418 research outputs found
Infinite-Dimensional Symmetries of Two-Dimensional Coset Models
It has long been appreciated that the toroidal reduction of any gravity or
supergravity to two dimensions gives rise to a scalar coset theory exhibiting
an infinite-dimensional global symmetry. This symmetry is an extension of the
finite-dimensional symmetry G in three dimensions, after performing a further
circle reduction. There has not been universal agreement as to exactly what the
extended symmetry algebra is, with different arguments seemingly concluding
either that it is , the affine Kac-Moody extension of G, or else a
subalgebra thereof. Exceptional in the literature for its explicit and
transparent exposition is the extremely lucid discussion by Schwarz, which we
take as our starting point for studying the simpler situation of
two-dimensional flat-space sigma models, which nonetheless capture all the
essential details. We arrive at the conclusion that the full symmetry is
described by the Kac-Moody algebra G, although truncations to subalgebras, such
as the one obtained by Schwarz, can be considered too. We then consider the
explicit example of the SL(2,R)/O(2) coset, and relate Schwarz's approach to an
earlier discussion that goes back to the work of Geroch.Comment: Typos corrected, some reorganisation; 36 page
Sensitivity of predicted bioaerosol exposure from open windrow composting facilities to ADMS dispersion model parameters
Bioaerosols are released in elevated quantities from composting facilities and are associated with negative health effects, although dose-response relationships are not well understood, and require improved exposure classification. Dispersion modelling has great potential to improve exposure classification, but has not yet been extensively used or validated in this context. We present a sensitivity analysis of the ADMS dispersion model specific to input parameter ranges relevant to bioaerosol emissions from open windrow composting. This analysis provides an aid for model calibration by prioritising parameter adjustment and targeting independent parameter estimation. Results showed that predicted exposure was most sensitive to the wet and dry deposition modules and the majority of parameters relating to emission source characteristics, including pollutant emission velocity, source geometry and source height. This research improves understanding of the accuracy of model input data required to provide more reliable exposure predictions
Melvin universe as a limit of the C-metric
It is demonstrated that the Melvin universe representing the spacetime with a
strong 'homogeneous' electric field can by obtained from the spacetime of two
accelerated charged black holes by a suitable limiting procedure. The behavior
of various invariantly defined geometrical quantities in this limit is also
studied.Comment: 5 pages, no figures [v2: two references added
Classical Symmetries of Some Two-Dimensional Models
It is well-known that principal chiral models and symmetric space models in
two-dimensional Minkowski space have an infinite-dimensional algebra of hidden
symmetries. Because of the relevance of symmetric space models to duality
symmetries in string theory, the hidden symmetries of these models are explored
in some detail. The string theory application requires including coupling to
gravity, supersymmetrization, and quantum effects. However, as a first step,
this paper only considers classical bosonic theories in flat space-time. Even
though the algebra of hidden symmetries of principal chiral models is confirmed
to include a Kac--Moody algebra (or a current algebra on a circle), it is
argued that a better interpretation is provided by a doubled current algebra on
a semi-circle (or line segment). Neither the circle nor the semi-circle bears
any apparent relationship to the physical space. For symmetric space models the
line segment viewpoint is shown to be essential, and special boundary
conditions need to be imposed at the ends. The algebra of hidden symmetries
also includes Virasoro-like generators. For both principal chiral models and
symmetric space models, the hidden symmetry stress tensor is singular at the
ends of the line segment.Comment: 51 pages, minor corrections and added reference
The Ernst Equation on a Riemann Surface
The Ernst equation is formulated on an arbitrary Riemann surface.
Analytically, the problem reduces to finding solutions of the ordinary Ernst
equation which are periodic along the symmetry axis. The family of (punctured)
Riemann surfaces admitting a non-trivial Ernst field constitutes a ``partially
discretized'' subspace of the usual moduli space. The method allows us to
construct new exact solutions of Einstein's equations in vacuo with non-trivial
topology, such that different ``universes'', each of which may have several
black holes on its symmetry axis, are connected through necks bounded by cosmic
strings. We show how the extra topological degrees of freedom may lead to an
extension of the Geroch group and discuss possible applications to string
theory.Comment: 22 page
Monodromy-data parameterization of spaces of local solutions of integrable reductions of Einstein's field equations
For the fields depending on two of the four space-time coordinates only, the
spaces of local solutions of various integrable reductions of Einstein's field
equations are shown to be the subspaces of the spaces of local solutions of the
``null-curvature'' equations constricted by a requirement of a universal (i.e.
solution independent) structures of the canonical Jordan forms of the unknown
matrix variables. These spaces of solutions of the ``null-curvature'' equations
can be parametrized by a finite sets of free functional parameters -- arbitrary
holomorphic (in some local domains) functions of the spectral parameter which
can be interpreted as the monodromy data on the spectral plane of the
fundamental solutions of associated linear systems. Direct and inverse problems
of such mapping (``monodromy transform''), i.e. the problem of finding of the
monodromy data for any local solution of the ``null-curvature'' equations with
given canonical forms, as well as the existence and uniqueness of such solution
for arbitrarily chosen monodromy data are shown to be solvable unambiguously.
The linear singular integral equations solving the inverse problems and the
explicit forms of the monodromy data corresponding to the spaces of solutions
of the symmetry reduced Einstein's field equations are derived.Comment: LaTeX, 33 pages, 1 figure. Typos, language and reference correction
The Effect of Planarization on Width
We study the effects of planarization (the construction of a planar diagram
from a non-planar graph by replacing each crossing by a new vertex) on
graph width parameters. We show that for treewidth, pathwidth, branchwidth,
clique-width, and tree-depth there exists a family of -vertex graphs with
bounded parameter value, all of whose planarizations have parameter value
. However, for bandwidth, cutwidth, and carving width, every graph
with bounded parameter value has a planarization of linear size whose parameter
value remains bounded. The same is true for the treewidth, pathwidth, and
branchwidth of graphs of bounded degree.Comment: 15 pages, 6 figures. To appear at the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
Pair creation of black holes joined by cosmic strings
We argue that production of charged black hole pairs joined by a cosmic
string in the presence of a magnetic field can be analyzed using the Ernst
metric. The effect of the cosmic string is to pull the black holes towards each
other, opposing to the background field. An estimation of the production rate
using the Euclidean action shows that the process is suppressed as compared to
the formation of black holes without strings.Comment: 7 pages, LaTeX. Minor typos corrected
Hawking Radiation of Dirac Particles in a Variable-mass Kerr Space-time
Hawking effect of Dirac particles in a variable-mass Kerr space-time is
investigated by using a method called as the generalized tortoise coordinate
transformation. The location and the temperature of the event horizon of the
non-stationary Kerr black hole are derived. It is shown that the temperature
and the shape of the event horizon depend not only on the time but also on the
angle. However, the Fermi-Dirac spectrum displays a residual term which is
absent from that of Bose-Einstein distribution.Comment: 12 pages in 12pt Revtex, no figure, to appear in Gen. Rel. Grav.
Vol.33, No.7 (2001
U-Duality and Symplectic Formulation of Dilaton-Axion Gravity
We study a bosonic four--dimensional effective action corresponding to the
heterotic string compactified on a 6--torus (dilaton--axion gravity with one
vector field) on a curved space--time manifold possessing a time--like Killing
vector field. Previously an existence of the global
symmetry (--duality) as well as the symmetric space property of the
corresponding --model have been established following Neugebauer and
Kramer approach. Here we present an explicit form of the generators
in terms of coset variables and construct a representation of the coset in
terms of the physical target space coordinates. Complex symmetric
matrix (``matrix dilaton --axion'') is introduced for which --duality
takes the matrix valued form. In terms of this matrix the theory is
further presented as a K\"ahler --model. This leads to a more concise
formulation which opens new ways to construct exact classical
solutions. New solution (corresponding to constant ) is obtained
which describes the system of point massless magnetic monopoles endowed with
axion charges equal to minus monopole charges. In such a system mutual magnetic
repulsion is exactly balanced by axion attraction so that the resulting space
time is locally flat but possesses multiple Taub--NUT singularities.Comment: LATEX, 20 pages, no figure
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