The CMV bispectral problem

A classical result due to Bochner classifies the orthogonal polynomials on the real line which are common eigenfunctions of a second order linear differential operator. We settle a natural version of the Bochner problem on the unit circle which answers a similar question concerning orthogonal Laurent polynomials and can be formulated as a bispectral problem involving CMV matrices. We solve this CMV bispectral problem in great generality proving that, except the Lebesgue measure, no other one on the unit circle yields a sequence of orthogonal Laurent polynomials which are eigenfunctions of a linear differential operator of arbitrary order. Actually, we prove that this is the case even if such an eigenfunction condition is imposed up to finitely many orthogonal Laurent polynomials.Comment: 25 pages, final version, to appear in International Mathematics Research Notice

New perspectives on the supernova remnant Puppis A based on a radio polarization study

We present a polarization study towards the supernova remnant (SNR) Puppis A based on original observations performed with the Australia Telescope Compact Array. Based on the analysis of a feature detected outside the SNR shell (called 'the tail' throughout the paper), it was possible to disentangle the emission with origin in Puppis A itself from that coming from the foreground Vela SNR. We found a very low polarization fraction, of about 3 per cent on average. The upper limit of the magnetic field component parallel to the line of sight is estimated to be B ~ 20 μG. The statistical behaviour of the magnetic vectors shows two preferential directions, almost perpendicular to each other, which are approximately aligned with the flat edges of Puppis A. A third, narrow peak oriented perpendicular to the Galactic plane suggests the existence of an interstellar magnetic field locally aligned in this direction. There is evidence that the magnetic vectors along the shell are aligned with the shock front direction. The low polarization fraction and the statistical behaviour of the magnetic vectors are compatible with a scenario where the SNR evolves inside a stellar wind bubble with a box-like morphology, produced by the interaction of the different stellar winds, one of them magnetized, launched by the SN progenitor. This scenario can furthermore explain the morphology of Puppis A, rendering little support to the previously accepted picture which involved strong density gradients to explain the flat, eastern edge of the shell.Fil: Reynoso, Estela Marta. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; ArgentinaFil: Velázquez, P. F.. Universidad Nacional Autónoma de México. Instituto de Ciencias Nucleares; MéxicoFil: Cichowolski, Silvina. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentin

A non-linear degenerate equation for direct aggregation and traveling wave dynamics

The gregarious behavior of individuals of populations is an important factor in avoiding predators or for reproduction. Here, by using a random biased walk approach, we build a model which, after a transformation, takes the general form [u_{t}=[D(u)u_{x}]_{x}+g(u)] . The model involves a density-dependent non-linear diffusion coefficient [D] whose sign changes as the population density [u] increases. For negative values of [D] aggregation occurs, while dispersion occurs for positive values of [D] . We deal with a family of degenerate negative diffusion equations with logistic-like growth rate [g] . We study the one-dimensional traveling wave dynamics for these equations and illustrate our results with a couple of examples. A discussion of the ill-posedness of the partial differential equation problem is included

An MHD study of SN 1006 and determination of the ambient magnetic field direction

In this work we employ an MHD numerical code to reproduce the morphology observed for SN 1006 in radio synchrotron and thermal X-ray emission. We introduce a density discontinuity, in the form of a flat cloud parallel to the Galactic Plane, in order to explain the NW filament observed in optical wavelengths and in thermal X-rays. We compare our models with observations. We also perform a test that contrasts the radio emitting bright limbs of the SNR against the central region, finding additional support to our results. Our main conclusion is that the most probable direction of the ambient magnetic field is on average perpendicular to the Galactic Plane.Comment: 7 pages, 5 figures, accepted by MNRA

3D MHD simulation of polarized emission in SN 1006

We use three dimensional magnetohydrodynamic (MHD) simulations to model the supernova remnant SN 1006. From our numerical results, we have carried out a polarization study, obtaining synthetic maps of the polarized intensity, the Stokes parameter $Q$, and the polar-referenced angle, which can be compared with observational results. Synthetic maps were computed considering two possible particle acceleration mechanisms: quasi-parallel and quasi-perpendicular. The comparison of synthetic maps of the Stokes parameter $Q$ maps with observations proves to be a valuable tool to discern unambiguously which mechanism is taking place in the remnant of SN 1006, giving strong support to the quasi-parallel model.Comment: 6 pages, 4 figures, accepted by MNRA

Emission lines from rotating proto-stellar jets with variable velocity profiles. I. Three-dimensional numerical simulation of the non-magnetic case

Using the Yguazu-a three-dimensional hydrodynamic code, we have computed a set of numerical simulations of heavy, supersonic, radiatively cooling jets including variabilities in both the ejection direction (precession) and the jet velocity (intermittence). In order to investigate the effects of jet rotation on the shape of the line profiles, we also introduce an initial toroidal rotation velocity profile, in agreement with some recent observational evidence found in jets from T Tauri stars which seems to support the presence of a rotation velocity pattern inside the jet beam, near the jet production region. Since the Yguazu-a code includes an atomic/ionic network, we are able to compute the emission coefficients for several emission lines, and we generate line profiles for the H, [O I]6300, [S II]6716 and [N II]6548 lines. Using initial parameters that are suitable for the DG Tau microjet, we show that the computed radial velocity shift for the medium-velocity component of the line profile as a function of distance from the jet axis is strikingly similar for rotating and non-rotating jet models. These findings lead us to put forward some caveats on the interpretation of the observed radial velocity distribution from a few outflows from young stellar objects, and we claim that these data should not be directly used as a doubtless confirmation of the magnetocentrifugal wind acceleration models.Comment: 15 pages, 8 figures. Accepted to publication in Astronomy and Astrophysic

The topological classification of one-dimensional symmetric quantum walks

We give a topological classification of quantum walks on an infinite 1D lattice, which obey one of the discrete symmetry groups of the tenfold way, have a gap around some eigenvalues at symmetry protected points, and satisfy a mild locality condition. No translation invariance is assumed. The classification is parameterized by three indices, taking values in a group, which is either trivial, the group of integers, or the group of integers modulo 2, depending on the type of symmetry. The classification is complete in the sense that two walks have the same indices if and only if they can be connected by a norm continuous path along which all the mentioned properties remain valid. Of the three indices, two are related to the asymptotic behaviour far to the right and far to the left, respectively. These are also stable under compact perturbations. The third index is sensitive to those compact perturbations which cannot be contracted to a trivial one. The results apply to the Hamiltonian case as well. In this case all compact perturbations can be contracted, so the third index is not defined. Our classification extends the one known in the translation invariant case, where the asymptotic right and left indices add up to zero, and the third one vanishes, leaving effectively only one independent index. When two translationally invariant bulks with distinct indices are joined, the left and right asymptotic indices of the joined walk are thereby fixed, and there must be eigenvalues at $1$ or $-1$ (bulk-boundary correspondence). Their location is governed by the third index. We also discuss how the theory applies to finite lattices, with suitable homogeneity assumptions.Comment: 36 pages, 7 figure