26,256 research outputs found
On the reconstruction of planar lattice-convex sets from the covariogram
A finite subset of is said to be lattice-convex if is
the intersection of with a convex set. The covariogram of
is the function associating to each u \in
\integer^d the cardinality of . Daurat, G\'erard, and Nivat and
independently Gardner, Gronchi, and Zong raised the problem on the
reconstruction of lattice-convex sets from . We provide a partial
positive answer to this problem by showing that for and under mild extra
assumptions, determines up to translations and reflections. As a
complement to the theorem on reconstruction we also extend the known
counterexamples (i.e., planar lattice-convex sets which are not
reconstructible, up to translations and reflections) to an infinite family of
counterexamples.Comment: accepted in Discrete and Computational Geometr
Polar features in the flagellar propulsion of E. coli bacteria
E. coli bacteria swim following a run and tumble pattern. In the run state
all flagella join in a single helical bundle that propels the cell body along
approximately straight paths. When one or more flagellar motors reverse
direction the bundle unwinds and the cell randomizes its orientation. This
basic picture represents an idealization of a much more complex dynamical
problem. Although it has been shown that bundle formation can occur at either
pole of the cell, it is still unclear whether this two run states correspond to
asymmetric propulsion features. Using holographic microscopy we record the 3D
motions of individual bacteria swimming in optical traps. We find that most
cells possess two run states characterised by different propulsion forces,
total torque and bundle conformations. We analyse the statistical properties of
bundle reversal and compare the hydrodynamic features of forward and backward
running states. Our method is naturally multi-particle and opens up the way
towards controlled hydrodynamic studies of interacting swimming cells
Galaxy evolution in groups. USGC U268 and USGC U376 in the Leo cloud
With the aim of investigating galaxy evolution in nearby galaxy groups, we
analysed the spectral energy distribution of 24 galaxies, members of two groups
in the Leo cloud, USGC U268 and USGC U376. We estimated the ages and stellar
masses of the galaxies by fitting their total apparent magnitudes from
far-ultraviolet to near-infrared with population synthesis models. The
comparison of the results for a subsample of galaxies with smooth particle
hydrodynamic (SPH) simulations with chemo-photometric implementation, shows
that in most cases the estimated stellar masses obtained with the two different
approaches are in good agreement. The kinematical and dynamical analysis
indicates that USGC U268 is in a pre-virial collapse phase while USGC U376 is
likely in a more evolved phase towards virialization.Comment: 16 pages, 6 figures; accepted for publication in Advances in Space
Research, Special Issue: Ultraviolet Astrophysic
Massive higher spins and holography
We review recent progress towards the understanding of higher spin gauge
symmetry breaking in AdS space from a holographic vantage point. According to
the AdS/CFT correspondence, N=4 SYM theory at vanishing coupling constant
should be dual to a theory in AdS which exhibits higher spin gauge symmetry
enhancement. When the SYM coupling is non-zero, all but a handful of HS
currents are violated by anomalies, and correspondingly local higher spin
symmetry in the bulk gets spontaneously broken. In agreement with previous
results and holographic expectations, we find that, barring one notable
exception (spin 1 eating spin 0), the Goldstone modes responsible for HS
symmetry breaking in AdS have non-vanishing mass even in the limit in which the
gauge symmetry is restored. We show that spontaneous breaking a' la
Stueckelberg implies that the mass of the relevant spin s'=s-1 Goldstone field
is exactly the one predicted by the correspondence.Comment: 8 pages, talk presented by M.B. at the "Fourth Meeting on Constrained
Dynamics and Quantum gravity" held in Cala Gonone (Sardinia, Italy),
September 12-16, 200
Galaxy Evolution in Local Group Analogs. I. A GALEX study of nearby groups
Understanding the astrophysical processes acting within galaxy groups and
their effects on the evolution of the galaxy population is one of the crucial
topic of modern cosmology, as almost 60% of galaxies in the Local Universe are
found in groups. We imaged in the far (FUV 1539 A) and near ultraviolet (NUV
2316 A) with GALEX three nearby groups, namely LGG93, LGG127 and LGG225. We
obtained the UV galaxy surface photometry and, for LGG225, the only group
covered by the SDSS, the photometry in u, g, r, i, z bands. We discuss galaxy
morphologies looking for interaction signatures and we analyze the SED of
galaxies to infer their luminosity-weighted ages. The UV and optical photometry
was also used to perform a kinematical and dynamical analysis of each group and
to evaluate the stellar mass. A few member galaxies in LGG225 show a distorted
UV morphology due to ongoing interactions. (FUV-NUV) colors suggest that
spirals in LGG93 and LGG225 host stellar populations in their outskirts younger
than that of M31 and M33 in the LG or with less extinction. The irregular
interacting galaxy NGC3447A has a significantly younger stellar population (few
Myr old) than the average of the other irregular galaxies in LGG225 suggesting
that the encounter triggered star formation. The early-type members of LGG225,
NGC3457 and NGC3522, have masses of the order of a few 10^9 Mo, comparable to
the Local Group ellipticals. For the most massive spiral in LGG225, we estimate
a stellar mass of ~4x10 Mo, comparable to M33 in the LG. Ages of stellar
populations range from a few to ~7 Gyr for the galaxies in LGG225. The
kinematical and dynamical analysis indicates that LGG127 and LGG225 are in a
pre-virial collapse phase, i.e. still undergoing dynamical relaxation, while
LGG93 is likely virialized. (Abridged)Comment: 20 pages, 13 figures, accepted for publication in Astronomy and
Astrophysic
Variable sequence of events during the past seven terminations in two deep-sea cores from the Southern Ocean
The relationships among internally consistent records of summer sea-surface temperature (SSST), winter sea
ice (WSI), and diatomaceous stable isotopes were studied across seven terminations over the last 660 ka in
sedimentary cores from ODP sites 1093 and 1094. The sequence of events at both sites indicates that SSST
and WSI changes led the carbon and nitrogen isotopic changes in three Terminations (TI, TII and TVI) and followed
them in the other four Terminations (TIII, TIV, TV and TVII). In both TIII and TIV, the leads and lags between
the proxies were related to weak glacial mode, while in TV and TVII they were due to the influence of
the mid-Pleistocene transition. We show that the sequence of events is not unique and does not follow the
same pattern across terminations, implying that the processes that initiated climate change in the Southern
Ocean has varied through time
The metal and dust yields of the first massive stars
We quantify the role of Population (Pop) III core-collapse supernovae (SNe)
as the first cosmic dust polluters. Starting from a homogeneous set of stellar
progenitors with masses in the range [13 - 80] Msun, we find that the mass and
composition of newly formed dust depend on the mixing efficiency of the ejecta
and the degree of fallback experienced during the explosion. For standard Pop
III SNe, whose explosions are calibrated to reproduce the average elemental
abundances of Galactic halo stars with [Fe/H] < -2.5, between 0.18 and 3.1 Msun
(0.39 - 1.76 Msun) of dust can form in uniformly mixed (unmixed) ejecta, and
the dominant grain species are silicates. We also investigate dust formation in
the ejecta of faint Pop III SN, where the ejecta experience a strong fallback.
By examining a set of models, tailored to minimize the scatter with the
abundances of carbon-enhanced Galactic halo stars with [Fe/H ] < -4, we find
that amorphous carbon is the only grain species that forms, with masses in the
range 2.7 10^{-3} - 0.27 Msun (7.5 10^{-4} - 0.11 Msun) for uniformly mixed
(unmixed) ejecta models. Finally, for all the models we estimate the amount and
composition of dust that survives the passage of the reverse shock, and find
that, depending on circumstellar medium densities, between 3 and 50% (10 - 80%)
of dust produced by standard (faint) Pop III SNe can contribute to early dust
enrichment.Comment: Accepted by MNRAS, 22 pages, 12 figures, 12 table
Hierarchy of general invariants for bivariate LPDOs
We study invariants under gauge transformations of linear partial
differential operators on two variables. Using results of BK-factorization, we
construct hierarchy of general invariants for operators of an arbitrary order.
Properties of general invariants are studied and some examples are presented.
We also show that classical Laplace invariants correspond to some particular
cases of general invariants.Comment: to appear in J. "Theor.Math.Phys." in May 200
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