399 research outputs found
Spherical Tuples of Hilbert Space Operators
We introduce and study a class of operator tuples in complex Hilbert spaces,
which we call spherical tuples. In particular, we characterize spherical
multi-shifts, and more generally, multiplication tuples on RKHS. We further use
these characterizations to describe various spectral parts including the Taylor
spectrum. We also find a criterion for the Schatten -class membership of
cross-commutators of spherical -shifts. We show, in particular, that
cross-commutators of non-compact spherical -shifts cannot belong to
for .
We specialize our results to some well-studied classes of multi-shifts. We
prove that the cross-commutators of a spherical joint -shift, which is a
-isometry or a -expansion, belongs to if and only if . We
further give an example of a spherical jointly hyponormal -shift, for which
the cross-commutators are compact but not in for any .Comment: a version close to final on
Elliptic instability in the Lagrangian-averaged Euler-Boussinesq-alpha equations
We examine the effects of turbulence on elliptic instability of rotating
stratified incompressible flows, in the context of the Lagragian-averaged
Euler-Boussinesq-alpha, or \laeba, model of turbulence. We find that the \laeba
model alters the instability in a variety of ways for fixed Rossby number and
Brunt-V\"ais\"al\"a frequency. First, it alters the location of the instability
domains in the parameter plane, where is the
angle of incidence the Kelvin wave makes with the axis of rotation and
is the eccentricity of the elliptic flow, as well as the size of the associated
Lyapunov exponent. Second, the model shrinks the width of one instability band
while simultaneously increasing another. Third, the model introduces bands of
unstable eccentric flows when the Kelvin wave is two-dimensional. We introduce
two similarity variables--one is a ratio of the Brunt-V\"ais\"al\"a frequency
to the model parameter , and the other is the
ratio of the adjusted inverse Rossby number to the same model parameter. Here,
is the turbulence correlation length, and is the Kelvin wave
number. We show that by adjusting the Rossby number and Brunt-V\"ais\"al\"a
frequency so that the similarity variables remain constant for a given value of
, turbulence has little effect on elliptic instability for small
eccentricities . For moderate and large eccentricities,
however, we see drastic changes of the unstable Arnold tongues due to the
\laeba model.Comment: 23 pages (sigle spaced w/figure at the end), 9 figures--coarse
quality, accepted by Phys. Fluid
Grating-coupled excitation of multiple surface plasmon-polariton waves
The excitation of multiple surface-plasmon-polariton (SPP) waves of different
linear polarization states and phase speeds by a surface-relief grating formed
by a metal and a rugate filter, both of finite thickness, was studied
theoretically, using rigorous coupled-wave-analysis. The incident plane wave
can be either p or s polarized. The excitation of SPP waves is indicated by the
presence of those peaks in the plots of absorbance vs. the incidence angle that
are independent of the thickness of the rugate filter. The absorbance peaks
representing the excitation of s-polarized SPP waves are narrower than those
representing p-polarized SPP waves. Two incident plane waves propagating in
different directions may excite the same SPP wave. A line source could excite
several SPP waves simultaneously
Multi-site breathers in Klein-Gordon lattices: stability, resonances, and bifurcations
We prove the most general theorem about spectral stability of multi-site
breathers in the discrete Klein-Gordon equation with a small coupling constant.
In the anti-continuum limit, multi-site breathers represent excited
oscillations at different sites of the lattice separated by a number of "holes"
(sites at rest). The theorem describes how the stability or instability of a
multi-site breather depends on the phase difference and distance between the
excited oscillators. Previously, only multi-site breathers with adjacent
excited sites were considered within the first-order perturbation theory. We
show that the stability of multi-site breathers with one-site holes change for
large-amplitude oscillations in soft nonlinear potentials. We also discover and
study a symmetry-breaking (pitchfork) bifurcation of one-site and multi-site
breathers in soft quartic potentials near the points of 1:3 resonance.Comment: 34 pages, 12 figure
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