Hydrodynamic limit for the Ginzburg-Landau ?? interface model with boundary conditions

2003 ◽  
Vol 127 (2) ◽  
pp. 205-227 ◽  
Author(s):  
Takao Nishikawa
Keyword(s):  
Boundary Conditions ◽  
Hydrodynamic Limit ◽  
Interface Model ◽  
Ginzburg Landau

Hydrodynamic limit for the Ginzburg–Landau ∇ϕ interface model with non-convex potential

2019 ◽  
Vol 129 (3) ◽  
pp. 924-953
Author(s):  
Jean-Dominique Deuschel ◽  
Takao Nishikawa ◽  
Yvon Vignaud
Keyword(s):  
Hydrodynamic Limit ◽  
Interface Model ◽  
Ginzburg Landau

scholarly journals Order parameter profiles in a system with Neumann – Neumann boundary conditions

2018 ◽  
Vol 145 ◽  
pp. 01009 ◽  
Author(s):  
Vassil M. Vassilev ◽  
Daniel M. Dantchev ◽  
Peter A. Djondjorov
Keyword(s):  
Boundary Conditions ◽  
Order Parameter ◽  
Neumann Boundary ◽  
Elliptic Functions ◽  
Thermodynamic System ◽  
Neumann Boundary Conditions ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
The One ◽  
Field Plane

In this article we consider a critical thermodynamic system with the shape of a thin film confined between two parallel planes. It is assumed that the state of the system at a given temperature and external ordering field is described by order-parameter profiles, which minimize the one-dimensional counterpart of the standard ϕ4 Ginzburg–Landau Hamiltonian and meet the so-called Neumann – Neumann boundary conditions. We give analytic representation of the extremals of this variational problem in terms ofWeierstrass elliptic functions. Then, depending on the temperature and ordering field we determine the minimizers and obtain the phase diagram in the temperature-field plane.

scholarly journals Minimax Critical Points in Ginzburg-Landau Problems with Semi-Stiff Boundary Conditions: Existence and Bubbling

2014 ◽  
Vol 39 (5) ◽  
pp. 946-1005 ◽  
Author(s):  
Leonid Berlyand ◽  
Petru Mironescu ◽  
Volodymyr Rybalko ◽  
Etienne Sandier
Keyword(s):  
Boundary Conditions ◽  
Critical Points ◽  
Ginzburg Landau
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