75 research outputs found
Universal Drinfeld-Sokolov Reduction and Matrices of Complex Size
We construct affinization of the algebra of ``complex size''
matrices, that contains the algebras for integral values of the
parameter. The Drinfeld--Sokolov Hamiltonian reduction of the algebra
results in the quadratic Gelfand--Dickey structure on the
Poisson--Lie group of all pseudodifferential operators of fractional order.
This construction is extended to the simultaneous deformation of orthogonal and
simplectic algebras that produces self-adjoint operators, and it has a
counterpart for the Toda lattices with fractional number of particles.Comment: 29 pages, no figure
A 3-component extension of the Camassa-Holm hierarchy
We introduce a bi-Hamiltonian hierarchy on the loop-algebra of sl(2) endowed
with a suitable Poisson pair. It gives rise to the usual CH hierarchy by means
of a bi-Hamiltonian reduction, and its first nontrivial flow provides a
3-component extension of the CH equation.Comment: 15 pages; minor changes; to appear in Letters in Mathematical Physic
Notes on Exact Multi-Soliton Solutions of Noncommutative Integrable Hierarchies
We study exact multi-soliton solutions of integrable hierarchies on
noncommutative space-times which are represented in terms of quasi-determinants
of Wronski matrices by Etingof, Gelfand and Retakh. We analyze the asymptotic
behavior of the multi-soliton solutions and found that the asymptotic
configurations in soliton scattering process can be all the same as commutative
ones, that is, the configuration of N-soliton solution has N isolated localized
energy densities and the each solitary wave-packet preserves its shape and
velocity in the scattering process. The phase shifts are also the same as
commutative ones. Furthermore noncommutative toroidal Gelfand-Dickey hierarchy
is introduced and the exact multi-soliton solutions are given.Comment: 18 pages, v3: references added, version to appear in JHE
HI in the Outskirts of Nearby Galaxies
The HI in disk galaxies frequently extends beyond the optical image, and can
trace the dark matter there. I briefly highlight the history of high spatial
resolution HI imaging, the contribution it made to the dark matter problem, and
the current tension between several dynamical methods to break the disk-halo
degeneracy. I then turn to the flaring problem, which could in principle probe
the shape of the dark halo. Instead, however, a lot of attention is now devoted
to understanding the role of gas accretion via galactic fountains. The current
cold dark matter theory has problems on galactic scales, such as
the core-cusp problem, which can be addressed with HI observations of dwarf
galaxies. For a similar range in rotation velocities, galaxies of type Sd have
thin disks, while those of type Im are much thicker. After a few comments on
modified Newtonian dynamics and on irregular galaxies, I close with statistics
on the HI extent of galaxies.Comment: 38 pages, 17 figures, invited review, book chapter in "Outskirts of
Galaxies", Eds. J. H. Knapen, J. C. Lee and A. Gil de Paz, Astrophysics and
Space Science Library, Springer, in pres
Interstellar MHD Turbulence and Star Formation
This chapter reviews the nature of turbulence in the Galactic interstellar
medium (ISM) and its connections to the star formation (SF) process. The ISM is
turbulent, magnetized, self-gravitating, and is subject to heating and cooling
processes that control its thermodynamic behavior. The turbulence in the warm
and hot ionized components of the ISM appears to be trans- or subsonic, and
thus to behave nearly incompressibly. However, the neutral warm and cold
components are highly compressible, as a consequence of both thermal
instability in the atomic gas and of moderately-to-strongly supersonic motions
in the roughly isothermal cold atomic and molecular components. Within this
context, we discuss: i) the production and statistical distribution of
turbulent density fluctuations in both isothermal and polytropic media; ii) the
nature of the clumps produced by thermal instability, noting that, contrary to
classical ideas, they in general accrete mass from their environment; iii) the
density-magnetic field correlation (or lack thereof) in turbulent density
fluctuations, as a consequence of the superposition of the different wave modes
in the turbulent flow; iv) the evolution of the mass-to-magnetic flux ratio
(MFR) in density fluctuations as they are built up by dynamic compressions; v)
the formation of cold, dense clouds aided by thermal instability; vi) the
expectation that star-forming molecular clouds are likely to be undergoing
global gravitational contraction, rather than being near equilibrium, and vii)
the regulation of the star formation rate (SFR) in such gravitationally
contracting clouds by stellar feedback which, rather than keeping the clouds
from collapsing, evaporates and diperses them while they collapse.Comment: 43 pages. Invited chapter for the book "Magnetic Fields in Diffuse
Media", edited by Elisabete de Gouveia dal Pino and Alex Lazarian. Revised as
per referee's recommendation
Feint Lines: Notes on the Creation of a Skateboard Choreography
Magnetic fields on a range of scales play a large role in the ecosystems of
galaxies, both in the galactic disk and in the extended layers of gas away from
the plane. Observing magnetic field strength, structure and orientation is
complex, and necessarily indirect. Observational data of magnetic fields in the
halo of the Milky Way are scarce, and non-conclusive about the large-scale
structure of the field. In external galaxies, various large-scale
configurations of magnetic fields are measured, but many uncertainties about
exact configurations and their origin remain. There is a strong interaction
between magnetic fields and other components in the interstellar medium such as
ionized and neutral gas and cosmic rays. The energy densities of these
components are comparable on large scales, indicating that magnetic fields are
not passive tracers but that magnetic field feedback on the other interstellar
medium components needs to be taken into account.Comment: 13 pages, 7 figures. Accepted in Space Science Review
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