2,121 research outputs found
Global existence of weak solutions for a nonlocal model for two-phase flows of incompressible fluids with unmatched densities
We consider a diffuse interface model for an incompressible isothermal
mixture of two viscous Newtonian fluids with different densities in a bounded
domain in two or three space dimensions. The model is the nonlocal version of
the one recently derived by Abels, Garcke and Gr\"{u}n and consists in a
Navier-Stokes type system coupled with a convective nonlocal Cahn-Hilliard
equation. The density of the mixture depends on an order parameter. For this
nonlocal system we prove existence of global dissipative weak solutions for the
case of singular double-well potentials and non degenerate mobilities. To this
goal we devise an approach which is completely independent of the one employed
by Abels, Depner and Garcke to establish existence of weak solutions for the
local Abels et al. model.Comment: 43 page
Strong solutions for two-dimensional nonlocal Cahn-Hilliard-Navier-Stokes systems
A well-known diffuse interface model for incompressible isothermal mixtures
of two immiscible fluids consists of the Navier-Stokes system coupled with a
convective Cahn-Hilliard equation. In some recent contributions the standard
Cahn-Hilliard equation has been replaced by its nonlocal version. The
corresponding system is physically more relevant and mathematically more
challenging. Indeed, the only known results are essentially the existence of a
global weak solution and the existence of a suitable notion of global attractor
for the corresponding dynamical system defined without uniqueness. In fact,
even in the two-dimensional case, uniqueness of weak solutions is still an open
problem. Here we take a step forward in the case of regular potentials. First
we prove the existence of a (unique) strong solution in two dimensions. Then we
show that any weak solution regularizes in finite time uniformly with respect
to bounded sets of initial data. This result allows us to deduce that the
global attractor is the union of all the bounded complete trajectories which
are strong solutions. We also demonstrate that each trajectory converges to a
single equilibrium, provided that the potential is real analytic and the
external forces vanish.Comment: 30 page
Spatially Resolved NMR Relaxation Rate in a Noncentrosymmetric Superconductor
We numerically study the spatially-resolved NMR around a single vortex in a
noncentrosymmetric superconductor such as CePt3Si.
The nuclear spin-lattice relaxation rate 1/T1 under the influence of the
vortex core states is calculated for an s+p-wave Cooper pairing state.
The result is compared with that for an s-wave pairing state.Comment: 2 pages; submitted to Proc. of SCES'0
Optimal distributed control of a nonlocal Cahn-Hilliard/Navier-Stokes system in 2D
We study a diffuse interface model for incompressible isothermal mixtures of
two immiscible fluids coupling the Navier--Stokes system with a convective
nonlocal Cahn--Hilliard equation in two dimensions of space. We apply recently
proved well-posedness and regularity results in order to establish existence of
optimal controls as well as first-order necessary optimality conditions for an
associated optimal control problem in which a distributed control is applied to
the fluid flow.Comment: 32 page
Landau-Fermi liquid analysis of the 2D t-t' Hubbard model
We calculate the Landau interaction function f(k,k') for the two-dimensional
t-t' Hubbard model on the square lattice using second and higher order
perturbation theory. Within the Landau-Fermi liquid framework we discuss the
behavior of spin and charge susceptibilities as function of the onsite
interaction and band filling. In particular we analyze the role of elastic
umklapp processes as driving force for the anisotropic reduction of the
compressibility on parts of the Fermi surface.Comment: 10 pages, 16 figure
Basic Properties of a Vortex in a Noncentrosymmetric Superconductor
We numerically study the vortex core structure in a noncentrosymmetric
superconductor such as CePt3Si without mirror symmetry about the xy plane.
A single vortex along the z axis and a mixed singlet-triplet Cooper pairing
model are considered.
The spatial profiles of the pair potential, local density of states,
supercurrent density, and radially-textured magnetic moment density around the
vortex are obtained in the clean limit on the basis of the quasiclassical
theory of superconductivity.Comment: 6 pages; submitted to Proc. of VORTEX I
Temperature Dependence of the Superfluid Density in a Noncentrosymmetric Superconductor
For a noncentrosymmetric superconductor such as CePt3Si, we consider a Cooper
pairing model with a two-component order parameter composed of spin-singlet and
spin-triplet pairing components.
We calculate the superfluid density tensor in the clean limit on the basis of
the quasiclassical theory of superconductivity.
We demonstrate that such a pairing model accounts for an experimentally
observed feature of the temperature dependence of the London penetration depth
in CePt3Si, i.e., line-node-gap behavior at low temperatures.Comment: 10 page
- …