TY - CHAP A1 - Wimmer, Georg A1 - Steinmetz, T. A1 - Clemens, M. T1 - Reuse, Recycle, Reduce (3R) BT - Strategies for the Calculation of Transient Magnetic Fields, Applied Numerical Mathematics, Vol. 59 T2 - NUMDIFF-11 Y1 - 2006 U6 - https://doi.org/10.1016/j.apnum.2008.03.015 SP - 830 EP - 844 CY - Halle ER - TY - BOOK A1 - Wimmer, Georg T1 - Complete Optimization of Three Dimensional Flight Trajectories for a Hypersonic Demonstrator BT - Diploma Thesis Y1 - 1998 CY - Munich University of Technology ER - TY - CHAP A1 - Wimmer, Georg A1 - Steinmetz, T. A1 - Clemens, M. T1 - Error Control Schemes for Adaptive Time Integration of Magnetodynamic Systems with Variable Spatial Mesh Resolution. Conference Proceedings BT - The 12th International IGTE Symposium on Numerical Field Calculation in Electrical Engineering(IGTE 2006) T2 - COMPEL Y1 - 2007 UR - http://permalink.bibkatalog.de/BV012873985 VL - 26 IS - 3 SP - 758 EP - 772 ER - TY - CHAP A1 - Wimmer, Georg A1 - Zhou, P. A1 - Lin, D. A1 - Cendes, Z. T1 - Determination of d-q Axis Parameters of Interior Permanent Magnet Machines BT - 17th Conference on the Computation of Electromagnetic Fields (COMPUMAG 2009) T2 - IEEE Transactions on Magnetics Y1 - 2010 UR - http://permalink.bibkatalog.de/BV013355032 VL - 46 IS - 8 SP - 3125 EP - 3128 ER - TY - CHAP A1 - Taube, Vera A1 - Unz, Dagmar ED - Borrmann, Stefan ED - Thiessen, Barbara T1 - Implementierung von evidenzbasierten Programmen in der Sozialen Arbeit BT - Forschungsergebnisse, Herausforderungen und Desiderata T2 - Wirkungen Sozialer Arbeit Y1 - 2022 SP - 125 EP - 143 PB - Budrich CY - Opladen ER - TY - JOUR A1 - Bartsch, Hendrik A1 - Bier, Markus A1 - Dietrich, S. T1 - The role of counterions in ionic liquid crystals JF - The Journal of Chemical Physics N2 - Previous theoretical studies of calamitic (i.e., rod-like) ionic liquid crystals (ILCs) based on an effective one-species model led to indications of a novel smectic-A phase with a layer spacing being much larger than the length of the mesogenic (i.e., liquid–crystal forming) ions. In order to rule out the possibility that this wide smectic-A phase is merely an artifact caused by the one-species approximation, we investigate an extension that accounts explicitly for cations and anions in ILCs. Our present findings, obtained by grand canonical Monte Carlo simulations, show that the phase transitions between the isotropic and the smectic-A phases of the cation–anion system are in qualitative agreement with the effective one-species model used in the preceding studies. In particular, for ILCs with mesogens (i.e., liquid–crystal forming species) carrying charged sites at their tips, the wide smectic-A phase forms, at low temperatures and within an intermediate density range, in between the isotropic and hexagonal crystal phases. We find that in the ordinary smectic-A phase, the spatial distribution of the counterions of the mesogens is approximately uniform, whereas in the wide smectic-A phase, the small counterions accumulate in between the smectic layers. Due to this phenomenology, the wide smectic-A phase could be interesting for applications, which hinge on the presence of conductivity channels for mobile ions. KW - Liquid crystals, Phase transitions, Electrostatics, Ions and properties, Crystal structure, Intermolecular forces, Monte Carlo methods, Classical statistical mechanics Y1 - 2021 UR - https://doi.org/10.1063/5.0034314 VL - 154 IS - 1 SP - 014901 ER - TY - JOUR A1 - Bier, Markus A1 - Mußotter, Maximilian A1 - Dietrich, S. T1 - Structure of electrolyte solutions at nonuniformly charged surfaces on a variety of length scales JF - Physical Review E N2 - The structures of dilute electrolyte solutions close to nonuniformly charged planar substrates are systematically studied within the entire spectrum of microscopic to macroscopic length scales by means of a unified classical density functional theory approach. This is in contrast to previous investigations, which are applicable either to short or to long length scales. It turns out that interactions with microscopic ranges, e.g., due to the hard cores of the fluid molecules and ions, have a negligible influence on the formation of nonuniform lateral structures of the electrolyte solutions. This partly justifies the Debye-Hückel approximation schemes applied in previous studies of that system. In general, a coupling between the lateral and the normal fluid structures leads to the phenomenology that, upon increasing the distance from the substrate, fewer details of the lateral nonuniformities contribute to the fluid structure, such that ultimately only large-scale surface features remain relevant. It can be expected that this picture also applies to other fluids characterized by several length scales. KW - Classical statistical mechanics, Electrostatic interactions, Interface & surface thermodynamics, Complex fluids, Ionic fluids, Liquid-solid interfaces, Polymers & Soft Matter, Statistical Physics Y1 - 2022 UR - https://doi.org/10.1103/PhysRevE.106.054801 VL - 106 IS - 5 SP - 054801 ER - TY - JOUR A1 - Majee, Arghya A1 - Bier, Markus A1 - Blossey, Ralf A1 - Podgornik, Rudolf T1 - Charge symmetry broken complex coacervation JF - Physical Review Research N2 - Liquid-liquid phase separation has emerged as one of the important paradigms in the chemical physics as well as biophysics of charged macromolecular systems. We elucidate an equilibrium phase separation mechanism based on charge regulation, i.e., protonation-deprotonation equilibria controlled by pH, in an idealized macroion system which can serve as a proxy for simple coacervation. First, a low-density density functional calculation reveals the dominance of two-particle configurations coupled by ion adsorption on neighboring macroions. Then a binary cell model, solved on the Debye-Hückel as well as the full nonlinear Poisson-Boltzmann level, unveils the charge symmetry breaking as inducing the phase separation between low- and high-density phases as a function of pH. These results can be identified as a charge symmetry broken complex coacervation between chemically identical macroions. KW - Aggregation, Biomolecular self-assembly, Electrostatic interactions, Charged colloids, Colloids, Proteins, Density functional calculations, Polymers & Soft Matter, Biological Physics, Statistical Physics Y1 - 2020 UR - https://doi.org/10.1103/PhysRevResearch.2.043417 VL - 2 IS - 4 ER - TY - JOUR A1 - Mußotter, Maximilian A1 - Bier, Markus A1 - Dietrich, S. T1 - Heterogeneous surface charge confining an electrolyte solution JF - The Journal of Chemical Physics N2 - The structure of dilute electrolyte solutions close to a surface carrying a spatially inhomogeneous surface charge distribution is investigated by means of classical density functional theory within the approach of fundamental measure theory. For electrolyte solutions, the influence of these inhomogeneities is particularly strong because the corresponding characteristic length scale is the Debye length, which is large compared to molecular sizes. Here, a fully three-dimensional investigation is performed, which accounts explicitly for the solvent particles, and thus provides insight into effects caused by ion–solvent coupling. The present study introduces a versatile framework to analyze a broad range of types of surface charge heterogeneities even beyond the linear response regime. This reveals a sensitive dependence of the number density profiles of the fluid components and of the electrostatic potential on the magnitude of the charge as well as on the details of the surface charge patterns at small scales. KW - Density functional theory, Fundamental measure theory, Electrostatics, Partial differential equations, Elementary particle interactions, Electrochemistry, Electrolytes, Interfaces Y1 - 2020 UR - https://doi.org/10.1063/5.0006208 VL - 152 IS - 23 ER - TY - JOUR A1 - Majee, Arghya A1 - Bier, Markus A1 - Blossey, Ralf A1 - Podgornik, Rudolf T1 - Charge regulation radically modifies electrostatics in membrane stacks JF - Physical Review E N2 - Motivated by biological membrane-containing organelles in plants and photosynthetic bacteria, we study charge regulation in a model membrane stack. Considering (de)protonation as the simplest mechanism of charge equilibration between the membranes and with the bathing environment, we uncover a symmetry-broken charge state in the stack with a quasiperiodic effective charge sequence. In the case of a monovalent bathing salt solution our model predicts complex, inhomogeneous charge equilibria depending on the strength of the (de)protonation reaction, salt concentration, and membrane size. Our results shed light on the basic reorganization mechanism of thylakoid membrane stacks. KW - Applications of soft matter, Classical statistical mechanics, Electrostatic double layer forces, Electrostatic interactions, Charged colloids, Complex fluids, Interfaces, Polymers & Soft Matter, Statistical Physics Y1 - 2019 UR - https://doi.org/10.1103/PhysRevE.100.050601 VL - 100 IS - 5 SP - 050601 ER - TY - JOUR A1 - Bittner, Boris A1 - Wabra, N. A1 - von Hodenberg, M. A1 - Schneider, S. A1 - Schneider, R. A1 - Mack, R. T1 - System correction from long timescales Y1 - 2014 ER - TY - JOUR A1 - Bittner, Boris A1 - Wabra, N. A1 - Schneider, S. A1 - Schneider, R. T1 - Method of operating a microlithographic projection apparatus Y1 - 2015 ER - TY - JOUR A1 - Bittner, Boris A1 - Walter, H. A1 - Rösch, M. T1 - Projection exposure apparatus with optimized adjustment possibility Y1 - 2010 ER - TY - JOUR A1 - Bittner, Boris T1 - Projection exposure apparatus with optimized adjustment capability Y1 - 2012 ER - TY - CHAP A1 - Wimmer, Georg A1 - Steinmetz, T. A1 - Clemens, M. T1 - Error Control Schemes for Adaptive Time Integration of Magnetodynamic Systems with Variable Spatial Mesh Resolution BT - Conference Proceedings T2 - The 12th International IGTE Symposium on Numerical Field Calculation in Electrical Engineering(IGTE 2006) Y1 - 2006 SN - 3-902465-56-5; ISBN-13: 978-3-902465-56-6 SP - 192 EP - 197 PB - Verlag der Technischen Universität Graz CY - Graz ER - TY - JOUR A1 - Wimmer, Georg A1 - Steinmetz, T. A1 - Clemens, M. A1 - Gödel, N. A1 - Kurz, S. A1 - Bebendorf, M. T1 - Efficient Symmetric FEM-BEM Coupled Simulations of Electro-Quasistatic Fields JF - IEEE Transactions on Magnetics Y1 - 2008 UR - http://permalink.bibkatalog.de/BV013355032 VL - 44 IS - 6 SP - 1346 EP - 1349 ER - TY - JOUR A1 - Wimmer, Georg A1 - Steinmetz, T. A1 - Helias, M. A1 - Fichte, L.O. A1 - Clemens, M. T1 - Quasistatic Electric Field Computations with Discrete Electromagnetism Formulations JF - IEEE Transactions on Magnetics Y1 - 2006 UR - http://permalink.bibkatalog.de/BV013355032 VL - 42 IS - 4 SP - 755 EP - 758 ER - TY - CHAP A1 - Wimmer, Georg A1 - Dutiné, J. A1 - Clemens, M. A1 - Richter, C. A1 - Schöps, S. T1 - Explicit time integration of eddy current problems with a weakly gauged Schur complement vector potential formulation T2 - Kleinheubach-Tagung Y1 - 2015 ER - TY - JOUR A1 - Wimmer, Georg A1 - Steinmetz, T. A1 - Clemens, M. T1 - Reuse, Recycle, Reduce (3R) BT - Strategies for the Calculation of Transient Magnetic Fields JF - Applied Numerical Mathematics Y1 - 2009 U6 - https://doi.org/10.1016/j.apnum.2008.03.015 VL - 59 SP - 830 EP - 844 CY - Halle ER - TY - CHAP A1 - Wimmer, Georg A1 - Clemens, M. A1 - Lang, J. ED - Breitner, M. ED - Denk, G. ED - Rentrop, P. T1 - Calculation of Magnetic Fields with Finite Elements T2 - From Nano to Space: Applied Mathematics Inspired by Roland Bulirsch Y1 - 2008 PB - Springer CY - Berlin, Heidelberg ER - TY - JOUR A1 - Wimmer, Georg A1 - Callies, R. T1 - Optimization of Hypersonic Flight Trajectories JF - ZAMM Y1 - 1999 UR - http://permalink.bibkatalog.de/BV012628875 VL - 79 IS - S3 SP - 929 EP - 930 ER - TY - JOUR A1 - Wimmer, Georg A1 - Callies, R. T1 - Stabilized Hypersonic Flight Trajectories JF - ZAMM Y1 - 2001 UR - http://permalink.bibkatalog.de/BV012628875 VL - 81 IS - S3 SP - 769 EP - 770 ER - TY - CHAP A1 - Wimmer, Georg T1 - Transient Magnetic Field Formulation for Solid Source Conductors with Axial Symmetry T2 - Proceedings of ICCCN 2014 Y1 - 2014 CY - Shanghai, China ER - TY - JOUR A1 - Janssen, Mathijs A1 - Bier, Markus T1 - Transient response of an electrolyte to a thermal quench JF - Physical Review E N2 - We study the transient response of an electrolytic cell subject to a small, suddenly applied temperature increase at one of its two bounding electrode surfaces. An inhomogeneous temperature profile then develops, causing, via the Soret effect, ionic rearrangements towards a state of polarized ionic charge density q and local salt density c. For the case of equal cationic and anionic diffusivities, we derive analytical approximations to q,c, and the thermovoltage VT for early (t≪τT) and late (t≫τT) times as compared to the relaxation time τT of the temperature. We challenge the conventional wisdom that the typically large Lewis number, the ratio a/D of thermal to ionic diffusivities, of most liquids implies a quickly reached steady-state temperature profile onto which ions relax slowly. Though true for the evolution of c, it turns out that q (and VT) can respond much faster. Particularly when the cell is much bigger than the Debye length, a significant portion of the transient response of the cell falls in the t≪τT regime, for which our approximated q (corroborated by numerics) exhibits a density wave that has not been discussed before in this context. For electrolytes with unequal ionic diffusivities, VT exhibits a two-step relaxation process, in agreement with experimental data of Bonetti et al. [J. Chem. Phys. 142, 244708 (2015)]. KW - Electrochemistry, Electrokinetic flows, Ionic transport, Nonequilibrium & irreversible thermodynamics, Thermoelectrics, Thermophoresis, Ionic fluids, Condensed Matter, Materials & Applied Physics, Statistical Physics, General Physics Y1 - 2019 UR - https://doi.org/10.1103/PhysRevE.99.042136 VL - 99 IS - 4 SP - 042136 ER - TY - JOUR A1 - Li, Hailong A1 - Bier, Markus A1 - Mars, Julian A1 - Weiss, Henning A1 - Dippel, Ann-Christin A1 - Gutowski, Olof A1 - Honkimäki, Veijo A1 - Mezger, Markus T1 - Interfacial premelting of ice in nano composite materials JF - Physical Chemistry Chemical Physics N2 - The interfacial premelting in ice/clay nano composites was studied by high energy X-ray diffraction. Below the melting point of bulk water, the formation of liquid water was observed for the ice/vermiculite and ice/kaolin systems. The liquid fraction is gradually increasing with temperature. For both minerals, similar effective premelting layer thicknesses of 2–3 nm are reached 3 K below the bulk melting point. For the quantitative description of the molten water fraction in wet clay minerals we developed a continuum model for short range interactions and arbitrary pore size distributions. This model quantitatively describes the experimental data over the entire temperature range. Model parameters were obtained by fitting using a maximum entropy (MaxEnt) approach. Pronounced differences in the deviation from Antonow's rule relating interfacial free energy between ice, water, and clay are observed for the charged vermiculite and uncharged kaolin minerals. The resultant parameters are discussed in terms of their ice nucleation efficiency. Using well defined and characterized ice/clay nano composite samples, this work bridges the gap between studies on single crystalline ice/solid model interfaces and naturally occurring soils and permafrost. Y1 - 2019 UR - https://doi.org/10.1039/C8CP05604H VL - 21 SP - 3734 EP - 3741 ER - TY - JOUR A1 - Majee, Arghya A1 - Bier, Markus A1 - Dietrich, Siegfried T1 - Electrostatic interaction of particles trapped at fluid interfaces: effects of geometry and wetting properties JF - Soft Matter N2 - The electrostatic interaction between pairs of spherical or macroscopically long, parallel cylindrical colloids trapped at fluid interfaces is studied theoretically for the case of small inter-particle separations. Starting from the effective interaction between two planar walls and by using the Derjaguin approximation, we address the issue of how the electrostatic interaction between such particles is influenced by their curvatures and by the wetting contact angle at their surfaces. Regarding the influence of curvature, our findings suggest that the discrepancies between linear and nonlinear Poisson–Boltzmann theory, which have been noticed before for planar walls, also occur for spheres and macroscopically long, parallel cylinders, though their magnitude depends on the wetting contact angle. Concerning the influence of the wetting contact angle θ simple relations are obtained for equally sized particles which indicate that the inter-particle force varies significantly with θ only within an interval around 90°. This interval depends on the Debye length of the fluids and on the size of the particles but not on their shape. For unequally sized particles, a more complicated relation is obtained for the variation of the inter-particle force with the wetting contact angle. Y1 - 2018 UR - https://doi.org/10.1039/C8SM01765D VL - 14 SP - 9436 EP - 9444 ER - TY - JOUR A1 - Bartsch, Hendrik A1 - Bier, Markus A1 - Dietrich, Siegfried T1 - Interface structures in ionic liquid crystals JF - Soft Matter N2 - Ionic liquid crystals (ILCs) are anisotropic mesogenic molecules which additionally carry charges. This combination gives rise to a complex interplay of the underlying (anisotropic) contributions to the pair interactions. It promises interesting and distinctive structural and orientational properties to arise in systems of ILCs, combining properties of liquid crystals and ionic liquids. While previous theoretical studies have focused on the phase behavior of ILCs and the structure of the respective bulk phases, in the present study we provide new results, obtained within density functional theory, concerning (planar) free interfaces between an isotropic liquid L and two types of smectic-A phases (SA or SAW). We discuss the structural and orientational properties of these interfaces in terms of the packing fraction profile η(r) and the orientational order parameter profile S2(r) concerning the tilt angle α between the (bulk) smectic layer normal and the interface normal. The asymptotic decay of η(r) and of S2(r) towards their values in the isotropic bulk is discussed, too. Y1 - 2019 UR - https://doi.org/10.1039/C9SM00062C VL - 15 SP - 4109 EP - 4126 ER - TY - JOUR A1 - Zarubin, Grigorii A1 - Bier, Markus A1 - Dietrich, S. T1 - A ferronematic slab in external magnetic fields JF - Soft Matter N2 - The behavior of a uniformly magnetized ferronematic slab is investigated numerically in a situation in which an external magnetic field is applied parallel and antiparallel, respectively, to its initial magnetization direction. The employed numerical method allows one to determine hysteresis curves from which a critical magnetic field strength (i.e., the one at which the ferronematic sample becomes distorted) as a function of the system parameters can be inferred. Two possible mechanisms of switching the magnetization by applying a magnetic field in the antiparallel direction are observed and characterized in terms of the coupling constant between the magnetization and the nematic director and in terms of the coupling strength of the nematic liquid crystal and the walls of the slab. Suitably prepared walls allow one to combine both switching mechanisms in one setup, such that one can construct a cell, the magnetization of which can be reversibly switched off. Y1 - 2018 UR - https://doi.org/10.1039/C8SM01813H VL - 14 SP - 9806 EP - 9818 ER - TY - JOUR A1 - Diethelm, Kai ED - Altenbach, Holm ED - Öchsner, Andreas T1 - Numerical Methods for the Fractional Differential Equations of Viscoelasticity JF - Encyclopedia of Continuum Mechanics N2 - Mathematical models based on differential operators of fractional order have proven to be very useful for describing the properties of viscoelastic materials. However, the associated differential equations can usually not be solved analytically. In this article, we provide a survey of the most important numerical methods. We restrict our attention to those types of fractional differential equations that are most important in the context of viscoelasticity, i.e., we discuss numerical methods for ordinary fractional differential equations and for certain types of time-fractional partial differential equations. Space-fractional partial differential equations are not discussed. Y1 - 2018 SN - 978-3-662-53605-6 U6 - https://doi.org/10.1007/978-3-662-53605-6_89-1 SP - 1 EP - 12 PB - Springer CY - Berlin ER - TY - JOUR A1 - Diethelm, Kai A1 - Ford, Neville J. T1 - A note on the well-posedness of terminal value problems for fractional differential equations JF - Journal of Integral Equations and Applications N2 - This note is intended to clarify some important points about the well-posedness of terminal value problems for fractional differential equations. It follows the recent publication of a paper by Cong and Tuan in this journal, in which a counter-example calls into question the earlier results in a paper by this note's authors. Here, we show in the light of these new insights, that a wide class of terminal value problems of fractional differential equations is well posed, and we identify those cases where the well-posedness question must be regarded as open. Y1 - 2018 U6 - https://doi.org/10.1216/JIE-2018-30-3-371 VL - 30 IS - 3 SP - 371 EP - 376 ER - TY - CHAP A1 - Diethelm, Kai ED - Cardone, Angelamaria ED - Donatelli, Marco ED - Durastante, Fabio ED - Garrappa, Roberto ED - Mazza, Mariarosa ED - Popolizio, Marina T1 - A New Diffusive Representation for Fractional Derivatives, Part I: Construction, Implementation and Numerical Examples T2 - Fractional Differential Equations: Modeling, Discretization, and Numerical Solvers N2 - Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known variants of this approach is that they require the numerical approximation of some integrals over an unbounded integral whose integrand decays rather slowly, which implies that their numerical handling is difficult and costly. We present a novel variant of such a diffusive representation. This form also requires the numerical approximation of an integral over an unbounded domain, but the integrand decays much faster. This property allows to use well established quadrature rules with much better convergence properties. Y1 - 2023 SN - 978-981-19-7715-2 SN - 978-981-19-7716-9 U6 - https://doi.org/10.1007/978-981-19-7716-9_1 SP - 1 EP - 15 PB - Springer CY - Singapore ER - TY - CHAP A1 - Diethelm, Kai T1 - Diffusive Representations for the Numerical Evaluation of Fractional Integrals T2 - Proceeding of the 2023 International Conference on Fractional Differentiation and its Applications (ICFDA) N2 - Diffusive representations of fractional differential and integral operators can provide a convenient means to construct efficient numerical algorithms for their approximate evaluation. In the current literature, many different variants of such representations have been proposed. Concentrating on Riemann-Liouville integrals whose order is in (0,1), we here present a general approach that comprises most of these variants as special cases and that allows a detailed investigation of the analytic properties of each variant. The availability of this information allows to choose concrete numerical methods for handling the representations that exploit the specific properties, thus allowing to construct very efficient overall methods. Y1 - 2023 UR - https://arxiv.org/abs/2301.11931 U6 - https://doi.org/10.48550/arXiv.2301.11931 PB - IEEE CY - Piscataway ER - TY - CHAP A1 - Diethelm, Kai T1 - Fast Solution Methods for Fractional Differential Equations in the Modeling of Viscoelastic Materials T2 - 2021 9th International Conference on Systems and Control (ICSC) N2 - Fractional order models have proven to be a very useful tool for the modeling of the mechanical behaviour of viscoelastic materials. Traditional numerical solution methods exhibit various undesired properties due to the non-locality of the fractional differential operators, in particular regarding the high computational complexity and the high memory requirements. The infinite state representation is an approach on which one can base numerical methods that overcome these obstacles. Such algorithms contain a number of parameters that influence the final result in nontrivial ways. Based on numerical experiments, we initiate a study leading to good choices of these parameters. Y1 - 2021 U6 - https://doi.org/10.1109/ICSC50472.2021.9666636 SP - 455 EP - 460 PB - IEEE ER - TY - JOUR A1 - Damelin, Steven B. A1 - Diethelm, Kai T1 - An Analytic and Numerical Analysis of Weighted Singular Cauchy Integrals with Exponential Weights on ℝ JF - Numerical Functional Analysis and Optimization N2 - This article concerns an analytic and numerical analysis of a class of weighted singular Cauchy integrals with exponential weights w:= exp (−Q) with finite moments and with smooth external fields Q:R→[0,∞), with varying smooth convex rate of increase for large argument. Our analysis relies in part on weighted polynomial interpolation at the zeros of orthonormal polynomials with respect to w2. We also study bounds for the first derivatives of a class of functions of the second kind for w2. Y1 - 2022 U6 - https://doi.org/10.1080/01630563.2022.2112051 VL - 43 IS - 13 SP - 1538 EP - 1577 ER - TY - JOUR A1 - Diethelm, Kai T1 - A New Diffusive Representation for Fractional Derivatives, Part II: Convergence Analysis of the Numerical Scheme JF - Mathematics N2 - Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately evident that the method is fast and memory-efficient. Moreover, the method’s design is such that good convergence properties may be expected. In this paper, we commence a systematic investigation of these convergence properties. Y1 - 2022 U6 - https://doi.org/10.3390/math10081245 VL - 10 IS - 8 ER - TY - CHAP A1 - Diethelm, Kai ED - Karniadakis, George Em T1 - Fundamental approaches for the numerical handling of fractional operators and time-fractional differential equations T2 - Handbook of Fractional Calculus with Applications, Vol. 3: Numerical Methods N2 - This article describes fundamental approaches for the numerical handling of problems arising in fractional calculus. This includes, in particular, methods for approximately computing fractional integrals and fractional derivatives, where the emphasis is placed on Caputo operators, as well as solvers for the associated differential and integral equations. Y1 - 2019 U6 - https://doi.org/10.1515/9783110571684-001 SP - 1 EP - 22 PB - De Gruyter CY - Berlin ER - TY - JOUR A1 - Günnel, Andreas A1 - Herzog, Roland T1 - Optimal Control Problems in Finite-Strain Elasticity by Inner Pressure and Fiber Tension JF - Frontiers in Applied Mathematics and Statistics N2 - Optimal control problems for finite-strain elasticity are considered. An inner pressure or an inner fiber tension is acting as a driving force. Such internal forces are typical, for instance, for the motion of heliotropic plants, and for muscle tissue. Non-standard objective functions relevant for elasticity problems are introduced. Optimality conditions are derived on a formal basis, and a limited-memory quasi-Newton algorithm for their solution is formulated in function space. Numerical experiments confirm the expected mesh-independent performance. KW - partial differential equations, optimal control, finite-strain elasticity, quasi-Newton method, multigrid preconditioning Y1 - 2016 U6 - https://doi.org/10.3389/fams.2016.00004 VL - 2 ER - TY - JOUR A1 - Makowski, Andreas A1 - Herzog, Roland T1 - Optimal Control of Large Deformation Elasticity by Fiber Tension JF - Proceedings in Applied Mathematics and Mechanics N2 - Object of our interest is an elastic body Ω ⊂ ℝ3 which we can deform by applying a tension along certain given short fibers inside the body. The deformation of the body is desribed by a hyperelastic model with polyconvex energy density and a special energy functional for the tension along the fibers. We seek to apply (possibly large) deformations to the body so that a desired shape is obtained. To this end, we formulate an optimal control problem for the fiber tension field. KW - partial differential equations, optimal control, finite-strain elasticity, quasi-Newton method, multigrid preconditioning Y1 - 2014 U6 - https://doi.org/10.1002/pamm.201410420 VL - 2014 IS - 14 SP - 879 EP - 880 ER - TY - RPRT A1 - Frühbrodt, Lutz T1 - Der Homo Varius: Das neue alternative Menschenbild der Ökonomik N2 - Das Konstrukt des Homo Oeconomicus hat bereits über Jahrhunderte die Modellbildung in den Wirtschaftswissenschaften beherrscht. In den vergangenen Jahrzehnten sind zwar alternative Menschenbilder entwickelt worden, doch auch der Homo Reciprocans, der Homo Sustinens und andere haben ihre Begrenzungen. In dem vorliegenden wissenschaftlichen Essay wurden deshalb die realistischen Aspekte der existierenden Bilder herausdestilliert, mit eigenen Beobachtungen kombiniert und zu einem neuen, umfassenden Leitbild zusammengeführt: dem des Homo Varius. KW - Homo Varius KW - Homo Oeconomicus KW - Menschenbild KW - Wirtschaftswissenschaften KW - Homo Reciprocans Y1 - 2026 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:863-opus-64193 ER -