scholarly journals Sharp-Interface Limit of a Ginzburg–Landau Functional with a Random External Field

2009 ◽  
Vol 41 (2) ◽  
pp. 781-824 ◽  
Author(s):  
Nicolas Dirr ◽  
Enza Orlandi
Keyword(s):  
External Field ◽  
Sharp Interface ◽  
Ginzburg Landau ◽  
Sharp Interface Limit ◽  
Random External Field

Higher Dimensional Bubble Profiles in a Sharp Interface Limit of the FitzHugh--Nagumo System

2018 ◽  
Vol 50 (5) ◽  
pp. 5072-5095 ◽  
Author(s):  
Chao-Nien Chen ◽  
Yung-Sze Choi ◽  
Yeyao Hu ◽  
Xiaofeng Ren
Keyword(s):  
Sharp Interface ◽  
Sharp Interface Limit ◽  
Higher Dimensional

On the mean-field Ising model in a random external field

1985 ◽  
Vol 41 (1-2) ◽  
pp. 299-313 ◽  
Author(s):  
S. R. Salinas ◽  
W. F. Wreszinski
Keyword(s):  
Ising Model ◽  
External Field ◽  
Mean Field ◽  
The Mean ◽  
Random External Field

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.

Phase diagram of an imprinted copolymer in a random external field

1995 ◽  
Vol 28 (13) ◽  
pp. 3657-3666 ◽  
Author(s):  
V S Pande ◽  
A Yu Grosberg ◽  
T Tanaka
Keyword(s):  
Phase Diagram ◽  
External Field ◽  
Random External Field
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