TY - JOUR A1 - Ayala, Rafael Ceja A1 - Harris, Isaac A1 - Kleefeld, Andreas T1 - Direct sampling method via Landweber iteration for an absorbing scatterer with a conductive boundary JF - Inverse Problems and Imaging N2 - 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. Y1 - 2024 U6 - https://doi.org/10.3934/ipi.2023051 SN - 1930-8337 SN - 1930-8345 (eISSN) VL - 18 IS - 3 SP - 708 EP - 729 PB - AIMS CY - Springfield ER - TY - CHAP A1 - Kahra, Marvin A1 - Breuß, Michael A1 - Kleefeld, Andreas A1 - Welk, Martin ED - Brunetti, Sara ED - Frosini, Andrea ED - Rinaldi, Simone T1 - An Approach to Colour Morphological Supremum Formation Using the LogSumExp Approximation T2 - Discrete Geometry and Mathematical Morphology N2 - Mathematical morphology is a part of image processing that has proven to be fruitful for numerous applications. Two main operations in mathematical morphology are dilation and erosion. These are based on the construction of a supremum or infimum with respect to an order over the tonal range in a certain section of the image. The tonal ordering can easily be realised in grey-scale morphology, and some morphological methods have been proposed for colour morphology. However, all of these have certain limitations. In this paper we present a novel approach to colour morphology extending upon previous work in the field based on the Loewner order. We propose to consider an approximation of the supremum by means of a log-sum exponentiation introduced by Maslov. We apply this to the embedding of an RGB image in a field of symmetric 2x2 matrices. In this way we obtain nearly isotropic matrices representing colours and the structural advantage of transitivity. In numerical experiments we highlight some remarkable properties of the proposed approach. Y1 - 2024 SN - 978-3-031-57793-2 U6 - https://doi.org/10.1007/978-3-031-57793-2_25 N1 - Third International Joint Conference, DGMM 2024, Florence, Italy, April 15–18, 2024 SP - 325 EP - 337 PB - Springer CY - Cham ER - TY - CHAP A1 - Pieronek, Lukas A1 - Kleefeld, Andreas ED - Constanda, Christian ED - Harris, Paul T1 - The Method of Fundamental Solutions for Computing Interior Transmission Eigenvalues of Inhomogeneous Media T2 - Integral Methods in Science and Engineering: Analytic Treatment and Numerical Approximations N2 - The method of fundamental solutions is applied to the approximate computation of interior transmission eigenvalues for a special class of inhomogeneous media in two dimensions. We give a short approximation analysis accompanied with numerical results that clearly prove practical convenience of our alternative approach. Y1 - 2019 SN - 978-3-030-16077-7 U6 - https://doi.org/10.1007/978-3-030-16077-7_28 SP - 353 EP - 365 PB - Birkhäuser CY - Cham ER - TY - CHAP A1 - Abele, Daniel A1 - Kleefeld, Andreas ED - Constanda, Christian T1 - New Numerical Results for the Optimization of Neumann Eigenvalues T2 - Computational and Analytic Methods in Science and Engineering N2 - We present new numerical results for shape optimization problems of interior Neumann eigenvalues. This field is not well understood from a theoretical standpoint. The existence of shape maximizers is not proven beyond the first two eigenvalues, so we study the problem numerically. We describe a method to compute the eigenvalues for a given shape that combines the boundary element method with an algorithm for nonlinear eigenvalues. As numerical optimization requires many such evaluations, we put a focus on the efficiency of the method and the implemented routine. The method is well suited for parallelization. Using the resulting fast routines and a specialized parametrization of the shapes, we found improved maxima for several eigenvalues. Y1 - 2020 SN - 978-3-030-48185-8 (Print) SN - 978-3-030-48186-5 (Online) U6 - https://doi.org/10.1007/978-3-030-48186-5_1 SP - 1 EP - 20 PB - Birkhäuser CY - Cham ER - TY - JOUR A1 - Aliazizi, Fereshteh A1 - Özsoylu, Dua A1 - Bakhshi Sichani, Soroush A1 - Khorshid, Mehran A1 - Glorieux, Christ A1 - Robbens, Johan A1 - Schöning, Michael Josef A1 - Wagner, Patrick T1 - Development and Calibration of a Microfluidic, Chip-Based Sensor System for Monitoring the Physical Properties of Water Samples in Aquacultures JF - Micromachines N2 - 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. KW - chip-based sensor setup KW - aquaculture KW - microfluidics KW - impedance spectroscopy KW - thermometry KW - electrical conductivity of liquids Y1 - 2024 U6 - https://doi.org/10.3390/mi15060755 SN - 2072-666X N1 - This article belongs to the Special Issue "Multisensor Arrays" N1 - Corresponding author: Michael J. Schöning VL - 15 IS - 6 PB - MDPI CY - Basel ER -