729 research outputs found
Approximate controllability of Lagrangian trajectories of the 3D Navier-Stokes system by a finite-dimensional force
In the Eulerian approach, the motion of an incompressible fluid is usually
described by the velocity field which is given by the Navier--Stokes system.
The velocity field generates a flow in the space of volume-preserving
diffeomorphisms. The latter plays a central role in the Lagrangian description
of a fluid, since it allows to identify the trajectories of individual
particles. In this paper, we show that the velocity field of the fluid and the
corresponding flow of diffeomorphisms can be simultaneously approximately
controlled using a finite-dimensional external force. The proof is based on
some methods from the geometric control theory introduced by Agrachev and
Sarychev
Scaling Properties of the Two-Chain Model
Scaling properties of a self-dual field-theoretical model, describing two
weakl$spinless Luttinger chains, are studied. A crossover to a sine-Gordon
massive phase, with strongly developed two-particleinterchain correlations, is
described. It is argued that, in a wide range of the in-chain interaction,
renormalization of the interchain hopping amplitude is determined by the
Luttinger liquid effects.Comment: 14 pages Latex, accepted Physics Letters
Lower Bound for the Fermi Level Density of States of a Disordered D-Wave Superconductor in Two Dimensions
We consider a disordered d--wave superconductor in two dimensions. Recently,
we have shown in an exact calculation that for a lattice model with a
Lorentzian distributed random chemical potential the quasiparticle density of
states at the Fermi level is nonzero. As the exact result holds only for the
special choice of the Lorentzian, we employ different methods to show that for
a large class of distributions, including the Gaussian distribution, one can
establish a nonzero lower bound for the Fermi level density of states. The fact
that the tails of the distributions are unimportant in deriving the lower bound
shows that the exact result obtained before is generic.Comment: 15 preprint pages, no figures, submitted to PR
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