@unpublished{DiethelmHashemishahrakiThaietal., author = {Diethelm, Kai and Hashemishahraki, Safoura and Thai, Ha Duc and Tuan, Hoang The}, title = {Stability properties of multi-order fractional differential systems in 3D}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:863-opus-51960}, pages = {6}, abstract = {This paper is devoted to studying three-dimensional non-commensurate fractional order differential equation systems with Caputo derivatives. Necessary and sufficient conditions are for the asymptotic stability of such systems are obtained.}, language = {en} } @unpublished{ChaudharyDiethelm, author = {Chaudhary, Renu and Diethelm, Kai}, title = {Novel variants of diffusive representation of fractional integrals: Construction and numerical computation}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:863-opus-51975}, pages = {6}, abstract = {In this paper, we revisit the diffusive representations of fractional integrals established in Diethelm (2023a) to explore novel variants of such representations which provide highly efficient numerical algorithms for the approximate numerical evaluation of fractional integrals.}, language = {en} } @article{HoefflinSauerSchiffleretal., author = {H{\"o}fflin, Dennis and Sauer, Christian and Schiffler, Andreas and Hartmann, J{\"u}rgen}, title = {Process Monitoring Using Synchronized Path Infrared Thermography in PBF-LB/M}, series = {Sensors}, volume = {22}, journal = {Sensors}, number = {16}, publisher = {MDPI}, doi = {10.3390/s22165943}, pages = {5943}, abstract = {Additive manufacturing processes, particularly Laser-Based Powder Bed Fusion of Metals (PBF-LB/M), enable the development of new application possibilities due to their manufacturing-specific freedom of design. These new fields of application require a high degree of component quality, especially in safety-relevant areas. This is currently ensured primarily via a considerable amount of downstream quality control. Suitable process monitoring systems promise to reduce this effort drastically. This paper introduces a novel monitoring method in order to gain process-specific thermal information during the manufacturing process. The Synchronized Path Infrared Thermography (SPIT) method is based on two synchronized galvanometer scanners allowing high-speed and high-resolution observations of the melt pool in the SWIR range. One scanner is used to steer the laser over the building platform, while the second scanner guides the field of view of an IR camera. With this setup, the melting process is observed at different laser powers, scan speeds and at different locations with respect to the laser position, in order to demonstrate the positioning accuracy of the system and to initially gain thermal process data of the melt pool and the heat-affected zone. Therefore, the SPIT system shows a speed independent overall accuracy of ±2 Pixel within the evaluated range. The system further allows detailed thermal observation of the melt pool and the surrounding heat-affected zone.}, language = {en} } @article{HoefflinHartmannRosiliusetal., author = {H{\"o}fflin, Dennis and Hartmann, J{\"u}rgen and Rosilius, Maximilian and Seitz, Philipp and Schiffler, Andreas}, title = {Opto-Thermal Investigation of Additively Manufactured Steel Samples as a Function of the Hatch Distance}, series = {Sensors}, volume = {22}, journal = {Sensors}, number = {1}, publisher = {MDPI}, issn = {1424-8220}, doi = {10.3390/s22010046}, pages = {46}, abstract = {Nowadays, additive manufacturing processes are becoming more and more appealing due to their production-oriented design guidelines, especially with regard to topology optimisation and minimal downstream production depth in contrast to conventional technologies. However, a scientific path in the areas of quality assurance, material and microstructural properties, intrinsic thermal permeability and dependent stress parameters inhibits enthusiasm for the potential degrees of freedom of the direct metal laser melting process (DMLS). Especially in quality assurance, post-processing destructive measuring methods are still predominantly necessary in order to evaluate the components adequately. The overall objective of these investigations is to gain process knowledge make reliable in situ statements about component quality and material properties based on the process parameters used and emission values measured. The knowledge will then be used to develop non-destructive tools for the quality management of additively manufactured components. To assess the effectiveness of the research design in relation to the objectives for further investigations, this pre-study evaluates the dependencies between the process parameters, process emission during manufacturing and resulting thermal diffusivity and the relative density of samples fabricated by DMLS. Therefore, the approach deals with additively built metal samples made on an EOS M290 apparatus with varying hatch distances while simultaneously detecting the process emission. Afterwards, the relative density of the samples is determined optically, and thermal diffusivity is measured using the laser flash method. As a result of this pre-study, all interactions of the within factors are presented. The process variable hatch distance indicates a strong influence on the resulting material properties, as an increase in the hatch distance from 0.11 mm to 1 mm leads to a drop in relative density of 57.4\%. The associated thermal diffusivity also reveals a sharp decrease from 5.3 mm2/s to 1.3 mm2/s with growing hatch distances. The variability of the material properties can also be observed in the measured process emissions. However, as various factors overlap in the thermal radiation signal, no clear assignment is possible within the scope of this work.}, language = {en} } @misc{OPUS4-1913, title = {FHWS Science Journal (5, 1)}, volume = {5 (2021)}, number = {1}, editor = {Grebner, Robert}, address = {W{\"u}rzburg}, organization = {Hochschule f{\"u}r Angewandte Wissenschaften W{\"u}rzburg-Schweinfurt}, issn = {2196-6095}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:863-opus-19135}, pages = {116}, abstract = {[D]ie Beitr{\"a}ge im vorliegenden FHWS Science Journal [dienen] dazu, einen Ein- und {\"U}berblick {\"u}ber eine Auswahl erfolgreicher Maßnahmen zu geben, die im Rahmen des BEST-FIT-Projektes entwickelt wurden und die erarbeiteten Methoden, Konzepte und Ergebnisse mit interessierten Lehrenden zu teilen. Nur wenn es gelingt, erfolgreiche Maßnahmen auch nach dem Ende der F{\"o}rderperiode an der FHWS weiterzuf{\"u}hren und auf weitere Studieng{\"a}nge und Fakult{\"a}ten zu {\"u}bertragen, k{\"o}nnen die Ziele von BEST-FIT und insgesamt des Qualit{\"a}tspakts Lehre nachhaltig und dauerhaft erreicht und gesichert werden.}, language = {de} } @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} }