Some properties of asymptotic energy of a class of functionals of Ginzburg-Landau type endowed with generalized lower-order oscillatory term in one dimension

PAMM ◽  
2014 ◽  
Vol 14 (1) ◽  
pp. 753-754 ◽  
Author(s):  
Andrija Raguž
Keyword(s):  
Lower Order ◽  
One Dimension ◽  
Ginzburg Landau ◽  
Asymptotic Energy

Relaxation of Ginzburg–Landau functional perturbed by continuous nonlinear lower-order term in one dimension

2014 ◽  
Vol 13 (01) ◽  
pp. 101-123 ◽  
Author(s):  
Andrija Raguž
Keyword(s):  
Asymptotic Behavior ◽  
Lower Order ◽  
Order Term ◽  
Lower Order Term ◽  
One Dimension ◽  
Young Measures ◽  
Ginzburg Landau ◽  
Carathéodory Function ◽  
Γ Convergence

We study the asymptotic behavior as ε → 0 of the Ginzburg–Landau functional [Formula: see text], where A(s, v, v′) is the nonlinear lower-order term generated by certain Carathéodory function a : (0, 1)2 × R2 → R. We obtain Γ-convergence for the rescaled functionals [Formula: see text] as ε → 0 by using the notion of Young measures on micropatterns, which was introduced in 2001 by Alberti and Müller. We prove that for ε ≈ 0 the minimal value of [Formula: see text] is close to [Formula: see text], where A∞(s) : = ½A(s, 0, -1) + ½A(s, 0, 1) and where E0 depends only on W. Further, we use this example to establish some general conclusions related to the approach of Alberti and Müller.

Nonequilibrium dynamics ofN-component Ginzburg-Landau fields in zero and one dimension

1984 ◽  
Vol 30 (2) ◽  
pp. 1026-1032 ◽  
Author(s):  
Jayanta K. Bhattacharjee ◽  
Paul Meakin ◽  
D. J. Scalapino
Keyword(s):  
Nonequilibrium Dynamics ◽  
One Dimension ◽  
Ginzburg Landau

ENERGY EXPANSION AND VORTEX LOCATION FOR A TWO-DIMENSIONAL ROTATING BOSE–EINSTEIN CONDENSATE

2006 ◽  
Vol 18 (02) ◽  
pp. 119-162 ◽  
Author(s):  
RADU IGNAT ◽  
VINCENT MILLOT
Keyword(s):  
Topological Charge ◽  
Einstein Condensate ◽  
Two Dimensional ◽  
Precise Location ◽  
Ginzburg Landau ◽  
Bose Einstein Condensate ◽  
Mass Constraint ◽  
Asymptotic Energy ◽  
Bose Einstein ◽  
Energy Expansion

We continue the analysis started in [14] on a model describing a two-dimensional rotating Bose–Einstein condensate. This model consists in minimizing under the unit mass constraint, a Gross–Pitaevskii energy defined in ℝ2. In this contribution, we estimate the critical rotational speeds Ωd for having exactly d vortices in the bulk of the condensate and we determine their topological charge and their precise location. Our approach relies on asymptotic energy expansion techniques developed by Serfaty [20–22] for the Ginzburg–Landau energy of superconductivity in the high κ limit.

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