TY - JOUR A1 - Staat, Manfred T1 - Problems and Chances for Probabilistic Fracture Mechanics in the Analysis of Steel Pressure Boundary Reliability JF - Technical feasibility and reliability of passive safety systems for nuclear power plants. Proceedings of an Advisory Group Meeting held in Jülich, 21-24 November 1994 Y1 - 1996 N1 - IAEA-TECDOC-920 ; Onlinezugriff erfolgt auf die überarb. Ausg. 2006 SP - 43 EP - 55 CY - Vienna ER - TY - JOUR A1 - Stulpe, Werner T1 - Conditional Expectations, Conditional Distributions, and A Posteriori Ensembles in Generalized Probability Theory JF - International Journal of Theoretical Physics. 27 (1988), H. 5 Y1 - 1988 SN - 1572-9575 SP - 587 EP - 611 ER - TY - JOUR A1 - Laack, Walter van T1 - Allgemeine physiotherapeutische Behandlung nach Hüft- und Kniegelenkoperationen JF - Physiotherapie. 77 (1986), H. 2 Y1 - 1986 SN - 0031-9392 SP - 68 EP - 72 ER - TY - JOUR A1 - Janus, Kevin Alexander A1 - Achtsnicht, Stefan A1 - Drinic, Aleksander A1 - Kopp, Alexander A1 - Keusgen, Michael A1 - Schöning, Michael Josef T1 - Transient magnesium-based thin-film temperature sensor on a flexible, bioabsorbable substrate for future medical applications JF - Applied Research N2 - In this work, the bioabsorbable materials, namely fibroin, polylactide acid (PLA), magnesium and magnesium oxide are investigated for their application as transient, resistive temperature detectors (RTD). For this purpose, a thin-film magnesium-based meander-like electrode is deposited onto a flexible, bioabsorbable substrate (fibroin or PLA) and encapsulated (passivated) by additional magnesium oxide layers on top and below the magnesium-based electrode. The morphology of different layered RTDs is analyzed by scanning electron microscopy. The sensor performance and lifetime of the RTD is characterized both under ambient atmospheric conditions between 30°C and 43°C, and wet tissue-like conditions with a constant temperature regime of 37°C. The latter triggers the degradation process of the magnesium-based layers. The 3-layers RTDs on a PLA substrate could achieve a lifetime of 8.5 h. These sensors also show the best sensor performance under ambient atmospheric conditions with a mean sensitivity of 0.48 Ω/°C ± 0.01 Ω/°C. KW - Silk fibroin KW - Polylactide acid KW - Bioabsorbable KW - Resistive temperature detector Y1 - 2023 U6 - https://doi.org/10.1002/appl.202300102 SN - 2702-4288 (Print) N1 - Corresponding author: Michael Josef Schöning IS - Accepted manuscript PB - Wiley-VCH ER - TY - JOUR A1 - Janus, Kevin Alexander A1 - Achtsnicht, Stefan A1 - Tempel, Laura A1 - Drinic, Aleksaner A1 - Kopp, Alexander A1 - Keusgen, Michael A1 - Schöning, Michael Josef T1 - Influence of fibroin membrane composition and curing parameters on the performance of a biodegradable enzymatic biosensor manufactured from Silicon-Free Carbon JF - Physica status solidi : pss. A, Applications and materials science N2 - Herein, fibroin, polylactide (PLA), and carbon are investigated for their suitability as biocompatible and biodegradable materials for amperometric biosensors. For this purpose, screen-printed carbon electrodes on the biodegradable substrates fibroin and PLA are modified with a glucose oxidase membrane and then encapsulated with the biocompatible material Ecoflex. The influence of different curing parameters of the carbon electrodes on the resulting biosensor characteristics is studied. The morphology of the electrodes is investigated by scanning electron microscopy, and the biosensor performance is examined by amperometric measurements of glucose (0.5–10 mM) in phosphate buffer solution, pH 7.4, at an applied potential of 1.2 V versus a Ag/AgCl reference electrode. Instead of Ecoflex, fibroin, PLA, and wound adhesive are tested as alternative encapsulation compounds: a series of swelling tests with different fibroin compositions, PLA, and Ecoflex has been performed before characterizing the most promising candidates by chronoamperometry. Therefore, the carbon electrodes are completely covered with the particular encapsulation material. Chronoamperometric measurements with H2O2 concentrations between 0.5 and 10 mM enable studying the leakage current behavior. KW - amperometric biosensors KW - biocompatible KW - biodegradabl KW - encapsulation materials KW - fibroin Y1 - 2023 U6 - https://doi.org/10.1002/pssa.202300081 SN - 1862-6300 (Print) SN - 1862-6319 (Online) N1 - Corresponding author: Michael J. Schöning VL - 220 IS - 22 PB - Wiley-VCH CY - Weinheim ER - TY - JOUR A1 - Karschuck, Tobias A1 - Poghossian, Arshak A1 - Ser, Joey A1 - Tsokolakyan, Astghik A1 - Achtsnicht, Stefan A1 - Wagner, Patrick A1 - Schöning, Michael Josef T1 - Capacitive model of enzyme-modified field-effect biosensors: Impact of enzyme coverage JF - Sensors and Actuators B: Chemical N2 - Electrolyte-insulator-semiconductor capacitors (EISCAP) belong to field-effect sensors having an attractive transducer architecture for constructing various biochemical sensors. In this study, a capacitive model of enzyme-modified EISCAPs has been developed and the impact of the surface coverage of immobilized enzymes on its capacitance-voltage and constant-capacitance characteristics was studied theoretically and experimentally. The used multicell arrangement enables a multiplexed electrochemical characterization of up to sixteen EISCAPs. Different enzyme coverages have been achieved by means of parallel electrical connection of bare and enzyme-covered single EISCAPs in diverse combinations. As predicted by the model, with increasing the enzyme coverage, both the shift of capacitance-voltage curves and the amplitude of the constant-capacitance signal increase, resulting in an enhancement of analyte sensitivity of the EISCAP biosensor. In addition, the capability of the multicell arrangement with multi-enzyme covered EISCAPs for sequentially detecting multianalytes (penicillin and urea) utilizing the enzymes penicillinase and urease has been experimentally demonstrated and discussed. KW - Field-effect biosensor KW - Capacitive model KW - Enzyme coverage KW - Multianalyte detection KW - Penicillin Y1 - 2024 U6 - https://doi.org/10.1016/j.snb.2024.135530 SN - 0925-4005 (Print) SN - 1873-3077 (Online) N1 - Corresponding Author: Michael J. Schöning VL - 408 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Molinnus, Denise A1 - Janus, Kevin Alexander A1 - Fang, Anyelina C. A1 - Drinic, Aleksander A1 - Achtsnicht, Stefan A1 - Köpf, Marius A1 - Keusgen, Michael A1 - Schöning, Michael Josef T1 - Thick-film carbon electrode deposited onto a biodegradable fibroin substrate for biosensing applications JF - Physica status solidi (a) N2 - This study addresses a proof-of-concept experiment with a biocompatible screen-printed carbon electrode deposited onto a biocompatible and biodegradable substrate, which is made of fibroin, a protein derived from silk of the Bombyx mori silkworm. To demonstrate the sensor performance, the carbon electrode is functionalized as a glucose biosensor with the enzyme glucose oxidase and encapsulated with a silicone rubber to ensure biocompatibility of the contact wires. The carbon electrode is fabricated by means of thick-film technology including a curing step to solidify the carbon paste. The influence of the curing temperature and curing time on the electrode morphology is analyzed via scanning electron microscopy. The electrochemical characterization of the glucose biosensor is performed by amperometric/voltammetric measurements of different glucose concentrations in phosphate buffer. Herein, systematic studies at applied potentials from 500 to 1200 mV to the carbon working electrode (vs the Ag/AgCl reference electrode) allow to determine the optimal working potential. Additionally, the influence of the curing parameters on the glucose sensitivity is examined over a time period of up to 361 days. The sensor shows a negligible cross-sensitivity toward ascorbic acid, noradrenaline, and adrenaline. The developed biocompatible biosensor is highly promising for future in vivo and epidermal applications. KW - biocompatible materials KW - biodegradable electronic devices KW - biosensors KW - carbon electrodes KW - glucose Y1 - 2022 U6 - https://doi.org/10.1002/pssa.202200100 SN - 1862-6319 N1 - Corresponding author: Michael J. Schöning VL - 219 IS - 23 SP - 1 EP - 9 PB - Wiley-VCH CY - Weinheim ER - TY - JOUR A1 - Özsoylu, Dua A1 - Kizildag, Sefa A1 - Schöning, Michael Josef A1 - Wagner, Torsten T1 - Differential chemical imaging of extracellular acidification within microfluidic channels using a plasma-functionalized light-addressable potentiometric sensor (LAPS) JF - Physics in Medicine N2 - Extracellular acidification is a basic indicator for alterations in two vital metabolic pathways: glycolysis and cellular respiration. Measuring these alterations by monitoring extracellular acidification using cell-based biosensors such as LAPS plays an important role in studying these pathways whose disorders are associated with numerous diseases including cancer. However, the surface of the biosensors must be specially tailored to ensure high cell compatibility so that cells can represent more in vivo-like behavior, which is critical to gain more realistic in vitro results from the analyses, e.g., drug discovery experiments. In this work, O2 plasma patterning on the LAPS surface is studied to enhance surface features of the sensor chip, e.g., wettability and biofunctionality. The surface treated with O2 plasma for 30 s exhibits enhanced cytocompatibility for adherent CHO–K1 cells, which promotes cell spreading and proliferation. The plasma-modified LAPS chip is then integrated into a microfluidic system, which provides two identical channels to facilitate differential measurements of the extracellular acidification of CHO–K1 cells. To the best of our knowledge, it is the first time that extracellular acidification within microfluidic channels is quantitatively visualized as differential (bio-)chemical images. Y1 - 2020 U6 - https://doi.org/10.1016/j.phmed.2020.100030 SN - 2352-4510 VL - 10 IS - 100030 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Engelmann, Ulrich M. A1 - Pourshahidi, Mohammad Ali A1 - Shalaby, Ahmed A1 - Krause, Hans-Joachim T1 - Probing particle size dependency of frequency mixing magnetic detection with dynamic relaxation simulation JF - Journal of Magnetism and Magnetic Materials N2 - Biomedical applications of magnetic nanoparticles (MNP) fundamentally rely on the particles’ magnetic relaxation as a response to an alternating magnetic field. The magnetic relaxation complexly depends on the interplay of MNP magnetic and physical properties with the applied field parameters. It is commonly accepted that particle core size is a major contributor to signal generation in all the above applications, however, most MNP samples comprise broad distribution spanning nm and more. Therefore, precise knowledge of the exact contribution of individual core sizes to signal generation is desired for optimal MNP design generally for each application. Specifically, we present a magnetic relaxation simulation-driven analysis of experimental frequency mixing magnetic detection (FMMD) for biosensing to quantify the contributions of individual core size fractions towards signal generation. Applying our method to two different experimental MNP systems, we found the most dominant contributions from approx. 20 nm sized particles in the two independent MNP systems. Additional comparison between freely suspended and immobilized MNP also reveals insight in the MNP microstructure, allowing to use FMMD for MNP characterization, as well as to further fine-tune its applicability in biosensing. Y1 - 2022 U6 - https://doi.org/10.1016/j.jmmm.2022.169965 SN - 0304-8853 VL - 563 IS - In progress, Art. No. 169965 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Achtsnicht, Stefan A1 - Tödter, Julia A1 - Niehues, Julia A1 - Telöken, Matthias A1 - Offenhäusser, Andreas A1 - Krause, Hans-Joachim A1 - Schröper, Florian T1 - 3D printed modular immunofiltration columns for frequency mixing-based multiplex magnetic immunodetection JF - Sensors N2 - For performing point-of-care molecular diagnostics, magnetic immunoassays constitute a promising alternative to established enzyme-linked immunosorbent assays (ELISA) because they are fast, robust and sensitive. Simultaneous detection of multiple biomolecular targets from one body fluid sample is desired. The aim of this work is to show that multiplex magnetic immunodetection based on magnetic frequency mixing by means of modular immunofiltration columns prepared for different targets is feasible. By calculations of the magnetic response signal, the required spacing between the modules was determined. Immunofiltration columns were manufactured by 3D printing and antibody immobilization was performed in a batch approach. It was shown experimentally that two different target molecules in a sample solution could be individually detected in a single assaying step with magnetic measurements of the corresponding immobilization filters. The arrangement order of the filters and of a negative control did not influence the results. Thus, a simple and reliable approach to multi-target magnetic immunodetection was demonstrated. Y1 - 2019 U6 - https://doi.org/10.3390/s19010148 SN - 1424-8220 VL - 19 IS - 1 PB - MDPI CY - Basel ER - TY - JOUR A1 - Engelmann, Ulrich M. A1 - Shalaby, Ahmed A1 - Shasha, Carolyn A1 - Krishnan, Kannan M. A1 - Krause, Hans-Joachim T1 - Comparative modeling of frequency mixing measurements of magnetic nanoparticles using micromagnetic simulations and Langevin theory JF - Nanomaterials N2 - Dual frequency magnetic excitation of magnetic nanoparticles (MNP) enables enhanced biosensing applications. This was studied from an experimental and theoretical perspective: nonlinear sum-frequency components of MNP exposed to dual-frequency magnetic excitation were measured as a function of static magnetic offset field. The Langevin model in thermodynamic equilibrium was fitted to the experimental data to derive parameters of the lognormal core size distribution. These parameters were subsequently used as inputs for micromagnetic Monte-Carlo (MC)-simulations. From the hysteresis loops obtained from MC-simulations, sum-frequency components were numerically demodulated and compared with both experiment and Langevin model predictions. From the latter, we derived that approximately 90% of the frequency mixing magnetic response signal is generated by the largest 10% of MNP. We therefore suggest that small particles do not contribute to the frequency mixing signal, which is supported by MC-simulation results. Both theoretical approaches describe the experimental signal shapes well, but with notable differences between experiment and micromagnetic simulations. These deviations could result from Brownian relaxations which are, albeit experimentally inhibited, included in MC-simulation, or (yet unconsidered) cluster-effects of MNP, or inaccurately derived input for MC-simulations, because the largest particles dominate the experimental signal but concurrently do not fulfill the precondition of thermodynamic equilibrium required by Langevin theory. KW - Magnetic nanoparticles KW - Frequency mixing magnetic detection KW - Langevin theory KW - Micromagnetic simulation KW - Nonequilibrium dynamics Y1 - 2021 SN - 2079-4991 U6 - https://doi.org/10.3390/nano11051257 N1 - This article belongs to the Special Issue Applications and Properties of Magnetic Nanoparticles VL - 11 IS - 5 SP - 1 EP - 16 PB - MDPI CY - Basel 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 - TY - JOUR A1 - Zhantlessova, Sirina A1 - Savitskaya, Irina A1 - Kistaubayeva, Aida A1 - Ignatova, Ludmila A1 - Talipova, Aizhan A1 - Pogrebnjak, Alexander A1 - Digel, Ilya T1 - Correction: Zhantlessova et al. advanced “Green” prebiotic composite of bacterial cellulose/pullulan based on synthetic biology-powered microbial coculture strategy. Polymers 2022, 14, 3224 JF - Polymers Y1 - 2024 U6 - https://doi.org/10.3390/polym16131802 SN - 2073-4360 N1 - This article belongs to the Special Issue Cellulose Based Composites VL - 16 IS - 13 PB - MDPI CY - Basel ER - TY - JOUR A1 - Harris, Isaac A1 - Kleefeld, Andreas T1 - Analysis and computation of the transmission eigenvalues with a conductive boundary condition JF - Applicable Analysis N2 - We provide a new analytical and computational study of the transmission eigenvalues with a conductive boundary condition. These eigenvalues are derived from the scalar inverse scattering problem for an inhomogeneous material with a conductive boundary condition. The goal is to study how these eigenvalues depend on the material parameters in order to estimate the refractive index. The analytical questions we study are: deriving Faber–Krahn type lower bounds, the discreteness and limiting behavior of the transmission eigenvalues as the conductivity tends to infinity for a sign changing contrast. We also provide a numerical study of a new boundary integral equation for computing the eigenvalues. Lastly, using the limiting behavior we will numerically estimate the refractive index from the eigenvalues provided the conductivity is sufficiently large but unknown. KW - Boundary integral equations KW - Inverse spectral problem KW - Conductive boundary condition KW - Transmission eigenvalues Y1 - 2020 U6 - https://doi.org/10.1080/00036811.2020.1789598 SN - 1563-504X VL - 101 IS - 6 SP - 1880 EP - 1895 PB - Taylor & Francis CY - London ER - TY - JOUR A1 - Zhen, Manghao A1 - Liang, Yunpei A1 - Staat, Manfred A1 - Li, Quanqui A1 - Li, Jianbo T1 - Discontinuous fracture behaviors and constitutive model of sandstone specimens containing non-parallel prefabricated fissures under uniaxial compression JF - Theoretical and Applied Fracture Mechanics N2 - The deformation and damage laws of non-homogeneous irregular structural planes in rocks are the basis for studying the stability of rock engineering. To investigate the damage characteristics of rock containing non-parallel fissures, uniaxial compression tests and numerical simulations were conducted on sandstone specimens containing three non-parallel fissures inclined at 0°, 45° and 90° in this study. The characteristics of crack initiation and crack evolution of fissures with different inclinations were analyzed. A constitutive model for the discontinuous fractures of fissured sandstone was proposed. The results show that the fracture behaviors of fissured sandstone specimens are discontinuous. The stress–strain curves are non-smooth and can be divided into nonlinear crack closure stage, linear elastic stage, plastic stage and brittle failure stage, of which the plastic stage contains discontinuous stress drops. During the uniaxial compression test, the middle or ends of 0° fissures were the first to crack compared to 45° and 90° fissures. The end with small distance between 0° and 45° fissures cracked first, and the end with large distance cracked later. After the final failure, 0° fissures in all specimens were fractured, while 45° and 90° fissures were not necessarily fractured. Numerical simulation results show that the concentration of compressive stress at the tips of 0°, 45° and 90° fissures, as well as the concentration of tensile stress on both sides, decreased with the increase of the inclination angle. A constitutive model for the discontinuous fractures of fissured sandstone specimens was derived by combining the logistic model and damage mechanic theory. This model can well describe the discontinuous drops of stress and agrees well with the whole processes of the stress–strain curves of the fissured sandstone specimens. KW - Constitutive model KW - Damage mechanics theory KW - Discontinuous fractures KW - Uniaxial compression test KW - Non-parallel fissures Y1 - 2024 U6 - https://doi.org/10.1016/j.tafmec.2024.104373 SN - 0167-8442 VL - 131 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Keutmann, Sabine A1 - Staat, Manfred A1 - Laack, Walter van T1 - Untersuchung der thermischen Auswirkung von therapeutischem Ultraschall N2 - Zusammenfassung: In der Orthopädie zählt der therapeutische Ultraschall als Mittel zur Prävention und Therapiebegleitung. Er hat mechanische, thermische und physiko-chemische Auswirkungen auf den menschlichen Körper. Um mehr Erkenntnisse über die thermischen Auswirkungen zu erlangen, wurden Versuche an einem Hydrogel-Phantom und an Probanden durchgeführt. Dabei entstand eine signifikante Erwärmung des Gewebes, welche beim Probandenversuch an der Oberfläche und beim Hydrogelversuch in der Tiefe gemessen wurde. Summary: In orthopaedics, therapeutic ultrasound is a tool of prevention and therapy support. It has mechanical, thermal and physico-chemical effects on the human body. Tests with a hydrogel phantom and with human probands have been performed in order to obtain more knowledge about their thermal effects. Both tests measured temperature increases in cell tissue, on the surface with the human proband test and in depth with the hydrogel phantom test. T2 - Research about the thermal effects of therapeutic ultrasound Y1 - 2018 SN - 2193-5793 SN - 2193-5785 (Druckausgabe) VL - 7 IS - 10 SP - 518 EP - 522 PB - Deutscher Ärzte-Verl. CY - Köln ER - TY - JOUR A1 - Dikta, Gerhard A1 - Reißel, Martin A1 - Harlaß, Carsten T1 - Semi-parametric survival function estimators deduced from an identifying Volterra type integral equation JF - Journal of multivariate analysis N2 - Based on an identifying Volterra type integral equation for randomly right censored observations from a lifetime distribution function F, we solve the corresponding estimating equation by an explicit and implicit Euler scheme. While the first approach results in some known estimators, the second one produces new semi-parametric and pre-smoothed Kaplan–Meier estimators which are real distribution functions rather than sub-distribution functions as the former ones are. This property of the new estimators is particular useful if one wants to estimate the expected lifetime restricted to the support of the observation time. Specifically, we focus on estimation under the semi-parametric random censorship model (SRCM), that is, a random censorship model where the conditional expectation of the censoring indicator given the observation belongs to a parametric family. We show that some estimated linear functionals which are based on the new semi-parametric estimator are strong consistent, asymptotically normal, and efficient under SRCM. In a small simulation study, the performance of the new estimator is illustrated under moderate sample sizes. Finally, we apply the new estimator to a well-known real dataset. KW - Volterra integral equation KW - Product-integration KW - Asymptotic efficiency KW - Semi-parametric random censorship model KW - Censored data KW - Survival analysis Y1 - 2016 U6 - https://doi.org/10.1016/j.jmva.2016.02.008 IS - 147 SP - 273 EP - 284 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Michael, Hackl A1 - Mayer, Katharina A1 - Weber, Mareike A1 - Staat, Manfred A1 - van Riet, Roger A1 - Burkhart, Klau Josef A1 - Müller, Lars Peter A1 - Wegmann, Kilian T1 - Plate osteosynthesis of proximal ulna fractures : a biomechanical micromotion analysis JF - The journal of hand surgery Y1 - 2017 U6 - https://doi.org/10.1016/j.jhsa.2017.05.014 SN - 0363-5023 VL - 42 IS - 10 SP - 834.e1 EP - 834.e7 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Clausnitzer, Julian A1 - Kleefeld, Andreas T1 - A spectral Galerkin exponential Euler time-stepping scheme for parabolic SPDEs on two-dimensional domains with a C² boundary JF - Discrete and Continuous Dynamical Systems - Series B N2 - 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. KW - Nonlinear eigenvalue problems KW - Boundary integral equations, KW - Exponential Euler scheme, KW - Parabolic SPDEs Y1 - 2024 U6 - https://doi.org/10.3934/dcdsb.2023148 SN - 1531-3492 SN - 1553-524X (eISSN) VL - 29 IS - 4 SP - 1624 EP - 1651 PB - AIMS CY - Springfield ER - TY - JOUR A1 - Martín-Vaquero, J. A1 - Kleefeld, Andreas T1 - Solving nonlinear parabolic PDEs in several dimensions: Parallelized ESERK codes JF - Journal of Computational Physics N2 - There is a very large number of very important situations which can be modeled with nonlinear parabolic partial differential equations (PDEs) in several dimensions. In general, these PDEs can be solved by discretizing in the spatial variables and transforming them into huge systems of ordinary differential equations (ODEs), which are very stiff. Therefore, standard explicit methods require a large number of iterations to solve stiff problems. But implicit schemes are computationally very expensive when solving huge systems of nonlinear ODEs. Several families of Extrapolated Stabilized Explicit Runge-Kutta schemes (ESERK) with different order of accuracy (3 to 6) are derived and analyzed in this work. They are explicit methods, with stability regions extended, along the negative real semi-axis, quadratically with respect to the number of stages s, hence they can be considered to solve stiff problems much faster than traditional explicit schemes. Additionally, they allow the adaptation of the step length easily with a very small cost. Two new families of ESERK schemes (ESERK3 and ESERK6) are derived, and analyzed, in this work. Each family has more than 50 new schemes, with up to 84.000 stages in the case of ESERK6. For the first time, we also parallelized all these new variable step length and variable number of stages algorithms (ESERK3, ESERK4, ESERK5, and ESERK6). These parallelized strategies allow to decrease times significantly, as it is discussed and also shown numerically in two problems. Thus, the new codes provide very good results compared to other well-known ODE solvers. Finally, a new strategy is proposed to increase the efficiency of these schemes, and it is discussed the idea of combining ESERK families in one code, because typically, stiff problems have different zones and according to them and the requested tolerance the optimum order of convergence is different. KW - Multi-dimensional partial differential equations KW - Higher-order codes KW - Nonlinear PDEs Y1 - 2020 U6 - https://doi.org/10.1016/j.jcp.2020.109771 SN - 0021-9991 IS - 423 PB - Elsevier CY - Amsterdam ER -