13,658 research outputs found
Multiscale expansion and integrability properties of the lattice potential KdV equation
We apply the discrete multiscale expansion to the Lax pair and to the first
few symmetries of the lattice potential Korteweg-de Vries equation. From these
calculations we show that, like the lowest order secularity conditions give a
nonlinear Schroedinger equation, the Lax pair gives at the same order the
Zakharov and Shabat spectral problem and the symmetries the hierarchy of point
and generalized symmetries of the nonlinear Schroedinger equation.Comment: 10 pages, contribution to the proceedings of the NEEDS 2007
Conferenc
Expanding perfect fluid generalizations of the C-metric
We reexamine Petrov type D gravitational fields generated by a perfect fluid
with spatially homogeneous energy density and in which the flow lines form a
timelike non-shearing and non-rotating congruence. It is shown that the
anisotropic such spacetimes, which comprise the vacuum C-metric as a limit
case, can have \emph{non-zero} expansion, contrary to the conclusion in the
original investigation by Barnes (Gen. Rel. Grav. 4, 105 (1973)). This class
consists of cosmological models with generically one and at most two Killing
vectors. We construct their line element and discuss some important properties.
The methods used in this investigation incite to deduce testable criteria
regarding shearfree normality and staticity op Petrov type spacetimes in
general, which we add in an appendix.Comment: 16 pages, extended and amended versio
A very low temperature STM for the local spectroscopy of mesoscopic structures
We present the design and operation of a very-low temperature Scanning
Tunneling Microscope (STM) working at in a dilution refrigerator. The
STM features both atomic resolution and micron-sized scanning range at low
temperature. This work is the first experimental realization of a local
spectroscopy of mesoscopic structures at very low temperature. We present
high-resolution current-voltage characteristics of tunnel contacts and the
deduced local density of states of hybrid Superconductor-Normal metal systems.Comment: 5 pages, 5 figures, slightly corrected versio
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