Hydrodynamic limit for the Ginzburg–Landau ∇ϕ interface model with a conservation law and Dirichlet boundary conditions

The effect of a finite geometry on the two-dimensional complex Ginzburg–Landau equation is addressed. Boundary effects induce the formation of novel states. For example, target-like solutions appear as robust solutions under Dirichlet boundary conditions. Synchronization of plane waves emitted by boundaries, entrainment by corner emission, and anchoring of defects by shock lines are also reported.

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Analytic solutions for the temperature-field behaviour of the Ginzburg-Landau Ising type mean-field model with Dirichlet boundary conditions

10.1063/1.5099022 ◽

2019 ◽

Author(s):

Peter A. Djondjorov ◽

Vassil M. Vassilev ◽

Daniel M. Danchev

Keyword(s):

Temperature Field ◽

Boundary Conditions ◽

Dirichlet Boundary ◽

Field Model ◽

Mean Field ◽

Analytic Solutions ◽

Dirichlet Boundary Conditions ◽

Mean Field Model ◽

Ginzburg Landau ◽

Field Behaviour

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Magnetic profile in a nanostructured superconducting sample

Modern Physics Letters B ◽

10.1142/s0217984914501504 ◽

2014 ◽

Vol 28 (18) ◽

pp. 1450150

Author(s):

J. Barba-Ortega ◽

J. D. González ◽

Miryam R. Joya

Keyword(s):

Magnetic Field ◽

Boundary Conditions ◽

Applied Magnetic Field ◽

Dirichlet Boundary ◽

Dirichlet Boundary Conditions ◽

Cooper Pairs ◽

Critical Fields ◽

Ginzburg Landau ◽

Superconducting Sample ◽

Magnetic Profile

We study the Cooper pairs configuration, the magnetic induction and the magnetization in a superconducting nanoscopic square with a central square tower embedder in a uniform applied magnetic field. We study the vortex configurations for a superconductor in two scenarios; in the vicinity of the Bogomolny point [Formula: see text] and with [Formula: see text]. We also considered the Neumann and Dirichlet boundary conditions via deGennes length penetration. We show that the critical fields depends both on the boundary conditions and Ginzburg–Landau parameter.

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General solutions in Chern-Simons gravity and $$ T\overline{T} $$-deformations

Journal of High Energy Physics ◽

10.1007/jhep01(2021)039 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Eva Llabrés

Keyword(s):

Variational Principle ◽

Boundary Conditions ◽

Dirichlet Boundary ◽

Mixed Boundary ◽

Mixed Boundary Conditions ◽

Dirichlet Boundary Conditions ◽

Spin Connection ◽

Departure Point ◽

Boundary Stress ◽

Chern Simons

Abstract We find the most general solution to Chern-Simons AdS3 gravity in Fefferman-Graham gauge. The connections are equivalent to geometries that have a non-trivial curved boundary, characterized by a 2-dimensional vielbein and a spin connection. We define a variational principle for Dirichlet boundary conditions and find the boundary stress tensor in the Chern-Simons formalism. Using this variational principle as the departure point, we show how to treat other choices of boundary conditions in this formalism, such as, including the mixed boundary conditions corresponding to a $$ T\overline{T} $$ T T ¯ -deformation.

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Charge algebra in Al(A)dSn spacetimes

Journal of High Energy Physics ◽

10.1007/jhep05(2021)210 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

Adrien Fiorucci ◽

Romain Ruzziconi

Keyword(s):

Boundary Conditions ◽

Dirichlet Boundary ◽

Three Dimensional ◽

Dirichlet Boundary Conditions ◽

Boundary Structure ◽

Asymptotic Symmetry ◽

Renormalization Procedure ◽

Field Dependent ◽

Odd Dimensions

Abstract The gravitational charge algebra of generic asymptotically locally (A)dS spacetimes is derived in n dimensions. The analysis is performed in the Starobinsky/Fefferman-Graham gauge, without assuming any further boundary condition than the minimal falloffs for conformal compactification. In particular, the boundary structure is allowed to fluctuate and plays the role of source yielding some symplectic flux at the boundary. Using the holographic renormalization procedure, the divergences are removed from the symplectic structure, which leads to finite expressions. The charges associated with boundary diffeomorphisms are generically non-vanishing, non-integrable and not conserved, while those associated with boundary Weyl rescalings are non-vanishing only in odd dimensions due to the presence of Weyl anomalies in the dual theory. The charge algebra exhibits a field-dependent 2-cocycle in odd dimensions. When the general framework is restricted to three-dimensional asymptotically AdS spacetimes with Dirichlet boundary conditions, the 2-cocycle reduces to the Brown-Henneaux central extension. The analysis is also specified to leaky boundary conditions in asymptotically locally (A)dS spacetimes that lead to the Λ-BMS asymptotic symmetry group. In the flat limit, the latter contracts into the BMS group in n dimensions.

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