523 research outputs found
Eigenvalues of even very nice Toeplitz matrices can be unexpectedly erratic
It was shown in a series of recent publications that the eigenvalues of
Toeplitz matrices generated by so-called simple-loop symbols admit
certain regular asymptotic expansions into negative powers of . On the
other hand, recently two of the authors considered the pentadiagonal Toeplitz
matrices generated by the symbol , which does not satisfy
the simple-loop conditions, and derived asymptotic expansions of a more
complicated form. We here use these results to show that the eigenvalues of the
pentadiagonal Toeplitz matrices do not admit the expected regular asymptotic
expansion. This also delivers a counter-example to a conjecture by Ekstr\"{o}m,
Garoni, and Serra-Capizzano and reveals that the simple-loop condition is
essential for the existence of the regular asymptotic expansion.Comment: 28 pages, 7 figure
Radiating instability of a meridional boundary current
Author Posting. Β© American Meteorological Society, 2008. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 38 (2008): 2294-2307, doi:10.1175/2008JPO3853.1.A linear stability analysis of a meridional boundary current on the beta plane is presented. The boundary current is idealized as a constant-speed meridional jet adjacent to a semi-infinite motionless far field. The far-field region can be situated either on the eastern or the western side of the jet, representing a western or an eastern boundary current, respectively. It is found that when unstable, the meridional boundary current generates temporally growing propagating waves that transport energy away from the locally unstable region toward the neutral far field. This is the so-called radiating instability and is found in both barotropic and two-layer baroclinic configurations. A second but important conclusion concerns the differences in the stability properties of eastern and western boundary currents. An eastern boundary current supports a greater number of radiating modes over a wider range of meridional wavenumbers. It generates waves with amplitude envelopes that decay slowly with distance from the current. The radiating waves tend to have an asymmetrical horizontal structureβthey are much longer in the zonal direction than in the meridional, a consequence of which is that unstable eastern boundary currents, unlike western boundary currents, have the potential to act as a source of zonal jets for the interior of the ocean.This work was supported by the
National Science Foundation through Grants OCE-
0423975 (MS, HH) and OCE-9901654 (JP). HH would
like to thank her thesis committee as well as the MITβ
WHOI Joint Program for partial financial support
Dynamic model of elastoplastic contact interaction of smooth bodies
Dynamic model of introducing rigid smooth sphere into homogeneous elastoplastic hardenable solid body has been considered. On the basis of the model numerical-analytical dependencies describing the behaviour of solid body in elastoplastic region of contact interaction were suggested. The numerical-analytical dependencies allow us to take into consideration additional approach of contacting bodies owing to dynamic loading
- β¦