3,767 research outputs found
The large sieve and random walks on left cosets of arithmetic groups
Applying E. Kowalski's recent generalization of the large sieve we prove that
certain properties expected to be typical (irreducibility of the characteristic
polynomial, absence of squares among the matrix coefficients...) are indeed
verified by most (in a very explicit sense) of the elements of GL(n,A) with
fixed determinant (where A is an intermediate ring between Z and Q that we
specify) or by (special) orthogonal matrices with integral entries and fixed
spinor norm.Comment: 39 page
The lollipop graph is determined by its spectrum
An even (resp. odd) lollipop is the coalescence of a cycle of even (resp.
odd) length and a path with pendant vertex as distinguished vertex. It is known
that the odd lollipop is determined by its spectrum and the question is asked
by W. Haemers, X. Liu and Y. Zhang for the even lollipop. We revisit the proof
for odd lollipop, generalize it for even lollipop and therefore answer the
question. Our proof is essentially based on a method of counting closed walks
Effects of turbulent pumping on stellar activity cycles
Stellar magnetic activity of solar like stars is thought to be due to an
internal dynamo. While the Sun has been the subject of intense research for
refining dynamo models, observations of magnetic cyclic activity in solar type
stars have become more and more available, opening a new path to understand the
underlying physics behind stellar cycles. For instance, it is key to understand
how stellar rotation rate influences magnetic cycle period \Pcyc. Recent
numerical simulations of advection-dominated Babcock Leighton models have
demonstrated that it is difficult to explain this observed trend given a) the
strong influence of the cycle period to the meridional circulation amplitude
and b) the fact that 3D models indicate that meridional flows become weaker as
the rotation rate increases. In this paper, we introduce the turbulent pumping
mechanism as another advective process capable also of transporting the
magnetic fields. We found that this model is now able to reproduce the
observations under the assumption that this effect increases as . The
turbulent pumping becomes indeed another major player able to circumvent the
meridional circulation. However, for high rotation rates (), its effects dominate those of the meridional circulation,
entering a new class of regime dominated by the advection of turbulent pumping
and thus leading to a cyclic activity qualitatively different from that of the
sun.Comment: Published in Astronomische Nachrichten; 11 pages, 8 figure
Global Dynamics of Subsurface Solar Active Regions
We present three-dimensional numerical simulations of a magnetic loop
evolving in either a convectively stable or unstable rotating shell. The
magnetic loop is introduced in the shell in such a way that it is buoyant only
in a certain portion in longitude, thus creating an \Omega-loop. Due to the
action of magnetic buoyancy, the loop rises and develops asymmetries between
its leading and following legs, creating emerging bipolar regions whose
characteristics are similar to the ones of observed spots at the solar surface.
In particular, we self-consistently reproduce the creation of tongues around
the spot polarities, which can be strongly affected by convection. We moreover
emphasize the presence of ring-shaped magnetic structures around our simulated
emerging regions, which we call "magnetic necklace" and which were seen in a
number of observations without being reported as of today. We show that those
necklaces are markers of vorticity generation at the periphery and below the
rising magnetic loop. We also find that the asymmetry between the two legs of
the loop is crucially dependent on the initial magnetic field strength. The
tilt angle of the emerging regions is also studied in the stable and unstable
cases and seems to be affected both by the convective motions and the presence
of a differential rotation in the convective cases.Comment: 23 pages (ApJ 2-column format), 19 figures, accepted for publication
in Ap
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