5,181 research outputs found
Factorization of the current algebra and integrable top-like systems
A hierarchy of integrable hamiltonian nonlinear ODEs is associated with any
decomposition of the Lie algebra of Laurent series with coefficients being
elements of a semi-simple Lie algebra into a sum of the subalgebra consisting
of the Taylor series and some complementary subalgebra. In the case of the Lie
algebra our scheme covers all classical integrable cases in the
Kirchhoff problem of the motion of a rigid body in an ideal fluid. Moreover,
the construction allows us to generate integrable deformations for known
integrable models.Comment: 21 page
Solar-Terrestrial Simulations of CMEs with a Realistic Initiation Mechanism: Case Study for Active Region 10069
Most simulations of coronal mass ejections (CMEs) to date either focus on the
interplanetary propagation of a giant plasma "blob" without paying too much
attention to its origin and to the formation process or they focus on the
complex evolution of the coronal magnetic field due to (sub-)photospheric
motions which result in an eruption. Here, we present global simulations of
CMEs where coronal motions are used to produce a realistic evolution of the
coronal magnetic field and cause an eruption. We focus on active region 10069,
which produced a number of eruptions in late August 2002, including the August
24, 2002 CME - a fast (~2000 km/s) eruption originating from W81-, as well as a
slower eruption on August 22, 2002 (originating from W62). Using a
three-dimensional magneto-hydrodynamic (MHD) simulation of these ejections with
the Space Weather Modeling Framework (SWMF), we show how a realistic initiation
mechanism enables us to study the deflection of the CME in the corona and in
the heliosphere. Reconnection of the erupting magnetic field with that of
neighboring streamers and active regions modify the solar connectivity of the
field lines connecting to Earth and change the expected solar energetic
particle fluxes. Comparing the results at 1 AU of our simulations with in situ
observations by the ACE spacecraft, we propose an alternate solar origin for
the shock wave observed at L1 on August 26.Comment: 4 pages, 2 figures, refereed proceedings for Solar Wind 1
The Spectra of Large Toeplitz Band Matrices with a Randomly Perturbed Entry
This report is concerned with the union of all possible spectra that may emerge when perturbing a large Toeplitz band matrix in the site by a number randomly chosen from some set . The main results give descriptive bounds and, in several interesting situations, even provide complete identifications of the limit of as . Also discussed are the cases of small and large sets as well as the "discontinuity of the infinite volume case", which means that in general does not converge to something close to as , where is the corresponding infinite Toeplitz matrix. Illustrations are provided for tridiagonal Toeplitz matrices, a notable special case. \ud
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The second author was supported by UK Enginering and Physical Sciences Research Council Grant GR/M1241
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