KH15D: a star eclipsed by a large scale dusty vortex?

We propose that the large photometric variations of KH15D are due to an eclipsing swarm of solid particles trapped in giant gaseous vortex rotating at \~0.2 AU from the star. The efficiency of the capture-in-vortex mechanism easily explains the observed large optical depth. The weaker opacity at mid-eclipse is consistent with a size segregation of the particles toward the center of the vortex. This dusty structure must extend over ~1/3 of an orbit to account for the long eclipse duration. The estimated size of the trapped particles is found to range from 1 to 10cm, consistent with the gray extinction of the star. The observations of KH15D support the idea that giant vortices can grow in circumstellar disks and play a central role in planet formation.Comment: Accepted in ApJ Letters - 4 pages - 2 figure

Baroclinic Vorticity Production in Protoplanetary Disks; Part I: Vortex Formation

The formation of vortices in protoplanetary disks is explored via pseudo-spectral numerical simulations of an anelastic-gas model. This model is a coupled set of equations for vorticity and temperature in two dimensions which includes baroclinic vorticity production and radiative cooling. Vortex formation is unambiguously shown to be caused by baroclinicity because (1) these simulations have zero initial perturbation vorticity and a nonzero initial temperature distribution; and (2) turning off the baroclinic term halts vortex formation, as shown by an immediate drop in kinetic energy and vorticity. Vortex strength increases with: larger background temperature gradients; warmer background temperatures; larger initial temperature perturbations; higher Reynolds number; and higher resolution. In the simulations presented here vortices form when the background temperatures are $\sim 200K$ and vary radially as $r^{-0.25}$, the initial vorticity perturbations are zero, the initial temperature perturbations are 5% of the background, and the Reynolds number is $10^9$. A sensitivity study consisting of 74 simulations showed that as resolution and Reynolds number increase, vortices can form with smaller initial temperature perturbations, lower background temperatures, and smaller background temperature gradients. For the parameter ranges of these simulations, the disk is shown to be convectively stable by the Solberg-H{\o}iland criteria.Comment: Originally submitted to The Astrophysical Journal April 3, 2006; resubmitted November 3, 2006; accepted Dec 5, 200

A toral diffeomorphism with a non-polygonal rotation set

We construct a diffeomorphism of the two-dimensional torus which is isotopic to the identity and whose rotation set is not a polygon

The Ingram Conjecture

We prove the Ingram Conjecture, i.e., we show that the inverse limit spaces of ev- ery two tent maps with di®erent slopes in the interval [1; 2] are non-homeomorphic. Based on the structure obtained from the proof, we also show that every self- homeomorphism of the inverse limit space of the tent map is pseudo-isotopic, on the core, to some power of the shift homeomorphism

A Conley index study of the evolution of the Lorenz strange set

In this paper we study the Lorenz equations using the perspective of the Conley index theory. More specifically, we examine the evolution of the strange set that these equations posses throughout the different values of the parameter. We also analyze some natural Morse decompositions of the global attractor of the system and the role of the strange set in these decompositions. We calculate the corresponding Morse equations and study their change along the successive bifurcations. In addition, we formulate and prove some theorems which are applicable in more general situations. These theorems refer to Poincar\'{e}-Andronov-Hopf bifurcations of arbitrary codimension, bifurcations with two homoclinic loops and a study of the role of the travelling repellers in the transformation of repeller-attractor pairs into attractor-repeller ones.Comment: 22 pages, 1 figur

Shape index, Brouwer degree and Poincaré-Hopf theorem

In this paper we study the relationship of the Brouwer degree of a vector field with the dynamics of the induced flow. Analogous relations are studied for the index of a vector field. We obtain new forms of the Poincaré-Hopf theorem and of the Borsuk and Hirsch antipodal theorems. As an application, we calculate the Brouwer degree of the vector field of the Lorenz equations in isolating blocks of the Lorenz strange set.Depto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasFALSEMinisterio de Ciencia, Innovación y Universidadesunpu