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- ItemSymmetries in transmission electron microscopy imaging of crystals with strain(London : [Verlag nicht ermittelbar], 2022) Koprucki, Thomas; Maltsi, Anieza; Mielke, AlexanderTransmission electron microscopy (TEM) images of strained crystals often exhibit symmetries, the source of which is not always clear. To understand these symmetries, we distinguish between symmetries that occur from the imaging process itself and symmetries of the inclusion that might affect the image. For the imaging process, we prove mathematically that the intensities are invariant under specific transformations. A combination of these invariances with specific properties of the strain profile can then explain symmetries observed in TEM images. We demonstrate our approach to the study of symmetries in TEM images using selected examples in the field of semiconductor nanostructures such as quantum wells and quantum dots.
- ItemEDP-convergence for nonlinear fast–slow reaction systems with detailed balance*(Bristol : IOP Publ., 2021) Mielke, Alexander; Peletier, Mark A.; Stephan, ArturWe consider nonlinear reaction systems satisfying mass-action kinetics with slow and fast reactions. It is known that the fast-reaction-rate limit can be described by an ODE with Lagrange multipliers and a set of nonlinear constraints that ask the fast reactions to be in equilibrium. Our aim is to study the limiting gradient structure which is available if the reaction system satisfies the detailed-balance condition. The gradient structure on the set of concentration vectors is given in terms of the relative Boltzmann entropy and a cosh-type dissipation potential. We show that a limiting or effective gradient structure can be rigorously derived via EDP-convergence, i.e. convergence in the sense of the energy-dissipation principle for gradient flows. In general, the effective entropy will no longer be of Boltzmann type and the reactions will no longer satisfy mass-action kinetics.
- ItemThermoviscoelasticity in Kelvin–Voigt Rheology at Large Strains(Berlin ; Heidelberg : Springer, 2020) Mielke, Alexander; Roubíček, TomášThe frame-indifferent thermodynamically-consistent model of thermoviscoelasticity at large strain is formulated in the reference configuration by using the concept of the second-grade nonsimple materials. We focus on physically correct viscous stresses that are frame indifferent under time-dependent rotations. Also elastic stresses are frame indifferent under rotations and respect positivity of the determinant of the deformation gradient. The heat transfer is governed by the Fourier law in the actual deformed configuration, which leads to a nontrivial description when pulled back to the reference configuration. The existence of weak solutions in the quasistatic setting, that is inertial forces are ignored, is shown by time discretization. © 2020, The Author(s).