5,541 research outputs found
Quasi-geostrophic kinematic dynamos at low magnetic Prandtl number
Rapidly rotating spherical kinematic dynamos are computed using the
combination of a quasi geostrophic (QG) model for the velocity field and a
classical spectral 3D code for the magnetic field. On one hand, the QG flow is
computed in the equatorial plane of a sphere and corresponds to Rossby wave
instabilities of a geostrophic internal shear layer produced by differential
rotation. On the other hand, the induction equation is computed in the full
sphere after a continuation of the QG flow along the rotation axis.
Differential rotation and Rossby-wave propagation are the key ingredients of
the dynamo process which can be interpreted in terms of dynamo.
Taking into account the quasi geostrophy of the velocity field to increase its
time and space resolution enables us to exhibit numerical dynamos with very low
Ekman (rapidly rotating) and Prandtl numbers (liquid metals) which are
asymptotically relevant to model planetary core dynamos
Spectra of large diluted but bushy random graphs
We compute an asymptotic expansion in of the limit in of the
empirical spectral measure of the adjacency matrix of an Erd\H{o}s-R\'enyi
random graph with vertices and parameter . We present two different
methods, one of which is valid for the more general setting of locally
tree-like graphs. The second order in the expansion gives some information
about the edge.Comment: 24 pages, 5 figure
An integral test for the transience of a Brownian path with limited local time
We study a one-dimensional Brownian motion conditioned on a self-repelling
behaviour. Given a nondecreasing positive function f(t), consider the measures
mu_t obtained by conditioning a Brownian path so that L_s< f(s), for all s<t,
where L_s is the local time spent at the origin by time s. It is shown that the
measures mu_t are tight, and that any weak limit of mu_t as t tends to infinity
is transient provided that t^{-3/2}f(t) is integrable. We conjecture that this
condition is sharp and present a number of open problems.Comment: 3 figures. Some typos corrected
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