Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-14568
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Main Title: Anisotropy in wavelet based phase field models
Author(s): Korzec, Maciek
Münch, Andreas
Süli, Endre
Wagner, Barbara
Type: Research Paper
URI: https://depositonce.tu-berlin.de/handle/11303/15795
http://dx.doi.org/10.14279/depositonce-14568
License: http://rightsstatements.org/vocab/InC/1.0/
Abstract: Anisotropy is an essential feature of phase-field models, in particular when describing the evolution of microstructures in solids. The symmetries of the crystalline phases are reflected in the interfacial energy by introducing corresponding directional dependencies in the gradient energy coefficients, which multiply the highest order derivative in the phase-field model. This paper instead considers an alternative approach, where the anisotropic gradient energy terms are replaced by a wavelet analogue that is intrinsically anisotropic and linear. In our studies we focus on the classical coupled temperature - Ginzburg-Landau type phase-field model for dendritic growth. For the resulting derivative-free wavelet analogue existence, uniqueness and continuous dependence on initial data for weak solutions is proved. The ability to capture dendritic growth similar to the results obtained from classical models is investigated numerically.
Subject(s): phase-field model
wavelets
sharp-interface model
free boundaries
Issue Date: 18-Dec-2014
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 34E13 Multiple scale methods
74N20 Dynamics of phase boundaries
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2014, 41
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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