2,212 research outputs found
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
and vary radially as , the initial vorticity
perturbations are zero, the initial temperature perturbations are 5% of the
background, and the Reynolds number is . 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 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 Poincar\'e-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 Poincar% \'{e}-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
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
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