16,770 research outputs found
Remark on "When Are All the Zeros of a Polynomial Real and Distinct?"
The purpose of this note is to point out that the main result of [M.
Chamberland, When Are All the Zeros of a Polynomial Real and Distinct? Amer.
Math. Monthly. 127 (2020) 449-451] is implicitly contained in the elementary
lore of the theory of orthogonal polynomials on the real line.Comment: This short piece will not be published anywhere els
Coral symbiodinium community composition across the Belize Mesoamerican barrier reef system is influenced by host species and thermal variability
Accepted manuscrip
Finite Larmor radius effects on non-diffusive tracer transport in a zonal flow
Finite Larmor radius (FLR) effects on non-diffusive transport in a
prototypical zonal flow with drift waves are studied in the context of a
simplified chaotic transport model. The model consists of a superposition of
drift waves of the linearized Hasegawa-Mima equation and a zonal shear flow
perpendicular to the density gradient. High frequency FLR effects are
incorporated by gyroaveraging the ExB velocity. Transport in the direction of
the density gradient is negligible and we therefore focus on transport parallel
to the zonal flows. A prescribed asymmetry produces strongly asymmetric non-
Gaussian PDFs of particle displacements, with L\'evy flights in one direction
but not the other. For zero Larmor radius, a transition is observed in the
scaling of the second moment of particle displacements. However, FLR effects
seem to eliminate this transition. The PDFs of trapping and flight events show
clear evidence of algebraic scaling with decay exponents depending on the value
of the Larmor radii. The shape and spatio-temporal self-similar anomalous
scaling of the PDFs of particle displacements are reproduced accurately with a
neutral, asymmetric effective fractional diffusion model.Comment: 14 pages, 13 figures, submitted to Physics of Plasma
On a new fixed point of the renormalization group operator for area-preserving maps
The breakup of the shearless invariant torus with winding number
is studied numerically using Greene's residue criterion in
the standard nontwist map. The residue behavior and parameter scaling at the
breakup suggests the existence of a new fixed point of the renormalization
group operator (RGO) for area-preserving maps. The unstable eigenvalues of the
RGO at this fixed point and the critical scaling exponents of the torus at
breakup are computed.Comment: 4 pages, 5 figure
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