343 research outputs found
Asymptotic geometry of negatively curved manifolds of finite volume
We study the asymptotic behaviour of simply connected, Riemannian manifolds
of strictly negative curvature admitting a non-uniform lattice . If
the quotient manifold is asymptotically
-pinched, we prove that is divergent and has finite
Bowen-Margulis measure (which is then ergodic and totally conservative with
respect to the geodesic flow); moreover, we show that, in this case, the volume
growth of balls in is asymptotically equivalent to a purely
exponential function , where is the topological
entropy of the geodesic flow of . \linebreak This generalizes Margulis'
celebrated theorem to negatively curved spaces of finite volume. In contrast,
we exhibit examples of lattices in negatively curved spaces (not
asymptotically -pinched) where, depending on the critical exponent of the
parabolic subgroups and on the finiteness of the Bowen-Margulis measure, the
growth function is exponential, lower-exponential or even upper-exponential.Comment: 25 p. This paper replaces arXiv:1503.03971, withdrawn by the authors
due to the Theorem 1.1 whose statement is far from the main subject of the
paper; for the sake of clearness, this new version concentrates only on the
question of volume growth (theorems 1.2, 1.3 and 1.4). Theorem 1.1 of
arXiv:1503.03971 is now the subject of another paper (Signed only by 2
authors Sambusetti and Peign\'e) focused on this rigidity problem with a much
better presentation of the context and another rigidity resul
Asymptotic geometry of negatively curved manifolds of finite volume
We study the asymptotic behavior of simply connected Riemannian manifolds X of strictly negative curvature admitting a non-uniform lattice Γ. If the quotient manifold X = Γ\X is asymptotically 1=4-pinched, we prove that Γ is divergent and U X has finite Bowen-Margulis measure (which is then ergodic and totally conservative with respect to the geodesic flow); moreover, we show that, in this case, the volume growth of balls B(x,R) in X is asymptotically equivalent to a purely exponential function c.x/eδR, where δ is the topological entropy of the geodesic flow of X . This generalizes Margulis' celebrated theorem to negatively curved spaces of finite volume. In contrast, we exhibit examples of lattices Γ in negatively curved spaces X (not asymptotically 1/4-pinched) where, depending on the critical exponent of the parabolic subgroups and on the finiteness of the Bowen- Margulis measure, the growth function is exponential, lower-exponential or even upper-exponential
Kick stability in groups and dynamical systems
We consider a general construction of ``kicked systems''. Let G be a group of
measure preserving transformations of a probability space. Given its
one-parameter/cyclic subgroup (the flow), and any sequence of elements (the
kicks) we define the kicked dynamics on the space by alternately flowing with
given period, then applying a kick. Our main finding is the following stability
phenomenon: the kicked system often inherits recurrence properties of the
original flow. We present three main examples. 1) G is the torus. We show that
for generic linear flows, and any sequence of kicks, the trajectories of the
kicked system are uniformly distributed for almost all periods. 2) G is a
discrete subgroup of PSL(2,R) acting on the unit tangent bundle of a Riemann
surface. The flow is generated by a single element of G, and we take any
bounded sequence of elements of G as our kicks. We prove that the kicked system
is mixing for all sufficiently large periods if and only if the generator is of
infinite order and is not conjugate to its inverse in G. 3) G is the group of
Hamiltonian diffeomorphisms of a closed symplectic manifold. We assume that the
flow is rapidly growing in the sense of Hofer's norm, and the kicks are
bounded. We prove that for a positive proportion of the periods the kicked
system inherits a kind of energy conservation law and is thus superrecurrent.
We use tools of geometric group theory and symplectic topology.Comment: Latex, 40 pages, revised versio
High precision microlensing maps of the Galactic bulge
We present detailed maps of the microlensing optical depth and event density
over an area of 195 sq. deg towards the Galactic bulge. The maps are computed
from synthetic stellar catalogues generated from the Besancon Galaxy Model,
which comprises four stellar populations and a three-dimensional extinction map
calibrated against the Two-Micron All-Sky Survey. The optical depth maps have a
resolution of 15 arcminutes, corresponding to the angular resolution of the
extinction map. We compute optical depth and event density maps for all
resolved sources above I=19, for unresolved (difference image) sources
magnified above this limit, and for bright standard candle sources in the
bulge. We show that the resulting optical depth contours are dominated by
extinction effects, exhibiting fine structure in stark contrast to previous
theoretical optical depth maps. Optical depth comparisons between Galactic
models and optical microlensing survey measurements cannot safely ignore
extinction or assume it to be smooth. We show how the event distribution for
hypothetical J and K-band microlensing surveys, using existing ground-based
facilities such as VISTA, UKIRT or CFHT, would be much less affected by
extinction, especially in the K band. The near infrared provides a substantial
sensitivity increase over current I-band surveys and a more faithful tracer of
the underlying stellar distribution, something which upcoming variability
surveys such as VVV will be able to exploit. Synthetic population models offer
a promising way forward to fully exploit large microlensing datasets for
Galactic structure studies.Comment: 8 pages, submitted to MNRA
The Milky Way's external disc constrained by 2MASS star counts
Context. Thanks to recent large scale surveys in the near infrared such as
2MASS, the galactic plane that most suffers from extinction is revealed and its
overall structure can be studied. Aims. This work aims at constraining the
structure of the Milky Way external disc as seen in 2MASS data, and in
particular the warp. Methods. We use the Two Micron All Sky Survey (hereafter
2MASS) along with the Stellar Population Synthesis Model of the Galaxy,
developed in Besancon, to constrain the external disc parameters such as its
scale length, its cutoff radius, and the slope of the warp. In order to
properly interpret the observations, the simulated stars are reddened using a
three dimensional extinction map. The shape of the stellar warp is then
compared with previous results and with similar structures in gas and dust.
Results. We find new constraints on the stellar disc, which is shown to be
asymmetrical, similar to observations of HI. The positive longitude side is
found to be easily modelled with a S shape warp but with a slope significantly
smaller than the slope seen in the HI warp. At negative longitudes, the disc
presents peculiarities which are not well reproduced by any simple model.
Finally, comparing with the warp seen in the dust, it seems to follow a slope
intermediate between the gas and the stars.Comment: 9 pages. Accepted for publication in Astronomy and Astrophysic
The EROS2 search for microlensing events towards the spiral arms: the complete seven season results
The EROS-2 project has been designed to search for microlensing events
towards any dense stellar field. The densest parts of the Galactic spiral arms
have been monitored to maximize the microlensing signal expected from the stars
of the Galactic disk and bulge. 12.9 million stars have been monitored during 7
seasons towards 4 directions in the Galactic plane, away from the Galactic
center. A total of 27 microlensing event candidates have been found. Estimates
of the optical depths from the 22 best events are provided. A first order
interpretation shows that simple Galactic models with a standard disk and an
elongated bulge are in agreement with our observations. We find that the
average microlensing optical depth towards the complete EROS-cataloged stars of
the spiral arms is , a number that is
stable when the selection criteria are moderately varied. As the EROS catalog
is almost complete up to , the optical depth estimated for the
sub-sample of bright target stars with () is easier to interpret. The set of microlensing events
that we have observed is consistent with a simple Galactic model. A more
precise interpretation would require either a better knowledge of the distance
distribution of the target stars, or a simulation based on a Galactic model.
For this purpose, we define and discuss the concept of optical depth for a
given catalog or for a limiting magnitude.Comment: 22 pages submitted to Astronomy & Astrophysic
Collision Dynamics and Solvation of Water Molecules in a Liquid Methanol Film
Environmental molecular beam experiments are used to examine water
interactions with liquid methanol films at temperatures from 170 K to 190 K. We
find that water molecules with 0.32 eV incident kinetic energy are efficiently
trapped by the liquid methanol. The scattering process is characterized by an
efficient loss of energy to surface modes with a minor component of the
incident beam that is inelastically scattered. Thermal desorption of water
molecules has a well characterized Arrhenius form with an activation energy of
0.47{\pm}0.11 eV and pre-exponential factor of 4.6 {\times} 10^(15{\pm}3)
s^(-1). We also observe a temperature dependent incorporation of incident water
into the methanol layer. The implication for fundamental studies and
environmental applications is that even an alcohol as simple as methanol can
exhibit complex and temperature dependent surfactant behavior.Comment: 8 pages, 5 figure
Tracing the long bar with red-clump giants
Over the last decade a series of results have lent support to the hypothesis
of the existence of a long thin bar in the Milky Way with a half-length of 4.5
kpc and a position angle of around 45 deg. This is apparently a very different
structure from the triaxial bulge of the Galaxy.
In this paper, we analyse the stellar distribution in the inner 4 kpc of the
Galaxy to see if there is clear evidence for two triaxial or barlike
structures, or whether there is only one. By using the red-clump population as
a tracer of the structure of the inner Galaxy we determine the apparent
morphology of the inner Galaxy. Star counts from 2MASS are used to provide
additional support for this analysis.
We show that there are two very different large-scale triaxial structures
coexisting in the inner Galaxy: a long thin stellar bar constrained to the
Galactic plane (|b|<2 deg) with a position angle of 43.1 +- 1.8 deg, and a
distinct triaxial bulge that extends to at least |b|<7.5 deg with a position
angle of 12.6 +- 3.2 deg. The scale height of the bar source distribution is
around 100 pc, whereas for the bulge the value of this parameter is five times
larger.Comment: 16 pages, 35 figures, accepted for publication in A&
PRIMA subretinal wireless photovoltaic microchip implantation in non-human primate and feline models
PURPOSE: To evaluate the surgical technique for subretinal implantation of two sizes of PRIMA photovoltaic wireless microchip in two animal models, and refine these surgical procedures for human trials. METHODS: Cats and Macaca fascicularis primates with healthy retina underwent vitrectomy surgery and were implanted with subretinal wireless photovoltaic microchip at the macula/central retina. The 1.5mm PRIMA chip was initially studied in feline eyes. PRIMA implant (2mm,1.5mm sizes) arrays were studied in primates. Feasibility of subretinal chip implantation was evaluated with a newly-developed surgical technique, with surgical complications and adverse events recorded. RESULTS: The 1.5mm implant was placed in the central retina of 11 feline eyes, with implantation duration 43-106 days. The 1.5mm implant was correctly positioned into central macula of 11 primate eyes, with follow-up periods of minimum 6 weeks (n = 11), 2 years (n = 2), and one eye for 3 years. One primate eye underwent multi-chip 1.5mm implantation using two 1.5mm chips. The 2mm implant was delivered to 4 primate eyes. Optical coherence tomography confirmed correct surgical placement of photovoltaic arrays in the subretinal space in all 26 eyes. Intraoperative complications in primate eyes included retinal tear, macular hole, retinal detachment, and vitreous hemorrhage that resolved spontaneously. Postoperatively, there was no case of significant ocular inflammation in the 1.5mm implant group. CONCLUSIONS: We report subretinal implantation of 1.5mm and 2mm photovoltaic arrays in the central retina of feline and central macula of primate eyes with a low rate of device-related complications. The in vivo PRIMA implantation technique has been developed and refined for use for a 2mm PRIMA implant in ongoing human trials
Microlensing as a probe of the Galactic structure; 20 years of microlensing optical depth studies
Microlensing is now a very popular observational astronomical technique. The
investigations accessible through this effect range from the dark matter
problem to the search for extra-solar planets. In this review, the techniques
to search for microlensing effects and to determine optical depths through the
monitoring of large samples of stars will be described. The consequences of the
published results on the knowledge of the Milky-Way structure and its dark
matter component will be discussed. The difficulties and limitations of the
ongoing programs and the perspectives of the microlensing optical depth
technique as a probe of the Galaxy structure will also be detailed.Comment: Accepted for publication in General Relativity and Gravitation.
General Relativity and Gravitation in press (2010) 0
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