Filters

20205

More filters

2021 - 20225
Reset filters

Settings

End date: 2020 × Start date: 2020 × DDC: 510 × DDC: 530 ×

Search Results

Now showing 1 - 5 of 5
  • Thumbnail Image
    Item
    Thermoviscoelasticity in Kelvin–Voigt Rheology at Large Strains
    (Berlin ; Heidelberg : Springer, 2020) Mielke, Alexander; Roubíček, Tomáš
    The 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).
  • Thumbnail Image
    Item
    Ice-Crystal Nucleation in Water: Thermodynamic Driving Force and Surface Tension. Part I: Theoretical Foundation
    (Basel : MDPI, 2020) Hellmuth, Olaf; Schmelzer, Jürn W.P.; Feistel, Rainer
    A recently developed thermodynamic theory for the determination of the driving force of crystallization and the crystal–melt surface tension is applied to the ice-water system employing the new Thermodynamic Equation of Seawater TEOS-10. The deviations of approximative formulations of the driving force and the surface tension from the exact reference properties are quantified, showing that the proposed simplifications are applicable for low to moderate undercooling and pressure differences to the respective equilibrium state of water. The TEOS-10-based predictions of the ice crystallization rate revealed pressure-induced deceleration of ice nucleation with an increasing pressure, and acceleration of ice nucleation by pressure decrease. This result is in, at least, qualitative agreement with laboratory experiments and computer simulations. Both the temperature and pressure dependencies of the ice-water surface tension were found to be in line with the le Chatelier–Braun principle, in that the surface tension decreases upon increasing degree of metastability of water (by decreasing temperature and pressure), which favors nucleation to move the system back to a stable state. The reason for this behavior is discussed. Finally, the Kauzmann temperature of the ice-water system was found to amount TK=116K , which is far below the temperature of homogeneous freezing. The Kauzmann pressure was found to amount to pK=−212MPa , suggesting favor of homogeneous freezing on exerting a negative pressure on the liquid. In terms of thermodynamic properties entering the theory, the reason for the negative Kauzmann pressure is the higher mass density of water in comparison to ice at the melting point.
  • Thumbnail Image
    Item
    Couplings via Comparison Principle and Exponential Ergodicity of SPDEs in the Hypoelliptic Setting
    (Berlin ; Heidelberg : Springer, 2020) Butkovsky, Oleg; Scheutzow, Michael
    We develop a general framework for studying ergodicity of order-preserving Markov semigroups. We establish natural and in a certain sense optimal conditions for existence and uniqueness of the invariant measure and exponential convergence of transition probabilities of an order-preserving Markov process. As an application, we show exponential ergodicity and exponentially fast synchronization-by-noise of the stochastic reaction–diffusion equation in the hypoelliptic setting. This refines and complements corresponding results of Hairer and Mattingly (Electron J Probab 16:658–738, 2011). © 2020, The Author(s).
  • Thumbnail Image
    Item
    Analysis of improved Nernst–Planck–Poisson models of compressible isothermal electrolytes
    (Cham (ZG) : Springer International Publishing AG, 2020) Dreyer, Wolfgang; Druet, Pierre-Étienne; Gajewski, Paul; Guhlke, Clemens
    We consider an improved Nernst–Planck–Poisson model first proposed by Dreyer et al. in 2013 for compressible isothermal electrolytes in non-equilibrium. The elastic deformation of the medium, that induces an inherent coupling of mass and momentum transport, is taken into account. The model consists of convection–diffusion–reaction equations for the constituents of the mixture, of the Navier–Stokes equation for the barycentric velocity and of the Poisson equation for the electrical potential. Due to the principle of mass conservation, cross-diffusion phenomena must occur, and the mobility matrix (Onsager matrix) has a non-trivial kernel. In this paper, we establish the existence of a global-in-time weak solution, allowing for a general structure of the mobility tensor and for chemical reactions with fast nonlinear rates in the bulk and on the active boundary. We characterise the singular states of the system, showing that the chemical species can vanish only globally in space, and that this phenomenon must be concentrated in a compact set of measure zero in time.
  • Thumbnail Image
    Item
    Analysis and simulations for a phase-field fracture model at finite strains based on modified invariants
    (Berlin : Wiley-VCH, 2020) Thomas, Marita; Bilgen, Carola; Weinberg, Kerstin
    Phase-field models have already been proven to predict complex fracture patterns for brittle fracture at small strains. In this paper we discuss a model for phase-field fracture at finite deformations in more detail. Among the identification of crack location and projection of crack growth the numerical stability is one of the main challenges in solid mechanics. Here we present a phase-field model at finite strains, which takes into account the anisotropy of damage by applying an anisotropic split of the modified invariants of the right Cauchy-Green strain tensor. We introduce a suitable weak notion of solution that also allows for a spatial and temporal discretization of the model. In this framework we study the existence of solutions and we show that the time-discrete solutions converge in a weak sense to a solution of the time-continuous formulation of the model. Numerical examples in two and three space dimensions illustrate the range of validity of the analytical results.