7,488 research outputs found
Classification of integrable two-component Hamiltonian systems of hydrodynamic type in 2+1 dimensions
Hamiltonian systems of hydrodynamic type occur in a wide range of
applications including fluid dynamics, the Whitham averaging procedure and the
theory of Frobenius manifolds. In 1+1 dimensions, the requirement of the
integrability of such systems by the generalised hodograph transform implies
that integrable Hamiltonians depend on a certain number of arbitrary functions
of two variables. On the contrary, in 2+1 dimensions the requirement of the
integrability by the method of hydrodynamic reductions, which is a natural
analogue of the generalised hodograph transform in higher dimensions, leads to
finite-dimensional moduli spaces of integrable Hamiltonians. In this paper we
classify integrable two-component Hamiltonian systems of hydrodynamic type for
all existing classes of differential-geometric Poisson brackets in 2D,
establishing a parametrisation of integrable Hamiltonians via
elliptic/hypergeometric functions. Our approach is based on the Godunov-type
representation of Hamiltonian systems, and utilises a novel construction of
Godunov's systems in terms of generalised hypergeometric functions.Comment: Latex, 34 page
Gap Probabilities for Edge Intervals in Finite Gaussian and Jacobi Unitary Matrix Ensembles
The probabilities for gaps in the eigenvalue spectrum of the finite dimension
random matrix Hermite and Jacobi unitary ensembles on some
single and disconnected double intervals are found. These are cases where a
reflection symmetry exists and the probability factors into two other related
probabilities, defined on single intervals. Our investigation uses the system
of partial differential equations arising from the Fredholm determinant
expression for the gap probability and the differential-recurrence equations
satisfied by Hermite and Jacobi orthogonal polynomials. In our study we find
second and third order nonlinear ordinary differential equations defining the
probabilities in the general case. For N=1 and N=2 the probabilities and
thus the solution of the equations are given explicitly. An asymptotic
expansion for large gap size is obtained from the equation in the Hermite case,
and also studied is the scaling at the edge of the Hermite spectrum as , and the Jacobi to Hermite limit; these last two studies make
correspondence to other cases reported here or known previously. Moreover, the
differential equation arising in the Hermite ensemble is solved in terms of an
explicit rational function of a {Painlev\'e-V} transcendent and its derivative,
and an analogous solution is provided in the two Jacobi cases but this time
involving a {Painlev\'e-VI} transcendent.Comment: 32 pages, Latex2
The molecular polar disc in NGC 2768
We present CO(1-0) and CO(2-1) maps of the molecular polar disc in the
elliptical galaxy NGC 2768 obtained at the IRAM Plateau de Bure Interferometer.
The maps have a resolution of 2.6" x 2.3" and 1.2" x 1.2" for the CO(1-0) and
CO(2-1) lines, respectively. The CO maps complete the unique picture of the
interstellar medium (ISM) of NGC 2768; the dust, molecular gas, ionised gas and
neutral hydrogen (HI) trace the recent acquisition of cold and cool gas over
two orders of magnitude in radii (and much more in density). In agreement with
the other ISM components, the CO distribution extends nearly perpendicularly to
the photometric major axis of the galaxy. Velocity maps of the CO show a
rotating polar disc or ring in the inner kiloparsec. This cool gas could lead
to kinematic substructure formation within NGC 2768. However, the stellar
velocity field and H-beta absorption linestrength maps from the optical
integral-field spectrograph SAURON give no indication of a young and
dynamically cold stellar population coincident with the molecular polar disc.
Very recent or weak star formation, undetectable in linestrengths, nevertheless
remains a possibility and could be at the origin of some of the ionised gas
observed. Millimetre continuum emission was also detected in NGC 2768, now one
of only a few low-luminosity active galactic nuclei with observed millimetre
continuum emission.Comment: Accepted for publication in MNRAS, 11 pages, 8 figure
Bar Diagnostics in Edge-On Spiral Galaxies. II. Hydrodynamical Simulations
We develop diagnostics based on gas kinematics to identify the presence of a
bar in an edge-on spiral galaxy and determine its orientation. We use
position-velocity diagrams (PVDs) obtained by projecting edge-on
two-dimensional hydrodynamical simulations of the gas flow in a barred galaxy
potential. We show that when a nuclear spiral is formed, the presence of a gap
in the PVDs, between the signature of the nuclear spiral and that of the outer
parts of the disk, reliably indicates the presence of a bar. This gap is due to
the presence of shocks and inflows in the simulations, leading to a depletion
of the gas in the outer bar region. If no nuclear spiral signature is present
in a PVD, only indirect arguments can be used to argue for the presence of a
bar. The shape of the signature of the nuclear spiral, and to a lesser extent
that of the outer bar region, allows to determine the orientation of the bar
with respect to the line-of-sight. The presence of dust can also help to
discriminate between viewing angles on either side of the bar. Simulations
covering a large fraction of parameter space constrain the bar properties and
mass distribution of observed galaxies. The strongest constraint comes from the
presence or absence of the signature of a nuclear spiral in the PVD.Comment: 25 pages (AASTeX, aaspp4.sty), 11 jpg figures. Accepted for
publication in The Astrophysical Journal. Online manuscript with PostScript
figures available at: http://www.strw.leidenuniv.nl/~bureau/pub_list.htm
Bar Diagnostics in Edge-On Spiral Galaxies. I. The Periodic Orbits Approach
We develop diagnostics to detect the presence and orientation of a bar in an
edge-on disk, using its kinematical signature in the position-velocity diagram
(PVD) of a spiral galaxy observed edge-on. Using a well-studied barred spiral
galaxy mass model, we briefly review the orbital properties of two-dimensional
non-axisymmetric disks and identify the main families of periodic orbits. We
use those families as building blocks to model real galaxies and calculate the
PVDs obtained for various realistic combinations of periodic orbit families and
for a number of viewing angles with respect to the bar. We show that the global
structure of the PVD is a reliable bar diagnostic in edge-on disks.
Specifically, the presence of a gap between the signatures of the families of
periodic orbits in the PVD follows directly from the non-homogeneous
distribution of the orbits in a barred galaxy. Similarly, material in the two
so-called forbidden quadrants of the PVD results from the elongated shape of
the orbits. We show how the shape of the signatures of the dominant x1 and x2
families of periodic orbits in the PVD can be used efficiently to determine the
viewing angle with respect to the bar and, to a lesser extent, to constrain the
mass distribution of an observed galaxy. We also address the limitations of the
models when interpreting observational data.Comment: 22 pages, 9 figures (AASTeX, aaspp4.sty). Accepted for publication in
The Astrophysical Journa
A critical-density closed Universe in Brans-Dicke theory
In a Brans-Dicke (BD) cosmological model, the energy density associated with
some scalar field decreases as \displaystyle a^{{-2}(\frac{\omega_{o}+
{\frac12}%}{\omega_{o}+1})} with the scale factor of the Universe,
giving a matter with an Equation of state . In this model, the Universe
could be closed but still have a nonrelativistic-matter density corresponding
to its critical value, . Different cosmological expressions, such
as, luminosity distance, angular diameter, number count and ratio of the
redshift tickness-angular size, are determined in terms of the redshift for
this model.Comment: To appear in MNRAS, 7 pages, 5 eps figure
Coalition theories: empirical evidence for dutch municipalities
The paper analyzes coalition formation in Dutch municipalities. After discussing the main features of the institutional setting, several theories are discussed, which are classified as size oriented, policy oriented and actor oriented models. A test statistic is proposed to determine the predictive power of these models. The empirical analysis shows that strategic positions as well as some of the distinguished preferences are important in the setting of Dutch municipalities. Especially, the dominant minimum number principle yields highly significant results for coalition formations in the period 1978â1986
Boxy/peanut/X bulges, barlenses and the thick part of galactic bars: What are they and how did they form?
Bars have a complex three-dimensional shape. In particular their inner part
is vertically much thicker than the parts further out. Viewed edge-on, the
thick part of the bar is what is commonly known as a boxy-, peanut- or X- bulge
and viewed face-on it is referred to as a barlens. These components are due to
disc and bar instabilities and are composed of disc material. I review here
their formation, evolution and dynamics, using simulations, orbital structure
theory and comparisons to observations.Comment: 21 pages, 7 figures, invited review to appear in "Galactic Bulges",
E. Laurikainen, R. Peletier, D. Gadotti, (eds.), Springe
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