27,337 research outputs found
Metric for attractor overlap
We present the first general metric for attractor overlap (MAO) facilitating
an unsupervised comparison of flow data sets. The starting point is two or more
attractors, i.e., ensembles of states representing different operating
conditions. The proposed metric generalizes the standard Hilbert-space distance
between two snapshots to snapshot ensembles of two attractors. A reduced-order
analysis for big data and many attractors is enabled by coarse-graining the
snapshots into representative clusters with corresponding centroids and
population probabilities. For a large number of attractors, MAO is augmented by
proximity maps for the snapshots, the centroids, and the attractors, giving
scientifically interpretable visual access to the closeness of the states. The
coherent structures belonging to the overlap and disjoint states between these
attractors are distilled by few representative centroids. We employ MAO for two
quite different actuated flow configurations: (1) a two-dimensional wake of the
fluidic pinball with vortices in a narrow frequency range and (2)
three-dimensional wall turbulence with broadband frequency spectrum manipulated
by spanwise traveling transversal surface waves. MAO compares and classifies
these actuated flows in agreement with physical intuition. For instance, the
first feature coordinate of the attractor proximity map correlates with drag
for the fluidic pinball and for the turbulent boundary layer. MAO has a large
spectrum of potential applications ranging from a quantitative comparison
between numerical simulations and experimental particle-image velocimetry data
to the analysis of simulations representing a myriad of different operating
conditions.Comment: 33 pages, 20 figure
Hydrodynamic Processes in Massive Stars
The hydrodynamic processes operating within stellar interiors are far richer
than represented by the best stellar evolution model available. Although it is
now widely understood, through astrophysical simulation and relevant
terrestrial experiment, that many of the basic assumptions which underlie our
treatments of stellar evolution are flawed, we lack a suitable, comprehensive
replacement. This is due to a deficiency in our fundamental understanding of
the transport and mixing properties of a turbulent, reactive, magnetized
plasma; a deficiency in knowledge which stems from the richness and variety of
solutions which characterize the inherently non-linear set of governing
equations. The exponential increase in availability of computing resources,
however, is ushering in a new era of understanding complex hydrodynamic flows;
and although this field is still in its formative stages, the sophistication
already achieved is leading to a dramatic paradigm shift in how we model
astrophysical fluid dynamics. We highlight here some recent results from a
series of multi-dimensional stellar interior calculations which are part of a
program designed to improve our one-dimensional treatment of massive star
evolution and stellar evolution in general.Comment: 10 pages, 4 figures, IAUS 252 Conference Proceeding (Sanya) - "The
Art of Modeling Stars in the 21st Century
Off-grid Direction of Arrival Estimation Using Sparse Bayesian Inference
Direction of arrival (DOA) estimation is a classical problem in signal
processing with many practical applications. Its research has recently been
advanced owing to the development of methods based on sparse signal
reconstruction. While these methods have shown advantages over conventional
ones, there are still difficulties in practical situations where true DOAs are
not on the discretized sampling grid. To deal with such an off-grid DOA
estimation problem, this paper studies an off-grid model that takes into
account effects of the off-grid DOAs and has a smaller modeling error. An
iterative algorithm is developed based on the off-grid model from a Bayesian
perspective while joint sparsity among different snapshots is exploited by
assuming a Laplace prior for signals at all snapshots. The new approach applies
to both single snapshot and multi-snapshot cases. Numerical simulations show
that the proposed algorithm has improved accuracy in terms of mean squared
estimation error. The algorithm can maintain high estimation accuracy even
under a very coarse sampling grid.Comment: To appear in the IEEE Trans. Signal Processing. This is a revised,
shortened version of version
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