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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.
This paper introduces a new maritime search and rescue system based on S-band illumination harmonic radar (HR). Passive and active tags have been developed and tested while attached to life jackets and a small boat. In this demonstration test carried out on the Baltic Sea, the system was able to detect and range the active tags up to a distance of 5800 m using an illumination signal transmit-power of 100 W. Special attention is given to the development, performance, and conceptual differences between passive and active tags used in the system. Guidelines for achieving a high HR dynamic range, including a system components description, are given and a comparison with other HR systems is performed. System integration with a commercial maritime X-band navigation radar is shown to demonstrate a solution for rapid search and rescue response and quick localization.
Biopharmaceuticals such as antibodies are produced in cultivated mammalian cells, which must be monitored to comply with good manufacturing practice. We, therefore, developed a fully automated system comprising a specific exhaust gas analyzer, inline analytics and a corresponding algorithm to precisely determine the oxygen uptake rate, carbon dioxide evolution rate, carbon dioxide transfer rate, transfer quotient and respiratory quotient without interrupting the ongoing cultivation, in order to assess its reproducibility. The system was verified using chemical simulation experiments and was able to measure the respiratory activity of hybridoma cells and DG44 cells (derived from Chinese hamster ovary cells) with satisfactory results at a minimum viable cell density of ~2.0 × 10⁵ cells ml⁻¹. The system was suitable for both batch and fed-batch cultivations in bubble-aerated and membrane-aerated reactors, with and without the control of pH and dissolved oxygen.
An immunochromatographic lateral flow dipstick assay for the fast detection of microcystin-LR was developed. Colloid gold particles with diameters of 40 nm were used as red-colored antibody labels for the visual detection of the antigen. The new dipstick sensor is capable of detecting down to 5 µg·l−1 (ppb; total inversion of the color signal) or 1 ppb (observation of color grading) of microcystin-LR. The course of the labeling reaction was observed via spectrometric wave shifts caused by the change of particle size during the binding of antibodies. Different stabilizing reagents showed that especially bovine serum albumin (BSA) and casein increase the assays sensitivity and the conjugate stability. Performance of the dipsticks was quantified by pattern processing of capture zone CCD images. Storage stability of dipsticks and conjugate suspensions over 115 days under different conditions were monitored. The ready-to-use dipsticks were successfully tested with microcystin-LR-spiked samples of outdoor drinking- and salt water and applied to the tissue of microcystin-fed mussels.
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.