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Interior transmission eigenvalue problems for the Helmholtz equation play an important role in inverse wave scattering. Some distribution properties of those eigenvalues in the complex plane are reviewed. Further, a new scattering model for the interior transmission eigenvalue problem with mixed boundary conditions is described and an efficient algorithm for computing the interior transmission eigenvalues is proposed. Finally, extensive numerical results for a variety of two-dimensional scatterers are presented to show the validity of the proposed scheme.
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.
Das Diskussionspapier beschreibt einen Prozess an der FH Aachen zur Entwicklung und Implementierung eines Self-Assessment-Tools für Studiengänge. Dieser Prozess zielte darauf ab, die Relevanz der Themen Digitalisierung, Internationalisierung und Nachhaltigkeit in Studiengängen zu stärken. Durch Workshops und kollaborative Entwicklung mit Studiendekan:innen entstand ein Fragebogen, der zur Reflexion und strategischen Weiterentwicklung der Studiengänge dient.
In this work, we present a compact, bifunctional chip-based sensor setup that measures the temperature and electrical conductivity of water samples, including specimens from rivers and channels, aquaculture, and the Atlantic Ocean. For conductivity measurements, we utilize the impedance amplitude recorded via interdigitated electrode structures at a single triggering frequency. The results are well in line with data obtained using a calibrated reference instrument. The new setup holds for conductivity values spanning almost two orders of magnitude (river versus ocean water) without the need for equivalent circuit modelling. Temperature measurements were performed in four-point geometry with an on-chip platinum RTD (resistance temperature detector) in the temperature range between 2 °C and 40 °C, showing no hysteresis effects between warming and cooling cycles. Although the meander was not shielded against the liquid, the temperature calibration provided equivalent results to low conductive Milli-Q and highly conductive ocean water. The sensor is therefore suitable for inline and online monitoring purposes in recirculating aquaculture systems.
As one class of molecular imprinted polymers (MIPs), surface imprinted polymer (SIP)-based biosensors show great potential in direct whole-bacteria detection. Micro-contact imprinting, that involves stamping the template bacteria immobilized on a substrate into a pre-polymerized polymer matrix, is the most straightforward and prominent method to obtain SIP-based biosensors. However, the major drawbacks of the method arise from the requirement for fresh template bacteria and often non-reproducible bacteria distribution on the stamp substrate. Herein, we developed a positive master stamp containing photolithographic mimics of the template bacteria (E. coli) enabling reproducible fabrication of biomimetic SIP-based biosensors without the need for the “real” bacteria cells. By using atomic force and scanning electron microscopy imaging techniques, respectively, the E. coli-capturing ability of the SIP samples was tested, and compared with non-imprinted polymer (NIP)-based samples and control SIP samples, in which the cavity geometry does not match with E. coli cells. It was revealed that the presence of the biomimetic E. coli imprints with a specifically designed geometry increases the sensor E. coli-capturing ability by an “imprinting factor” of about 3. These findings show the importance of geometry-guided physical recognition in bacterial detection using SIP-based biosensors. In addition, this imprinting strategy was employed to interdigitated electrodes and QCM (quartz crystal microbalance) chips. E. coli detection performance of the sensors was demonstrated with electrochemical impedance spectroscopy (EIS) and QCM measurements with dissipation monitoring technique (QCM-D).
Electrolyte-insulator-semiconductor capacitors (EISCAP) belong to field-effect sensors having an attractive transducer architecture for constructing various biochemical sensors. In this study, a capacitive model of enzyme-modified EISCAPs has been developed and the impact of the surface coverage of immobilized enzymes on its capacitance-voltage and constant-capacitance characteristics was studied theoretically and experimentally. The used multicell arrangement enables a multiplexed electrochemical characterization of up to sixteen EISCAPs. Different enzyme coverages have been achieved by means of parallel electrical connection of bare and enzyme-covered single EISCAPs in diverse combinations. As predicted by the model, with increasing the enzyme coverage, both the shift of capacitance-voltage curves and the amplitude of the constant-capacitance signal increase, resulting in an enhancement of analyte sensitivity of the EISCAP biosensor. In addition, the capability of the multicell arrangement with multi-enzyme covered EISCAPs for sequentially detecting multianalytes (penicillin and urea) utilizing the enzymes penicillinase and urease has been experimentally demonstrated and discussed.
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.
The artificial olfactory image was proposed by Lundström et al. in 1991 as a new strategy for an electronic nose system which generated a two-dimensional mapping to be interpreted as a fingerprint of the detected gas species. The potential distribution generated by the catalytic metals integrated into a semiconductor field-effect structure was read as a photocurrent signal generated by scanning light pulses. The impact of the proposed technology spread beyond gas sensing, inspiring the development of various imaging modalities based on the light addressing of field-effect structures to obtain spatial maps of pH distribution, ions, molecules, and impedance, and these modalities have been applied in both biological and non-biological systems. These light-addressing technologies have been further developed to realize the position control of a faradaic current on the electrode surface for localized electrochemical reactions and amperometric measurements, as well as the actuation of liquids in microfluidic devices.