scholarly journals An anisotropic phase-field model for solid-state dewetting and its sharp-interface limit

Nonlinearity ◽  
2017 ◽  
Vol 30 (4) ◽  
pp. 1465-1496 ◽  
Author(s):  
Marion Dziwnik ◽  
Andreas Münch ◽  
Barbara Wagner
Keyword(s):  
Solid State ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Sharp Interface ◽  
Sharp Interface Limit ◽  
Anisotropic Phase

scholarly journals Sharp interface limits of an anisotropic phase field model for solid-state dewetting★

2015 ◽  
Vol 48 (1) ◽  
pp. 394-395 ◽  
Author(s):  
Marion Dziwnik ◽  
Andreas Münch ◽  
Barbara Wagner
Keyword(s):  
Solid State ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Sharp Interface ◽  
Anisotropic Phase

On the van der Waals–Cahn–Hilliard phase-field model and its equilibria conditions in the sharp interface limit

2010 ◽  
Vol 140 (6) ◽  
pp. 1161-1186 ◽  
Author(s):  
Wolfgang Dreyer ◽  
Christiane Kraus
Keyword(s):  
Free Energy ◽  
Phase Field ◽  
Field Model ◽  
Van Der Waals ◽  
Phase Field Model ◽  
Entropy Inequality ◽  
Sharp Interface ◽  
Energy Estimates ◽  
Sharp Interface Limit ◽  
Entropy Flux

We study the thermodynamic consistency of phase-field models, which include gradient terms of the density ρ in the free-energy functional such as the van der Waals–Cahn–Hilliard model. It is well known that the entropy inequality admits gradient and higher-order gradient terms of ρ in the free energy only if either the energy flux or the entropy flux is represented by a non-classical form. We identify a non-classical entropy flux, which is not restricted to isothermal processes, so that gradient contributions are possible.We then investigate equilibrium conditions for the van der Waals–Cahn–Hilliard phase-field model in the sharp interface limit. For a single substance thermodynamics provides two jump conditions at the sharp interface, namely the continuity of the Gibbs free energies of the adjacent phases and the discontinuity of the corresponding pressures, which is balanced by the mean curvature. We show that these conditions can be also extracted from the van der Waals–Cahn–Hilliard phase-field model in the sharp interface limit. To this end we prove an asymptotic expansion of the density up to the first order. The results are based on local energy estimates and uniform convergence results for the density.

scholarly journals Phase-field model of cell motility: Traveling waves and sharp interface limit

2016 ◽  
Vol 354 (10) ◽  
pp. 986-992 ◽  
Author(s):  
Leonid Berlyand ◽  
Mykhailo Potomkin ◽  
Volodymyr Rybalko
Keyword(s):  
Cell Motility ◽  
Traveling Waves ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Sharp Interface ◽  
Sharp Interface Limit

scholarly journals Sharp Interface Limit for a Phase Field Model in Structural Optimization

2016 ◽  
Vol 54 (3) ◽  
pp. 1558-1584 ◽  
Author(s):  
Luise Blank ◽  
Harald Garcke ◽  
Claudia Hecht ◽  
Christoph Rupprecht
Keyword(s):  
Structural Optimization ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Sharp Interface ◽  
Sharp Interface Limit

scholarly journals Sharp interface limit in a phase field model of cell motility

2017 ◽  
Vol 12 (4) ◽  
pp. 551-590 ◽  
Author(s):  
Leonid Berlyand ◽  
◽  
Mykhailo Potomkin ◽  
Volodymyr Rybalko ◽  
Keyword(s):  
Cell Motility ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Sharp Interface ◽  
Sharp Interface Limit

Non-axisymmetric growth of dendrite with arbitrary symmetry in two and three dimensions: sharp interface model vs phase-field model

2020 ◽  
Vol 229 (19-20) ◽  
pp. 2899-2909
Author(s):  
L. V. Toropova ◽  
P. K. Galenko ◽  
D. V. Alexandrov ◽  
M. Rettenmayr ◽  
A. Kao ◽  
...  
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Sharp Interface ◽  
Three Dimensions ◽  
Interface Model ◽  
Sharp Interface Model

scholarly journals A regularized phase-field model for faceting in a kinetically controlled crystal growth

2020 ◽  
Vol 476 (2241) ◽  
pp. 20200227
Author(s):  
T. Philippe ◽  
H. Henry ◽  
M. Plapp
Keyword(s):  
Crystal Growth ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Sharp Interface ◽  
Diffuse Interface ◽  
Interface Problem ◽  
Kinetically Controlled ◽  
Interface Theory ◽  
Coarsening Dynamics

At equilibrium, the shape of a strongly anisotropic crystal exhibits corners when for some orientations the surface stiffness is negative. In the sharp-interface problem, the surface free energy is traditionally augmented with a curvature-dependent term in order to round the corners and regularize the dynamic equations that describe the motion of such interfaces. In this paper, we adopt a diffuse interface description and present a phase-field model for strongly anisotropic crystals that is regularized using an approximation of the Willmore energy. The Allen–Cahn equation is employed to model kinetically controlled crystal growth. Using the method of matched asymptotic expansions, it is shown that the model converges to the sharp-interface theory proposed by Herring. Then, the stress tensor is used to derive the force acting on the diffuse interface and to examine the properties of a corner at equilibrium. Finally, the coarsening dynamics of the faceting instability during growth is investigated. Phase-field simulations reveal the existence of a parabolic regime, with the mean facet length evolving in t , with t the time, as predicted by the sharp-interface theory. A specific coarsening mechanism is observed: a hill disappears as the two neighbouring valleys merge.

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