10,102 research outputs found
A Contraction Analysis of the Convergence of Risk-Sensitive Filters
A contraction analysis of risk-sensitive Riccati equations is proposed. When
the state-space model is reachable and observable, a block-update
implementation of the risk-sensitive filter is used to show that the N-fold
composition of the Riccati map is strictly contractive with respect to the
Riemannian metric of positive definite matrices, when N is larger than the
number of states. The range of values of the risk-sensitivity parameter for
which the map remains contractive can be estimated a priori. It is also found
that a second condition must be imposed on the risk-sensitivity parameter and
on the initial error variance to ensure that the solution of the risk-sensitive
Riccati equation remains positive definite at all times. The two conditions
obtained can be viewed as extending to the multivariable case an earlier
analysis of Whittle for the scalar case.Comment: 22 pages, 6 figure
Robust Kalman Filtering: Asymptotic Analysis of the Least Favorable Model
We consider a robust filtering problem where the robust filter is designed
according to the least favorable model belonging to a ball about the nominal
model. In this approach, the ball radius specifies the modeling error tolerance
and the least favorable model is computed by performing a Riccati-like backward
recursion. We show that this recursion converges provided that the tolerance is
sufficiently small
Recognizing the fingerprints of the Galactic bar: a quantitative approach to comparing model (l,v) distributions to observation
We present a new method for fitting simple hydrodynamical models to the (l,v)
distribution of atomic and molecular gas observed in the Milky Way. The method
works by matching features found in models and observations. It is based on the
assumption that the large-scale features seen in (l,v) plots, such as
ridgelines and the terminal velocity curve, are influenced primarily by the
underlying large-scale Galactic potential and are only weakly dependent on
local ISM heating and cooling processes. In our scheme one first identifies by
hand the features in the observations: this only has to be done once. We
describe a procedure for automatically extracting similar features from simple
hydrodynamical models and quantifying the "distance" between each model's
features and the observations. Application to models of the Galactic Bar region
(|l|<30deg) shows that our feature-fitting method performs better than \chi^2
or envelope distances at identifying the correct underlying galaxy model.Comment: Accepted for publication in MNRA
Gas flow in barred potentials
We use a Cartesian grid to simulate the flow of gas in a barred Galactic
potential and investigate the effects of varying the sound speed in the gas and
the resolution of the grid. For all sound speeds and resolutions, streamlines
closely follow closed orbits at large and small radii. At intermediate radii
shocks arise and the streamlines shift between two families of closed orbits.
The point at which the shocks appear and the streamlines shift between orbit
families depends strongly on sound speed and resolution. For sufficiently large
values of these two parameters, the transfer happens at the cusped orbit as
hypothesised by Binney et al. over two decades ago. For sufficiently high
resolutions the flow downstream of the shocks becomes unsteady. If this
unsteadiness is physical, as appears to be the case, it provides a promising
explanation for the asymmetry in the observed distribution of CO.Comment: Accepted for publication in MNRA
Gas flow in barred potentials II. Bar Driven Spiral Arms
Spiral arms that emerge from the ends of a galactic bar are important in
interpreting observations of our and external galaxies. It is therefore
important to understand the physical mechanism that causes them. We find that
these spiral arms can be understood as kinematic density waves generated by
librations around underlying ballistic closed orbits. This is even true in the
case of a strong bar, provided the librations are around the appropriate closed
orbits and not around the circular orbits that form the basis of the epicycle
approximation. An important consequence is that it is a potential's orbital
structure that determines whether a bar should be classified as weak or strong,
and not crude estimates of the potential's deviation from axisymmetry.Comment: Accepted for publication in MNRA
Models of rotating coronae
Fitting equilibrium dynamical models to observational data is an essential
step in understanding the structure of the gaseous hot haloes that surround our
own and other galaxies. However, the two main categories of models that are
used in the literature are poorly suited for this task: (i) simple barotropic
models are analytic and can therefore be adjusted to match the observations,
but are clearly unrealistic because the rotational velocity does
not depend on the distance from the galactic plane, while (ii) models
obtained as a result of cosmological galaxy formation simulations are more
realistic, but are impractical to fit to observations due to high computational
cost. Here we bridge this gap by presenting a general method to construct
axisymmetric baroclinic equilibrium models of rotating galactic coronae in
arbitrary external potentials. We consider in particular a family of models
whose equipressure surfaces in the plane are ellipses of varying axis
ratio. These models are defined by two one-dimensional functions, the axial
ratio of pressure and the value of the pressure along the galaxy's symmetry axis. These models can have a rotation
speed that realistically decreases as one moves away from the
galactic plane, and can reproduce the angular momentum distribution found in
cosmological simulations. The models are computationally cheap to construct and
can thus be used in fitting algorithms. We provide a python code that given
, and returns ,
, , . We show a few examples of these models using
the Milky Way as a case study.Comment: Accepted for publication in MNRA
Nuclear Spirals in the inner Milky Way
We use hydrodynamical simulations to construct a new coherent picture for the
gas flow in the Central Molecular Zone (CMZ), the region of our Galaxy within
. We relate connected structures observed in
data cubes of molecular tracers to nuclear spiral arms. These arise naturally
in hydrodynamical simulations of barred galaxies, and are similar to those that
can be seen in external galaxies such as NGC4303 or NGC1097. We discuss a
face-on view of the CMZ including the position of several prominent molecular
clouds, such as Sgr B2, the and
clouds, the polar arc, Bania Clump 2 and Sgr C. Our model is also consistent
with the larger scale gas flow, up to , thus providing a
consistent picture of the entire Galactic bar region.Comment: Accepted for publication in MNRAS, 12 pages, 12 figure
Periodicity makes galactic shocks unstable - I. Linear analysis
We study the dynamical stability of stationary galactic spiral shocks. The
steady-state equilibrium flow contains a shock of the type derived by Roberts
in the tightly wound approximation. We find that boundary conditions are
critical in determining whether the solutions are stable or not. Shocks are
unstable if periodic boundary conditions are imposed. For intermediate
strengths of the spiral potential, the instability disappears if boundary
conditions are imposed such that the upstream flow is left unperturbed as in
the classic analysis of D'yakov and Kontorovich. This reconciles apparently
contradictory findings of previous authors regarding the stability of spiral
shocks. This also shows that the instability is distinct from the
Kelvin-Helmholtz instability, confirming the findings of Kim et al. We suggest
that instability is a general characteristics of periodic shocks, regardless of
the presence of shear, and provide a physical picture as to why this is the
case. For strong spiral potentials, high post-shock shear makes the system
unstable also to parasitic Kelvin-Helmholtz instability regardless of the
boundary conditions. Our analysis is performed in the context of a simplified
problem that, while preserving all the important characteristics of the
original problem, strips it from unnecessary complications, and assumes that
the gas is isothermal, non self-gravitating, non-magnetised.Comment: Accepted for publication in MNRA
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