@article{DiethelmUhlig, author = {Diethelm, Kai and Uhlig, Frank}, title = {A New Approach to Shooting Methods for Terminal Value Problems of Fractional Differential Equations}, series = {Journal of Scientific Computing}, volume = {97}, journal = {Journal of Scientific Computing}, number = {2}, issn = {0885-7474}, abstract = {For terminal value problems of fractional differential equations of order α∈(0,1) that use Caputo derivatives, shooting methods are a well developed and investigated approach. Based on recently established analytic properties of such problems, we develop a new technique to select the required initial values that solves such shooting problems quickly and accurately. Numerical experiments indicate that this new proportional secting technique converges very quickly and accurately to the solution. Run time measurements indicate a speedup factor of between 4 and 10 when compared to the standard bisection method.}, language = {en} } @article{Bier, author = {Bier, Markus}, title = {Non-equilibrium steady states of electrolyte interfaces}, series = {New Journal of Physics}, volume = {26}, journal = {New Journal of Physics}, number = {1}, pages = {013008}, abstract = {The non-equilibrium steady states of a semi-infinite quasi-one-dimensional univalent binary electrolyte solution, characterised by non-vanishing electric currents, are investigated by means of Poisson-Nernst-Planck (PNP) theory. Exact analytical expressions of the electric field, the charge density and the number density are derived, which depend on the electric current density as a parameter. From a non-equilibrium version of the Grahame equation, which relates the total space charge per cross-sectional area and the corresponding contribution of the electric potential drop, the current-dependent differential capacitance of the diffuse layer is derived. In the limit of vanishing electric current these results reduce to those within Gouy-Chapman theory. It is shown that improperly chosen boundary conditions lead to non-equilibrium steady state solutions of the PNP equations with negative ion number densities. A necessary and sufficient criterion on surface conductivity constitutive relations is formulated which allows one to detect such unphysical solutions.}, language = {en} } @article{StorathWeinmann, author = {Storath, Martin and Weinmann, Andreas}, title = {Smoothing Splines for Discontinuous Signals}, series = {Journal of Computational and Graphical Statistics}, volume = {33}, journal = {Journal of Computational and Graphical Statistics}, number = {2}, publisher = {Informa UK Limited}, issn = {1061-8600}, doi = {10.1080/10618600.2023.2262000}, pages = {651 -- 664}, language = {en} } @inproceedings{StorathWeinmann2024, author = {Storath, Martin and Weinmann, Andreas}, title = {Solving higher-order Mumford-Shah models}, series = {INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: ICNAAM2022}, booktitle = {INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: ICNAAM2022}, publisher = {AIP Publishing}, issn = {0094-243X}, doi = {10.1063/5.0210598}, year = {2024}, language = {en} } @incollection{ZieglerIsingDobhanetal.2023, author = {Ziegler, Cedric C. and Ising, Julia and Dobhan, Alexander and Storath, Martin}, title = {Computer Vision in Reusable Container Management : Requirements, Conception, and Data Acquisition}, series = {Logistik und Supply Chain Management}, booktitle = {Logistik und Supply Chain Management}, publisher = {University of Bamberg Press}, isbn = {9783863099411}, issn = {2750-8277}, doi = {https://10.20378/irb-92408}, pages = {107 -- 122}, year = {2023}, abstract = {In container management, the reuse of small load carriers is a business alternative to disposal carriers. Reusable container management is furthermore a solution to improve the environmental impact of the logistic industry. The sorting and stock management of small load carriers are today primarily manual work and have consequently a low level of automation. In order to increase the automation of returnable containers, it is crucial to establish a computer vision system that (i) classifies the containers and (ii) detects potential defects or stains. This paper provides an overview and a discussion of the applications that are already in use. Object detection is necessary for many actions in the container management business processes, such as inventory and stock management. Detection of defects on the small load carrier is required for scrapping the carriers to ensure a smooth process in any business process involving the carrier and to decide whether additional process steps, e.g., cleaning, are required. The literature review in this paper establishes the demand for computer vision detection and shows the project setup necessary to conduct research in this area. The comparison with other applications of defect and anomaly detection supports the applicability and shows the need for further research in this specific academic field. This leads to a project outline and the research provides the technical implementation of the detections in container management. Accordingly, the research provides a work- flow guide from data acquisition to a high-quality dataset of labeled anomalies of small load carriers.}, language = {en} }