3,569 research outputs found
Fuzzy Fluid Mechanics in Three Dimensions
We introduce a rotation invariant short distance cut-off in the theory of an
ideal fluid in three space dimensions, by requiring momenta to take values in a
sphere. This leads to an algebra of functions in position space is
non-commutative. Nevertheless it is possible to find appropriate analogues of
the Euler equations of an ideal fluid. The system still has a hamiltonian
structure. It is hoped that this will be useful in the study of possible
singularities in the evolution of Euler (or Navier-Stokes) equations in three
dimensions.Comment: Additional reference
Doppler images and the underlying dynamo. The case of AF Leporis
The (Zeeman-)Doppler imaging studies of solar-type stars very often reveal
large high-latitude spots. This also includes F stars that possess relatively
shallow convection zones, indicating that the dynamo operating in these stars
differs from the solar dynamo. We aim to determine whether mean-field dynamo
models of late-F type dwarf stars can reproduce the surface features recovered
in Doppler maps. In particular, we wish to test whether the models can
reproduce the high-latitude spots observed on some F dwarfs. The photometric
inversions and the surface temperature maps of AF Lep were obtained using the
Occamian-approach inversion technique. Low signal-to-noise spectroscopic data
were improved by applying the least-squares deconvolution method. The locations
of strong magnetic flux in the stellar tachocline as well as the surface fields
obtained from mean-field dynamo solutions were compared with the observed
surface temperature maps. The photometric record of AF Lep reveals both long-
and short-term variability. However, the current data set is too short for
cycle-length estimates. From the photometry, we have determined the rotation
period of the star to be 0.9660+-0.0023 days. The surface temperature maps show
a dominant, but evolving, high-latitude (around +65 degrees) spot. Detailed
study of the photometry reveals that sometimes the spot coverage varies only
marginally over a long time, and at other times it varies rapidly. Of a suite
of dynamo models, the model with a radiative interior rotating as fast as the
convection zone at the equator delivered the highest compatibility with the
obtained Doppler images.Comment: accepted for publication in Astronomy & Astrophysic
The relation between stellar magnetic field geometry and chromospheric activity cycles - I. The highly variable field of ɛ Eridani at activity minimum
The young and magnetically active K dwarf Epsilon Eridani exhibits a chromospheric activity cycle of about 3 years. Previous reconstructions of its large-scale magnetic field show strong variations at yearly epochs. To understand how Epsilon Eridani's large-scale magnetic field geometry evolves over its activity cycle we focus on high cadence observations spanning 5 months at its activity minimum. Over this timespan we reconstruct 3 maps of Epsilon Eridani's large-scale magnetic field using the tomographic technique of Zeeman Doppler Imaging. The results show that at the minimum of its cycle, Epsilon Eridani's large-scale field is more complex than the simple dipolar structure of the Sun and 61 Cyg A at minimum. Additionally we observe a surprisingly rapid regeneration of a strong axisymmetric toroidal field as Epsilon Eridani emerges from its S-index activity minimum. Our results show that all stars do not exhibit the same field geometry as the Sun and this will be an important constraint for the dynamo models of active solar-type stars
The Dynamics of a Rigid Body in Potential Flow with Circulation
We consider the motion of a two-dimensional body of arbitrary shape in a
planar irrotational, incompressible fluid with a given amount of circulation
around the body. We derive the equations of motion for this system by
performing symplectic reduction with respect to the group of volume-preserving
diffeomorphisms and obtain the relevant Poisson structures after a further
Poisson reduction with respect to the group of translations and rotations. In
this way, we recover the equations of motion given for this system by Chaplygin
and Lamb, and we give a geometric interpretation for the Kutta-Zhukowski force
as a curvature-related effect. In addition, we show that the motion of a rigid
body with circulation can be understood as a geodesic flow on a central
extension of the special Euclidian group SE(2), and we relate the cocycle in
the description of this central extension to a certain curvature tensor.Comment: 28 pages, 2 figures; v2: typos correcte
Non-ergodicity of the motion in three dimensional steep repelling dispersing potentials
It is demonstrated numerically that smooth three degrees of freedom
Hamiltonian systems which are arbitrarily close to three dimensional strictly
dispersing billiards (Sinai billiards) have islands of effective stability, and
hence are non-ergodic. The mechanism for creating the islands are corners of
the billiard domain.Comment: 6 pages, 8 figures, submitted to Chao
Complete integrability versus symmetry
The purpose of this article is to show that on an open and dense set,
complete integrability implies the existence of symmetry
Discrete Nonholonomic LL Systems on Lie Groups
This paper applies the recently developed theory of discrete nonholonomic
mechanics to the study of discrete nonholonomic left-invariant dynamics on Lie
groups. The theory is illustrated with the discrete versions of two classical
nonholonomic systems, the Suslov top and the Chaplygin sleigh. The preservation
of the reduced energy by the discrete flow is observed and the discrete
momentum conservation is discussed.Comment: 32 pages, 13 figure
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