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 $\Omega^2$. The turbulent pumping becomes indeed another major player able to circumvent the meridional circulation. However, for high rotation rates ($\Omega \simeq 5 \Omega_\odot$), 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