Filters

2017110

More filters

2019 - 2019982020 - 202212
Reset filters

Settings

End date: 2017 × Start date: 2017 × Type: Text × WGL Institute: WIAS ×

Search Results

Now showing 1 - 10 of 110
  • Thumbnail Image
    Item
    Anisotropic solid-liquid interface kinetics in silicon: An atomistically informed phase-field model
    (Bristol : IOP Publ., 2017) Bergmann, S.; Albe, K.; Flege, E.; Barragan-Yani, D.A.; Wagner, B.
    We present an atomistically informed parametrization of a phase-field model for describing the anisotropic mobility of liquid–solid interfaces in silicon. The model is derived from a consistent set of atomistic data and thus allows to directly link molecular dynamics and phase field simulations. Expressions for the free energy density, the interfacial energy and the temperature and orientation dependent interface mobility are systematically fitted to data from molecular dynamics simulations based on the Stillinger–Weber interatomic potential. The temperature-dependent interface velocity follows a Vogel–Fulcher type behavior and allows to properly account for the dynamics in the undercooled melt.
  • Thumbnail Image
    Item
    Boundary conditions for electrochemical interfaces
    (Bristol : IOP Publishing, 2017) Landstorfer, Manuel
    Consistent boundary conditions for electrochemical interfaces, which cover double layer charging, pseudo-capacitive effects and transfer reactions, are of high demand in electrochemistry and adjacent disciplines. Mathematical modeling and optimization of electrochemical systems is a strongly emerging approach to reduce cost and increase efficiency of super-capacitors, batteries, fuel cells, and electro-catalysis. However, many mathematical models which are used to describe such systems lack a real predictive value. Origin of this shortcoming is the usage of oversimplified boundary conditions. In this work we derive the boundary conditions for some general electrode-electrolyte interface based on non-equilibrium thermodynamics for volumes and surfaces. The resulting equations are widely applicable and cover also tangential transport. The general framework is then applied to a specific material model which allows the deduction of a current-voltage relation and thus a comparison to experimental data. Some simplified 1D examples show the range of applicability of the new approach.
  • Thumbnail Image
    Item
    Scattering matrices and Dirichlet-to-Neumann maps
    (Amsterdam [u.a.] : Elsevier, 2017) Behrndt, Jussi; Malamud, Mark M.; Neidhardt, Hagen
    A general representation formula for the scattering matrix of a scattering system consisting of two self-adjoint operators in terms of an abstract operator valued Titchmarsh–Weyl m-function is proved. This result is applied to scattering problems for different self-adjoint realizations of Schrödinger operators on unbounded domains, Schrödinger operators with singular potentials supported on hypersurfaces, and orthogonal couplings of Schrödinger operators. In these applications the scattering matrix is expressed in an explicit form with the help of Dirichlet-to-Neumann maps.
  • Thumbnail Image
    Item
    Optimal Entropy-Transport problems and a new Hellinger–Kantorovich distance between positive measures
    (Berlin ; Heidelberg : Springer, 2017) Liero, Matthias; Mielke, Alexander; Savaré, Giuseppe
    We develop a full theory for the new class of Optimal Entropy-Transport problems between nonnegative and finite Radon measures in general topological spaces. These problems arise quite naturally by relaxing the marginal constraints typical of Optimal Transport problems: given a pair of finite measures (with possibly different total mass), one looks for minimizers of the sum of a linear transport functional and two convex entropy functionals, which quantify in some way the deviation of the marginals of the transport plan from the assigned measures. As a powerful application of this theory, we study the particular case of Logarithmic Entropy-Transport problems and introduce the new Hellinger–Kantorovich distance between measures in metric spaces. The striking connection between these two seemingly far topics allows for a deep analysis of the geometric properties of the new geodesic distance, which lies somehow between the well-known Hellinger–Kakutani and Kantorovich–Wasserstein distances.
  • Thumbnail Image
    Item
    Option pricing in the moderate deviations regime
    (Oxford [u.a.] : Wiley-Blackwell, 2017) Friz, Peter; Gerhold, Stefan; Pinter, Arpad
    We consider call option prices close to expiry in diffusion models, in an asymptotic regime (“moderately out of the money”) that interpolates between the well-studied cases of at-the-money and out-of-the-money regimes. First and higher order small-time moderate deviation estimates of call prices and implied volatilities are obtained. The expansions involve only simple expressions of the model parameters, and we show how to calculate them for generic local and stochastic volatility models. Some numerical computations for the Heston model illustrate the accuracy of our results.
  • Thumbnail Image
    Item
    On the regularity of SLE trace
    (Cambridge : Cambridge Univ. Press, 2017) Friz, Peter K.; Tran, Huy
    We revisit regularity of SLE trace, for all κ≠8, and establish Besov regularity under the usual half-space capacity parametrization. With an embedding theorem of Garsia–Rodemich–Rumsey type, we obtain finite moments (and hence almost surely) optimal variation regularity with index min(1+κ/8,2), improving on previous works of Werness, and also (optimal) Hölder regularity à la Johansson Viklund and Lawler.
  • Thumbnail Image
    Item
    Death and rebirth of neural activity in sparse inhibitory networks
    ([London] : IOP, 2017) Angulo-Garcia, David; Luccioli, Stefano; Olmi, Simona; Torcini, Alessandro
    Inhibition is a key aspect of neural dynamics playing a fundamental role for the emergence of neural rhythms and the implementation of various information coding strategies. Inhibitory populations are present in several brain structures, and the comprehension of their dynamics is strategical for the understanding of neural processing. In this paper, we clarify the mechanisms underlying a general phenomenon present in pulse-coupled heterogeneous inhibitory networks: inhibition can induce not only suppression of neural activity, as expected, but can also promote neural re-activation. In particular, for globally coupled systems, the number of firing neurons monotonically reduces upon increasing the strength of inhibition (neuronal death). However, the random pruning of connections is able to reverse the action of inhibition, i.e. in a random sparse network a sufficiently strong synaptic strength can surprisingly promote, rather than depress, the activity of neurons (neuronal rebirth). Thus, the number of firing neurons reaches a minimum value at some intermediate synaptic strength. We show that this minimum signals a transition from a regime dominated by neurons with a higher firing activity to a phase where all neurons are effectively sub-threshold and their irregular firing is driven by current fluctuations. We explain the origin of the transition by deriving a mean field formulation of the problem able to provide the fraction of active neurons as well as the first two moments of their firing statistics. The introduction of a synaptic time scale does not modify the main aspects of the reported phenomenon. However, for sufficiently slow synapses the transition becomes dramatic, and the system passes from a perfectly regular evolution to irregular bursting dynamics. In this latter regime the model provides predictions consistent with experimental findings for a specific class of neurons, namely the medium spiny neurons in the striatum.
  • Thumbnail Image
    Item
    From nonlinear to linear elasticity in a coupled rate-dependent/independent system for brittle delamination
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Rossi, Riccarda; Thomas, Marita
    We revisit the weak, energetic-type existence results obtained in [RT15] for a system for rateindependent, brittle delamination between two visco-elastic, physically nonlinear bulk materials and explain how to rigorously extend such results to the case of visco-elastic, linearly elastic bulk materials. Our approximation result is essentially based on deducing the MOSCO-convergence of the functionals involved in the energetic formulation of the system. We apply this approximation result in two different situations at small strains: Firstly, to pass from a nonlinearly elastic to a linearly elastic, brittle model on the time-continuous level, and secondly, to pass from a time-discrete to a time-continuous model using an adhesive contact approximation of the brittle model, in combination with a vanishing, super-quadratic regularization of the bulk energy. The latter approach is beneficial if the model also accounts for the evolution of temperature.
  • Thumbnail Image
    Item
    Large deviations of specific empirical fluxes of independent Markov chains, with implications for Macroscopic Fluctuation Theory
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Renger, D.R. Michiel
    We consider a system of independent particles on a finite state space, and prove a dynamic large-deviation principle for the empirical measure-empirical flux pair, taking the specific fluxes rather than net fluxes into account. We prove the large deviations under deterministic initial conditions, and under random initial conditions satisfying a large-deviation principle. We then show how to use this result to generalise a number of principles from Macroscopic Fluctuation Theory to the finite-space setting.
  • Thumbnail Image
    Item
    Phase sensitive excitability of a limit cycle
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Franovic, Igor; Omelchenko, Oleh E.; Wolfrum, Matthias
    The classical notion of excitability refers to an equilibrium state that shows under the influence of perturbations a nonlinear threshold-like behavior. Here, we extend this concept by demonstrating how periodic orbits can exhibit a specific form of excitable behavior where the nonlinear threshold-like response appears only after perturbations applied within a certain part of the periodic orbit, i.e the excitability happens to be phase sensitive. As a paradigmatic example of this concept we employ the classical FitzHugh-Nagumo system. The relaxation oscillations, appearing in the oscillatory regime of this system, turn out to exhibit a phase sensitive nonlinear thresholdlike response to perturbations, which can be explained by the nonlinear behavior in the vicinity of the canard trajectory. Triggering the phase sensitive excitability of the relaxation oscillations by noise we find a characteristic non-monotone dependence of the mean spiking rate of the relaxation oscillation on the noise level. We explain this non-monotone dependence as a result of an interplay of two competing effects of the increasing noise: the growing efficiency of the excitation and the degradation of the nonlinear response.