage for the determination of growth and yield parameters. The results demonstrated that the LHA treatments had a significant effect on increasing potato growth (54.9%) and tuber yield (66.4%) when compared to the control. The findings highlight the importance of amending leonardite-based humic products for maintaining the biogeochemical stability of soils, for keeping their healthy microbial community structure, and for increasing the agronomic productivity of potato plants.
The Crystal Clear Collaboration has developed a modular system for a small animal PET scanner (ClearPET). The modularity allows the assembly of scanners of different sizes and characteristics in order to satisfy the specific needs of the individual member institutions. The system performs depth of interaction detection by using a phoswich arrangement combining LSO and LuYAP scintillators which are coupled to Multichannel Photomultipliers (PMTs). For each PMT a free running 40 MHz ADC digitizes the signal and the complete scintillation pulse is sampled by an FPGA and sent with 20 MB/s to a PC for preprocessing. The pulse provides information about the gamma energy and the scintillator material which identifies the interaction layer. Furthermore, the exact pulse starting time is obtained from the sampled data. This is important as no hardware coincidence detection is implemented. All single events are recorded and coincidences are identified by software. The system in Jülich (ClearPET Neuro) is equipped with 10240 crystals on 80 PMTs. The paper will present an overview of the data acquisition system.
Following the success of PET/CT during the last decade and the recent increasing proliferation of SPECT/CT, another hybrid imaging instrument has been gaining more and more interest: MR-PET. First combined, simultaneous PET and MR studies carried out in small animals demonstrated the feasibility of the new approach. Concurrently, some prototypes of an MR-PET scanner for simultaneous human brain studies have been built, their performance is being tested and preliminary applications have already been shown. Through this pioneering work, it has become clear that advances in the detector design are necessary for further optimization.
Recently, the different issues related to the present state and future prospects of MR-PET were presented and discussed during an international 2-day workshop at the Forschungszentrum Jülich, Germany, held after, and in conjunction with, the 2008 IEEE Nuclear Science Symposium and Medical Imaging Conference in Dresden, Germany on October 27–28, 2008. The topics ranged from small animal MR-PET imaging to human MR-BrainPET imaging, new detector developments, challenges/opportunities for ultra-high field MR-PET imaging and considerations of possible future research and clinical applications. This report presents a critical summary of the contributions made to the workshop.