1,649 research outputs found
Dual Isomonodromic Deformations and Moment Maps to Loop Algebras
The Hamiltonian structure of the monodromy preserving deformation equations
of Jimbo {\it et al } is explained in terms of parameter dependent pairs of
moment maps from a symplectic vector space to the dual spaces of two different
loop algebras. The nonautonomous Hamiltonian systems generating the
deformations are obtained by pulling back spectral invariants on Poisson
subspaces consisting of elements that are rational in the loop parameter and
identifying the deformation parameters with those determining the moment maps.
This construction is shown to lead to ``dual'' pairs of matrix differential
operators whose monodromy is preserved under the same family of deformations.
As illustrative examples, involving discrete and continuous reductions, a
higher rank generalization of the Hamiltonian equations governing the
correlation functions for an impenetrable Bose gas is obtained, as well as dual
pairs of isomonodromy representations for the equations of the Painleve
transcendents and .Comment: preprint CRM-1844 (1993), 28 pgs. (Corrected date and abstract.
Distributions of flux vacua
We give results for the distribution and number of flux vacua of various
types, supersymmetric and nonsupersymmetric, in IIb string theory compactified
on Calabi-Yau manifolds. We compare this with related problems such as counting
attractor points.Comment: 43 pages, 7 figures. v2: improved discussion of finding vacua with
discrete flux, references adde
Twisted brane charges for non-simply connected groups
The charges of the twisted branes for strings on the group manifold SU(n)/Z_d
are determined. To this end we derive explicit (and remarkably simple) formulae
for the relevant NIM-rep coefficients. The charge groups of the twisted and
untwisted branes are compared and found to agree for the cases we consider.Comment: 30 page
One-Up On L1: Can X-rays Provide Longer Advanced Warning of Solar Wind Flux Enhancements Than Upstream Monitors?
Observations of strong solar wind proton flux correlations with ROSAT X-ray
rates along with high spectral resolution Chandra observations of X-rays from
the dark Moon show that soft X-ray emission mirrors the behavior of the solar
wind. In this paper, based on an analysis of an X-ray event observed by
XMM-Newton resulting from charge exchange of high charge state solar wind ions
and contemporaneous neutral solar wind data, we argue that X-ray observations
may be able to provide reliable advance warning, perhaps by as much as half a
day, of dramatic increases in solar wind flux at Earth. Like neutral atom
imaging, this provides the capability to monitor the solar wind remotely rather
than in-situ.Comment: in press in Adv. Space Research, 7 pages, 6 eps figures, resolution
reduced for Astro-ph submission, see http://lena.gsfc.nasa.gov for full
versio
Tracking bifurcating solutions of a model biological pattern generator
We study heterogeneous steady-state solutions of a cell-chemotaxis model for generating biological spatial patterns in two-dimensional domains with zero flux boundary conditions. We use the finite-element package ENTWIFE to investigate bifurcation from the uniform solution as the chemotactic parameter varies and as the domain scale and geometry change. We show that this simple cell-chemotaxis model can produce a remarkably wide and surprising range of complex spatial patterns
Charges of twisted branes: the exceptional cases
The charges of the twisted D-branes for the two exceptional cases (SO(8) with
the triality automorphism and E_6 with charge conjugation) are determined. To
this end the corresponding NIM-reps are expressed in terms of the fusion rules
of the invariant subalgebras. As expected the charge groups are found to agree
with those characterising the untwisted branes.Comment: 15 page
Character Expansion Methods for Matrix Models of Dually Weighted Graphs
We consider generalized one-matrix models in which external fields allow
control over the coordination numbers on both the original and dual lattices.
We rederive in a simple fashion a character expansion formula for these models
originally due to Itzykson and Di Francesco, and then demonstrate how to take
the large N limit of this expansion. The relationship to the usual matrix model
resolvent is elucidated. Our methods give as a by-product an extremely simple
derivation of the Migdal integral equation describing the large limit of
the Itzykson-Zuber formula. We illustrate and check our methods by analyzing a
number of models solvable by traditional means. We then proceed to solve a new
model: a sum over planar graphs possessing even coordination numbers on both
the original and the dual lattice. We conclude by formulating equations for the
case of arbitrary sets of even, self-dual coupling constants. This opens the
way for studying the deep problem of phase transitions from random to flat
lattices.Comment: 22 pages, harvmac.tex, pictex.tex. All diagrams written directly into
the text in Pictex commands. (Two minor math typos corrected.
Acknowledgements added.
Modular Invariants in the Fractional Quantum Hall Effect
We investigate the modular properties of the characters which appear in the
partition functions of nonabelian fractional quantum Hall states. We first give
the annulus partition function for nonabelian FQH states formed by spinon and
holon (spinon-holon state). The degrees of freedom of spin are described by the
affine SU(2) Kac-Moody algebra at level . The partition function and the
Hilbert space of the edge excitations decomposed differently according to
whether is even or odd. We then investigate the full modular properties of
the extended characters for nonabelian fractional quantum Hall states. We
explicitly verify the modular invariance of the annulus grand partition
functions for spinon-holon states, the Pfaffian state and the 331 states. This
enables one to extend the relation between the modular behavior and the
topological order to nonabelian cases. For the Haldane-Rezayi state, we find
that the extended characters do not form a representation of the modular group,
thus the modular invariance is broken.Comment: Latex,21 pages.version to appear in Nucl.Phys.
Large-N limit of the two-dimensinal Non-Local Yang-Mills theory on arbitrary surfaces with boundary
The large-N limit of the two-dimensional non-local U Yang-Mills theory
on an orientable and non-orientable surface with boundaries is studied. For the
case which the holonomies of the gauge group on the boundaries are near the
identity, , it is shown that the phase structure of these theories
is the same as that obtain for these theories on orientable and non-orientable
surface without boundaries, with same genus but with a modified area
.Comment: 10 pages, no figure
Fast Algorithm for Partial Covers in Words
A factor of a word is a cover of if every position in lies
within some occurrence of in . A word covered by thus
generalizes the idea of a repetition, that is, a word composed of exact
concatenations of . In this article we introduce a new notion of
-partial cover, which can be viewed as a relaxed variant of cover, that
is, a factor covering at least positions in . We develop a data
structure of size (where ) that can be constructed in time which we apply to compute all shortest -partial covers for a
given . We also employ it for an -time algorithm computing
a shortest -partial cover for each
- …