3,292 research outputs found
A method for the reconstruction of unknown non-monotonic growth functions in the chemostat
We propose an adaptive control law that allows one to identify unstable
steady states of the open-loop system in the single-species chemostat model
without the knowledge of the growth function. We then show how one can use this
control law to trace out (reconstruct) the whole graph of the growth function.
The process of tracing out the graph can be performed either continuously or
step-wise. We present and compare both approaches. Even in the case of two
species in competition, which is not directly accessible with our approach due
to lack of controllability, feedback control improves identifiability of the
non-dominant growth rate.Comment: expansion of ideas from proceedings paper (17 pages, 8 figures),
proceedings paper is version v
Asteroid families classification: exploiting very large data sets
The number of asteroids with accurately determined orbits increases fast. The
catalogs of asteroid physical observations have also increased, although the
number of objects is still smaller than in the orbital catalogs. We developed a
new approach to the asteroid family classification by combining the
Hierarchical Clustering Method (HCM) with a method to add new members to
existing families. This procedure makes use of the much larger amount of
information contained in the proper elements catalogs, with respect to
classifications using also physical observations for a smaller number of
asteroids. Our work is based on the large catalog of the high accuracy
synthetic proper elements (available from AstDyS). We first identify a number
of core families; to these we attribute the next layer of smaller objects.
Then, we remove all the family members from the catalog, and reapply the HCM to
the rest. This gives both halo families which extend the core families and new
independent families, consisting mainly of small asteroids. These two cases are
discriminated by another step of attribution of new members and by merging
intersecting families. By using information from absolute magnitudes, we take
advantage of the larger size range in some families to analyze their shape in
the proper semimajor axis vs. inverse diameter plane. This leads to a new
method to estimate the family age (or ages). The results from the previous
steps are then analyzed, using also auxiliary information on physical
properties including WISE albedos and SDSS color indexes. This allows to solve
some difficult cases of families overlapping in the proper elements space but
generated by different collisional events. We analyze some examples of
cratering families (Massalia, Vesta, Eunomia) which show internal structures,
interpreted as multiple collisions. We also discuss why Ceres has no family
Time-dependent radio emission from evolving jets
We investigated the time-dependent radiative and dynamical properties of
light supersonic jets launched into an external medium, using hydrodynamic
simulations and numerical radiative transfer calculations. These involved
various structural models for the ambient media, with density profiles
appropriate for galactic and extragalactic systems. The radiative transfer
formulation took full account of emission, absorption, re-emission, Faraday
rotation and Faraday conversion explicitly. High time-resolution intensity maps
were generated, frame-by-frame, to track the spatial hydrodynamical and
radiative properties of the evolving jets. Intensity light curves were computed
via integrating spatially over the emission maps. We apply the models to jets
in active galactic nuclei (AGN). From the jet simulations and the
time-dependent emission calculations we derived empirical relations for the
emission intensity and size for jets at various evolutionary stages. The
temporal properties of jet emission are not solely consequences of intrinsic
variations in the hydrodynamics and thermal properties of the jet. They also
depend on the interaction between the jet and the ambient medium. The
interpretation of radio jet morphology therefore needs to take account of
environmental factors. Our calculations have also shown that the environmental
interactions can affect specific emitting features, such as internal shocks and
hotspots. Quantification of the temporal evolution and spatial distribution of
these bright features, together with the derived relations between jet size and
emission, would enable us to set constraints on the hydrodynamics of AGN and
the structure of the ambient medium.Comment: 16 pages, 18 figures, MNRAS in press
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