11,263 research outputs found
Low-temperature renormalization group study of uniformly frustrated models for type-II superconductors
We study phase transitions in uniformly frustrated SU(N)-symmetric
-dimensional lattice models describing type-II superconductors
near the upper critical magnetic field . The low-temperature
renormalization-group approach is employed for calculating the beta-function
with an arbitrary rational magnetic frustration. The
phase-boundary line is the ultraviolet-stable fixed point found
from the equation , the corresponding critical exponents being
identical to those of the non-frustrated continuum system. The critical
properties of the SU(N)-symmetric complex Ginzburg-Landau (GL) model are then
examined in dimensions. The possibility of a continuous phase
transition into the mixed state in such a model is suggested.Comment: REVTeX, 12 pages, to appear in the Phys.Rev.
Accurate macroscale modelling of spatial dynamics in multiple dimensions
Developments in dynamical systems theory provides new support for the
macroscale modelling of pdes and other microscale systems such as Lattice
Boltzmann, Monte Carlo or Molecular Dynamics simulators. By systematically
resolving subgrid microscale dynamics the dynamical systems approach constructs
accurate closures of macroscale discretisations of the microscale system. Here
we specifically explore reaction-diffusion problems in two spatial dimensions
as a prototype of generic systems in multiple dimensions. Our approach unifies
into one the modelling of systems by a type of finite elements, and the
`equation free' macroscale modelling of microscale simulators efficiently
executing only on small patches of the spatial domain. Centre manifold theory
ensures that a closed model exist on the macroscale grid, is emergent, and is
systematically approximated. Dividing space either into overlapping finite
elements or into spatially separated small patches, the specially crafted
inter-element/patch coupling also ensures that the constructed discretisations
are consistent with the microscale system/PDE to as high an order as desired.
Computer algebra handles the considerable algebraic details as seen in the
specific application to the Ginzburg--Landau PDE. However, higher order models
in multiple dimensions require a mixed numerical and algebraic approach that is
also developed. The modelling here may be straightforwardly adapted to a wide
class of reaction-diffusion PDEs and lattice equations in multiple space
dimensions. When applied to patches of microscopic simulations our coupling
conditions promise efficient macroscale simulation.Comment: some figures with 3D interaction when viewed in Acrobat Reader. arXiv
admin note: substantial text overlap with arXiv:0904.085
Unstable manifolds and Schroedinger dynamics of Ginzburg-Landau vortices
The time evolution of several interacting Ginzburg-Landau vortices according
to an equation of Schroedinger type is approximated by motion on a
finite-dimensional manifold. That manifold is defined as an unstable manifold
of an auxiliary dynamical system, namely the gradient flow of the
Ginzburg-Landau energy functional. For two vortices the relevant unstable
manifold is constructed numerically and the induced dynamics is computed. The
resulting model provides a complete picture of the vortex motion for arbitrary
vortex separation, including well-separated and nearly coincident vortices.Comment: 23 pages amslatex, 5 eps figures, minor typos correcte
Ginzburg-Landau Approach to Holographic Superconductivity
We construct a family of minimal phenomenological models for holographic
superconductors in d=4+1 AdS spacetime and study the effect of scalar and gauge
field fluctuations. By making a Ginzburg-Landau interpretation of the dual
field theory, we determine through holographic techniques a phenomenological
Ginzburg-Landau Lagrangian and the temperature dependence of physical
quantities in the superconducting phase. We obtain insight on the behaviour of
the Ginzburg-Landau parameter and whether the systems behaves as a Type I or
Type II superconductor. Finally, we apply a constant external magnetic field in
a perturbative approach following previous work by D'Hoker and Kraus, and
obtain droplet solutions which signal the appearance of the Meissner effect.Comment: 41 pages, 31 figures, calculations adde
A hierarchy of models for type-II superconductors
A hierarchy of models for type-II superconductors is presented. Through appropriate asymptotic limits we pass from the mesoscopic Ginzburg-Landau model to the London model with isolated superconducting vortices as line singularities, to vortex-density models, and finally to macroscopic critical-state models
Mirror Symmetry and the Web of Landau-Ginzburg String Vacua
We present some mathematical aspects of Landau-Ginzburg string vacua in terms
of toric geometry. The one-to-one correspondence between toric divisors and
some of (-1,1) states in Landau-Ginzburg model is presented for superpotentials
of typical types. The Landau-Ginzburg interpretation of non-toric divisors is
also presented. Using this interpretation, we propose a method to solve the
so-called "twisted sector problem" by orbifold construction. Moreover,this
construction shows that the moduli spaces of the original Landau-Ginzburg
string vacua and their orbifolds are connected. By considering the mirror map
of Landau-Ginzburg models, we obtain the relation between Mori vectors and the
twist operators of our orbifoldization. This consideration enables us to argue
the embedding of the Seiberg-Witten curve in the defining equation of the
Calabi-Yau manifoulds on which the type II string gets compactified. Related
topics concerning the Calabi-Yau fourfolds and the extremal transition are
discussed.Comment: Section 5 is largely extended, 23 pages, Latex 2.09, no figur
An optimal linear solver for the Jacobian system of the extreme type-II Ginzburg--Landau problem
This paper considers the extreme type-II Ginzburg--Landau equations, a
nonlinear PDE model for describing the states of a wide range of
superconductors. Based on properties of the Jacobian operator and an AMG
strategy, a preconditioned Newton--Krylov method is constructed. After a
finite-volume-type discretization, numerical experiments are done for
representative two- and three-dimensional domains. Strong numerical evidence is
provided that the number of Krylov iterations is independent of the dimension
of the solution space, yielding an overall solver complexity of O(n)
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