45,806 research outputs found
A detector of small harmonic displacements based on two coupled microwave cavities
The design and test of a detector of small harmonic displacements is
presented. The detector is based on the principle of the parametric conversion
of power between the resonant modes of two superconducting coupled microwave
cavities. The work is based on the original ideas of Bernard, Pegoraro, Picasso
and Radicati, who, in 1978, suggested that superconducting coupled cavities
could be used as sensitive detectors of gravitational waves, and on the work of
Reece, Reiner and Melissinos, who, {in 1984}, built a detector of this kind.
They showed that an harmonic modulation of the cavity length l produced an
energy transfer between two modes of the cavity, provided that the frequency of
the modulation was equal to the frequency difference of the two modes. They
achieved a sensitivity to fractional deformations of dl/l~10^{-17} Hz^{-1/2}.
We repeated the Reece, Reiner and Melissinos experiment, and with an improved
experimental configuration and better cavity quality, increased the sensitivity
to dl/l~10^{-20} Hz^{-1/2}. In this paper the basic principles of the device
are discussed and the experimental technique is explained in detail. Possible
future developments, aiming at gravitational waves detection, are also
outlined.Comment: 28 pages, 12 eps figures, ReVteX. \tightenlines command added to
reduce number of pages. The following article has been accepted by Review of
Scientific Instruments. After it is published, it will be found at
http://link.aip.org/link/?rs
Lagrangian 3-torus fibrations
We prove that Mark Gross' topological Calabi-Yau compactifications can be made into symplectic compactifications. To prove this we develop a method to construct singular Lagrangian 3-torus fibrations over certain a priori given integral affine manifolds with singularities, which we call simple. This produces pairs of compact symplectic 6-manifolds homeomorphic to mirror pairs of Calabi-Yau 3-folds together with Lagrangian fibrations whose underlying integral affine structures are dual
Counting eigenvalues in domains of the complex field
A procedure for counting the number of eigenvalues of a matrix in a region
surrounded by a closed curve is presented. It is based on the application of
the residual theorem. The quadrature is performed by evaluating the principal
argument of the logarithm of a function. A strategy is proposed for selecting a
path length that insures that the same branch of the logarithm is followed
during the integration. Numerical tests are reported for matrices obtained from
conventional matrix test sets.Comment: 21 page
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