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- ItemHysteresis and phase transition in many-particle storage systems(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Dreyer, Wolfgang; Guhlke, Clemens; Herrmann, MichaelWe study the behavior of systems consisting of ensembles of interconnected storage particles. Our examples concern the storage of lithium in many-particle electrodes of rechargeable lithium-ion batteries and the storage of air in a system of interconnected rubber balloons. We are particularly interested in those storage systems whose constituents exhibit non-monotone material behavior leading to transitions between two coexisting phases and to hysteresis. In the current study we consider the case that the time to approach equilibrium of a single storage particle is much smaller than the time for full charging of the ensemble. In this regime the evolution of the probability to find a particle of the ensemble in a certain state, may be described by a nonlocal conservation law of Fokker-Planck type. Two constant parameter control whether the ensemble transits the 2-phase region along a Maxwell line or along a hysteresis path or if the ensemble shows the same non-monotone behavior as its constituents.
- ItemHysteresis in the context of hydrogen storage and lithium-ion batteries(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Dreyer, Wolfgang; Guhlke, Clemens; Huth, RobertThe processes of reversible storage of hydrogen in a metal by loading and unloading and of charging and discharging of lithium-ion batteries have many things in common. The both processes are accompanied by a phase transition and loading and unloading run along different paths, so that hysteretic behavior is observed. For hydrogen storage we consider a fine powder of magnesium (Mg) particles and lithium storage is studied for iron phosphate (FePO_4) particles forming the cathode of a lithium-ion battery. The mathematical models that are established in citeDGJ08 and citeDGH09a, describe phase transitions and hysteresis exclusively in a single particle and on that basis they can predict the observed hysteretic plots with almost horizontal plateaus. Interestingly the models predict that the coexistence of a 2-phase system in an individual particle disappears, if its size is below a critical value. However, measurements reveal that this is qualitatively not reflected by the mentioned hysteretic plots of loading and unloading. In other words: The behavior of a storage system consisting of many particles is qualitatively independent of the fact whether the individual particles itself develop a 2-phase system or if they remain in a single phase state. This apparent paradoxical observation will be resolved in this article. It will be shown that if each of the individual particles homogeneously distributes the supplied matter, nevertheless the many particle ensemble exhibits phase transition and hysteresis, because one of the two phases is realized in some part of the particles while the remaining part is in the other phase.
- ItemRigorous derivation of a plate theory in linear elastoplasticity via [Gamma]-convergence(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Liero, Matthias; Roche, ThomasThis paper deals with dimension reduction in linearized elastoplasticity in the rate-independent case. The reference configuration of the elastoplastic body is given by a two-dimensional middle surface and a small but positive thickness. We derive a limiting model for the case in which the thickness of the plate tends to 0. This model contains membrane and plate deformations which are coupled via plastic strains. The convergence analysis is based on an abstract Gamma convergence theory for rate-independent evolution formulated in the framework of energetic solutions. This concept is based on an energy-storage functional and a dissipation functional, such that the notion of solution is phrased in terms of a stability condition and an energy balance.
- ItemA molecular dynamics view of hysteresis and functional fatigue in martensitic transformations(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Kastner, Oliver; Ackland, Graeme J.; Eggeler, Gunther; Weiss, WolfShape memory alloys (SMA) exhibit a number of features which are not easily explained by equilibrium thermodynamics, including hysteresis in the phase transformation and ?reverse? shape memory in the high symmetry phase. Processing can change these features: repeated cycling can ?train? the reverse shape memory effect, while changing the amount of hysteresis and other functional properties. These effects are likely to be due to creation of persistent localised defects, which are impossible to study using non-atomistic methods. Here we present a molecular dynamics simulation study of this behaviour. To ensure the largest possible system size, we use a two dimensional binary Lennard-Jones model, which represents a reliable qualitative model system for martensite/austenite transformations. The evolution of the defect structure and its excess energy is investigated in simulations of cyclic transformation/ reverse transformation processes with 160,000 atoms. The simulations show that the transformation proceeds by non-diffusive nucleation and growth processes and produces distinct microstructure. Upon transformation, lattice defects are generated which affect subsequent transformations and vary the potential energy landscape of the sample. Some of the defects persist through the transformation, providing nucleation centres for subsequent cycles. Such defects may provide a memory of previous structures, and thereby may be the basis of a reversible shape memory effect.
- ItemSelf-heating, bistability, and thermal switching in organic semiconductors(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Fischer, Axel; Pahner, Paul; Lüssem, Björn; Scholz, Reinhard; Koprucki, Thomas; Gärtner, Klaus; Glitzky, AnnegretWe demonstrate electric bistability induced by the positive feedback of self-heating onto the thermally activated conductivity in a two-terminal device based on the organic semiconductor C60. The central undoped layer with a thickness of 200 nm is embedded between thinner n-doped layers adjacent to the contacts minimizing injection barriers. The observed current-voltage characteristics follow the general theory for thermistors described by an Arrhenius-like conductivity law. Our findings including hysteresis phenomena are of general relevance for the entire material class since most organic semiconductors can be described by a thermally activated conductivity.
- ItemSolvability of an unsaturated porous media flow problem with thermomechanical interaction(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Albers, Bettina; Krejc̆í, Pavel; Rocca, ElisabettaA PDE system consisting of the momentum balance, mass balance, and energy balance equations for displacement, capillary pressure, and temperature as a model for unsaturated fluid flow in a porous viscoelastoplastic solid is shown to admit a solution under appropriate assumptions on the constitutive behavior. The problem involves two hysteresis operators accounting for plastic and capillary hysteresis.
- ItemPeriodic solutions of isotone hybrid systems(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Seidman, Thomas I.; Klein, OlafSuggested by conversations in 1991 (Mark Krasnosel'skii and Aleksei Pokrovskii with TIS), this paper generalizes earlier work (Krasnosel'skii-Pokrovskii 1974) of theirs by defining a setting of hybrid systems with isotone switching rules for a partially ordered set of modes and then obtaining a periodicity result in that context. An application is given to a partial differential equation modeling calcium release and diffusion in cardiac cells.
- ItemFrom discrete visco-elasticity to continuum rate-independent plasticity : rigorous results(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Mielke, Alexander; Truskinovsky, LevWe show that continuum models for ideal plasticity can be obtained as a rigorous mathematical limit starting from a discrete microscopic model describing a visco-elastic crystal lattice with quenched disorder. The constitutive structure changes as a result of two concurrent limiting procedures: the vanishing-viscosity limit and the discrete to continuum limit. In the course of these limits a non-convex elastic problem transforms into a convex elastic problem while the quadratic rate-dependent dissipation of visco-elastic solid transforms into a singular rate-independent dissipation of an ideally plastic solid. In order to emphasize ideas we employ in our proofs the simplest prototypical system describing transformational plasticity of shape-memory alloys. The approach, however, is sufficiently general and can be used for similar reductions in the cases of more general plasticity and damage models.
- ItemSystem identification of a hysteresis-controlled pump system using SINDy(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Thiele, Gregor; Fey, Arne; Sommer, David; Krüger, JörgHysteresis-controlled devices are widely used in industrial applications. For example, cooling devices usually contain a two-point controller, resulting in a nonlinear hybrid system with two discrete states. Dynamic models of systems are essential for optimizing such industrial supply technology. However, conventional system identification approaches can hardly handle hysteresis-controlled devices. Thus, the new identification method Sparse Identification of Nonlinear Dynamics (SINDy) is extended to consider hybrid systems. SINDy composes models from basis functions out of a customized library in a data-driven manner. For modeling systems that behave dependent on their own past as in the case of natural hysteresis, Ferenc Preisach introduced the relay hysteron as an elementary mathematical description. In this new method (SINDyHybrid), tailored basis functions in form of relay hysterons are added to the library which is used by SINDy. Experiments with a hysteresis controlled water basin show that this approach correctly identifies state transitions of hybrid systems and also succeeds in modeling the dynamics of the discrete system states. A novel proximity hysteron achieves the robustness of this method. The impacts of the sampling rate and the signal noise ratio of the measurement data are examined accordingly.
- ItemAsymptotic behavior of a Neumann parabolic problem with hysteresis(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Eleuteri, Michela; Krejčí, PavelA parabolic equation in two or three space variables with a Preisach hysteresis operator and with homogeneous Neumann boundary conditions is shown to admit a unique global regular solution. A detailed investigation of the Preisach memory dynamics shows that the system converges to an equilibrium in the state space of all admissible Preisach memory configurations as time tends to infinity.