9,561 research outputs found
Asymptotic dimension and uniform embeddings
We show that the type function of a space with finite asymptotic dimension
estimates its Hilbert (or any ) compression. The method allows to obtain
the lower bound of the compression of the lamplighter group , which has
infinite asymptotic dimension.Comment: 17 pages, no figure
Euler characteristic of the configuration space of a complex
A closed form formula (generating function) for the Euler characteristic of
the configuration space of particles in a simplicial complex
is given.Comment: 6 pages, no figure
The Universal Aspect Ratio of Vortices in Rotating Stratified Flows: Theory and Simulation
We derive a relationship for the vortex aspect ratio (vertical
half-thickness over horizontal length scale) for steady and slowly evolving
vortices in rotating stratified fluids, as a function of the Brunt-Vaisala
frequencies within the vortex and in the background fluid outside the
vortex , the Coriolis parameter , and the Rossby number of the
vortex: . This relation is valid for
cyclones and anticyclones in either the cyclostrophic or geostrophic regimes;
it works with vortices in Boussinesq fluids or ideal gases, and the background
density gradient need not be uniform. Our relation for has many
consequences for equilibrium vortices in rotating stratified flows. For
example, cyclones must have ; weak anticyclones (with . We verify our relation for with numerical simulations of
the three-dimensional Boussinesq equations for a wide variety of vortices,
including: vortices that are initially in (dissipationless) equilibrium and
then evolve due to an imposed weak viscous dissipation or density radiation;
anticyclones created by the geostrophic adjustment of a patch of locally mixed
density; cyclones created by fluid suction from a small localised region;
vortices created from the remnants of the violent breakups of columnar
vortices; and weakly non-axisymmetric vortices. The values of the aspect ratios
of our numerically-computed vortices validate our relationship for ,
and generally they differ significantly from the values obtained from the
much-cited conjecture that in quasi-geostrophic vortices.Comment: Submitted to the Journal of Fluid Mechanics. Also see the companion
paper by Aubert et al. "The Universal Aspect Ratio of Vortices in Rotating
Stratified Flows: Experiments and Observations" 201
Photometric validation of a model independent procedure to extract galaxy clusters
By means of CCD photometry in three bands (Gunn g, r, i) we investigate the
existence of 12 candidate clusters extracted via a model independent peak
finding algorithm (\cite{memsait}) from DPOSS data. The derived color-magnitude
diagrams allow us to confirm the physical nature of 9 of the cluster
candidates, and to estimate their photometric redshifts. Of the other
candidates, one is a fortuitous detection of a true cluster at z~0.4, one is a
false detection and the last is undecidable on the basis of the available data.
The accuracy of the photometric redshifts is tested on an additional sample of
8 clusters with known spectroscopic redshifts. Photometric redshifts turn out
to be accurate within z~0.01 (interquartile range).Comment: A&A in pres
The Universal Aspect Ratio of Vortices in Rotating Stratifi?ed Flows: Experiments and Observations
We validate a new law for the aspect ratio of vortices in a
rotating, stratified flow, where and are the vertical half-height and
horizontal length scale of the vortices. The aspect ratio depends not only on
the Coriolis parameter f and buoyancy (or Brunt-Vaisala) frequency of
the background flow, but also on the buoyancy frequency within the vortex
and on the Rossby number of the vortex such that . This law for is obeyed precisely by the
exact equilibrium solution of the inviscid Boussinesq equations that we show to
be a useful model of our laboratory vortices. The law is valid for both
cyclones and anticyclones. Our anticyclones are generated by injecting fluid
into a rotating tank filled with linearly-stratified salt water. The vortices
are far from the top and bottom boundaries of the tank, so there is no Ekman
circulation. In one set of experiments, the vortices viscously decay, but as
they do, they continue to obey our law for , which decreases over time.
In a second set of experiments, the vortices are sustained by a slow continuous
injection after they form, so they evolve more slowly and have larger |Ro|, but
they also obey our law for . The law for is not only validated
by our experiments, but is also shown to be consistent with observations of the
aspect ratios of Atlantic meddies and Jupiter's Great Red Spot and Oval BA. The
relationship for is derived and examined numerically in a companion
paper by Hassanzadeh et al. (2012).Comment: Submitted to the Journal of Fluid Mechanics. Also see the companion
paper by Hassanzadeh et al. "The Universal Aspect Ratio of Vortices in
Rotating Stratifi?ed Flows: Theory and Simulation" 201
- …