22 research outputs found
Row-switched states in two-dimensional underdamped Josephson junction arrays
When magnetic flux moves across layered or granular superconductor
structures, the passage of vortices can take place along channels which develop
finite voltage, while the rest of the material remains in the zero-voltage
state. We present analytical studies of an example of such mixed dynamics: the
row-switched (RS) states in underdamped two-dimensional Josephson arrays,
driven by a uniform DC current under external magnetic field but neglecting
self-fields. The governing equations are cast into a compact
differential-algebraic system which describes the dynamics of an assembly of
Josephson oscillators coupled through the mesh current. We carry out a formal
perturbation expansion, and obtain the DC and AC spatial distributions of the
junction phases and induced circulating currents. We also estimate the interval
of the driving current in which a given RS state is stable. All these
analytical predictions compare well with our numerics. We then combine these
results to deduce the parameter region (in the damping coefficient versus
magnetic field plane) where RS states can exist.Comment: latex, 48 pages, 15 figs using psfi
Anosov representations: Domains of discontinuity and applications
The notion of Anosov representations has been introduced by Labourie in his
study of the Hitchin component for SL(n,R). Subsequently, Anosov
representations have been studied mainly for surface groups, in particular in
the context of higher Teichmueller spaces, and for lattices in SO(1,n). In this
article we extend the notion of Anosov representations to representations of
arbitrary word hyperbolic groups and start the systematic study of their
geometric properties. In particular, given an Anosov representation of
into G we explicitly construct open subsets of compact G-spaces, on which
acts properly discontinuously and with compact quotient.
As a consequence we show that higher Teichmueller spaces parametrize locally
homogeneous geometric structures on compact manifolds. We also obtain
applications regarding (non-standard) compact Clifford-Klein forms and
compactifications of locally symmetric spaces of infinite volume.Comment: 63 pages, accepted for publication in Inventiones Mathematica