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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.
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.
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.
Characterisation of polymeric materials as passivation layer for calorimetric H2O2 gas sensors
(2012)
Calorimetric gas sensors for monitoring the H₂O₂ concentration at elevated temperatures in industrial sterilisation processes have been presented in previous works. These sensors are built up in form of a differential set-up of a catalytically active and passive temperature-sensitive structure. Although, various types of catalytically active dispersions have been studied, the passivation layer has to be established and therefore, chemically as well as physically characterised. In the present work, fluorinated ethylene propylene (FEP), perfluoralkoxy (PFA) and epoxy-based SU-8 photoresist as temperature-stable polymeric materials have been investigated for sensor passivation in terms of their chemical inertness against H₂O₂, their hygroscopic properties as well as their morphology. The polymeric materials were deposited via spin-coating on the temperature-sensitive structure, wherein spin-coated FEP and PFA show slight agglomerates. However, they possess a low absorption of humidity due to their hydrophobic surface, whereas the SU-8 layer has a closed surface but shows a slightly higher absorption of water. All of them were inert against gaseous H₂O₂ during the characterisation in H₂O₂ atmosphere that demonstrates their suitability as passivation layer for calorimetric H₂O₂ gas sensors.
A wireless sensor system based on the industrial ZigBee standard for low-rate wireless networking was developed that enables real-time monitoring of gaseous H2O2 during the package sterilization in aseptic food processes. The sensor system consists of a remote unit connected to a calorimetric gas sensor, which was already established in former works, and an external base unit connected to a laptop computer. The remote unit was built up by an XBee radio frequency (RF) module for data communication and a programmable system-on-chip controller to read out the sensor signal and process the sensor data, whereas the base unit is a second XBee RF module. For the rapid H2O2 detection on various locations inside the package that has to be sterilized, a novel read-out strategy of the calorimetric gas sensor was established, wherein the sensor response is measured within the short sterilization time and correlated with the present H2O2 concentration. In an exemplary measurement application in an aseptic filling machinery, the suitability of the new, wireless sensor system was demonstrated, wherein the influence of the gas velocity on the H2O2 distribution inside a package was determined and verified with microbiological tests.
In the present work, a novel method for monitoring sterilisation processes with gaseous H2O2 in combination with heat activation by means of a specially designed calorimetric gas sensor was evaluated. Therefore, the sterilisation process was extensively studied by using test specimens inoculated with Bacillus atrophaeus spores in order to identify the most influencing process factors on its microbicidal effectiveness. Besides the contact time of the test specimens with gaseous H2O2 varied between 0.2 and 0.5 s, the present H2O2 concentration in a range from 0 to 8% v/v (volume percent) had a strong influence on the microbicidal effectiveness, whereas the change of the vaporiser temperature, gas flow and humidity were almost negligible. Furthermore, a calorimetric H2O2 gas sensor was characterised in the sterilisation process with gaseous H2O2 in a wide range of parameter settings, wherein the measurement signal has shown a linear response against the H2O2 concentration with a sensitivity of 4.75 °C/(% v/v). In a final step, a correlation model by matching the measurement signal of the gas sensor with the microbial inactivation kinetics was established that demonstrates its suitability as an efficient method for validating the microbicidal effectiveness of sterilisation processes with gaseous H2O2.