36 research outputs found
Isomonodromic deformations of connections with singularities of parahoric formal type
In previous work, the authors have developed a geometric theory of
fundamental strata to study connections on the projective line with irregular
singularities of parahoric formal type. In this paper, the moduli space of
connections that contain regular fundamental strata with fixed combinatorics at
each singular point is constructed as a smooth Poisson reduction. The authors
then explicitly compute the isomonodromy equations as an integrable system.
This result generalizes work of Jimbo, Miwa, and Ueno to connections whose
singularities have parahoric formal type.Comment: 32 pages. One of the main theorems (Theorem 5.1) has been
significantly strengthened. It now states that the isomonodromy equations
give rise to an integrable system on the moduli space of framed connections
with fixed combinatorics instead of only on a principal GL_n bundle over this
space. Sections 5 and 6 have been substantially rewritte
Dark mammoth trunks in the merging galaxy NGC 1316 and a mechanism of cosmic double helices
NGC 1316 is a giant, elliptical galaxy containing a complex network of dark,
dust features. The morphology of these features has been examined in some
detail using a Hubble Space Telescope, Advanced Camera for Surveys image. It is
found that most of the features are constituted of long filaments. There also
exist a great number of dark structures protruding inwards from the filaments.
Many of these structures are strikingly similar to elephant trunks in H II
regions in the Milky Way Galaxy, although much larger. The structures, termed
mammoth trunks, generally are filamentary and often have shapes resembling the
letters V or Y. In some of the mammoth trunks the stem of the Y can be resolved
into two or more filaments, many of which showing signs of being intertwined. A
model of the mammoth trunks, related to a recent theory of elephant trunks, is
proposed. Based on magnetized filaments, the model is capable of giving an
account of the various shapes of the mammoth trunks observed, including the
twined structures.Comment: Accepted for publication in Astrophysics & Space Scienc