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Subject: Fokker-Planck equation ×

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Now showing 1 - 3 of 3
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    A revisited Johnson-Mehl-Avrami-Kolmogorov model and the evolution of grain-size distributions in steel
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Hömberg, Dietmar; Patacchini, Francesco Saverio; Sakamoto, Kenichi; Zimmer, Johannes
    The classical Johnson-Mehl-Avrami-Kolmogorov approach for nucleation and growth models of diffusive phase transitions is revisited and applied to model the growth of ferrite in multiphase steels. For the prediction of mechanical properties of such steels, a deeper knowledge of the grain structure is essential. To this end, a Fokker-Planck evolution law for the volume distribution of ferrite grains is developed and shown to exhibit a log-normally distributed solution. Numerical parameter studies are given and confirm expected properties qualitatively. As a preparation for future work on parameter identification, a strategy is presented for the comparison of volume distributions with area distributions experimentally gained from polished micrograph sections.
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    Noise-induced dynamical regimes in a system of globally coupled excitable units
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Klinshov, Vladimir V.; Kirillov, Sergey Yu.; Nekorkin, Vladimir I.; Wolfrum, Matthias
    We study the interplay of global attractive coupling and individual noise in a system of identical active rotators in the excitable regime. Performing a numerical bifurcation analysis of the nonlocal nonlinear Fokker-Planck equation for the thermodynamic limit, we identify a complex bifurcation scenario with regions of different dynamical regimes, including collective oscillations and coexistence of states with different levels of activity. In systems of finite size this leads to additional dynamical features, such as collective excitability of different types, noise-induced switching and bursting. Moreover, we show how characteristic quantities such as macroscopic and microscopic variability of inter spike intervals can depend in a non-monotonous way on the noise level.
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    Modeling of chemical reaction systems with detailed balance using gradient structures
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Maas, Jan; Mielke, Alexander
    We consider various modeling levels for spatially homogeneous chemical reaction systems, namely the chemical master equation, the chemical Langevin dynamics, and the reaction-rate equation. Throughout we restrict our study to the case where the microscopic system satisfies the detailed-balance condition. The latter allows us to enrich the systems with a gradient structure, i.e. the evolution is given by a gradient-flow equation. We present the arising links between the associated gradient structures that are driven by the relative entropy of the detailed-balance steady state. The limit of large volumes is studied in the sense of evolutionary Γ-convergence of gradient flows. Moreover, we use the gradient structures to derive hybrid models for coupling different modeling levels.