2,496 research outputs found
Monodromy dependence and connection formulae for isomonodromic tau functions
We discuss an extension of the Jimbo-Miwa-Ueno differential 1-form to a form
closed on the full space of extended monodromy data of systems of linear
ordinary differential equations with rational coefficients. This extension is
based on the results of M. Bertola generalizing a previous construction by B.
Malgrange. We show how this 1-form can be used to solve a long-standing problem
of evaluation of the connection formulae for the isomonodromic tau functions
which would include an explicit computation of the relevant constant factors.
We explain how this scheme works for Fuchsian systems and, in particular,
calculate the connection constant for generic Painlev\'e VI tau function. The
result proves the conjectural formula for this constant proposed in
\cite{ILT13}. We also apply the method to non-Fuchsian systems and evaluate
constant factors in the asymptotics of Painlev\'e II tau function.Comment: 54 pages, 6 figures; v4: rewritten Introduction and Subsection 3.3,
added few refs to match published articl
On birational involutions of
Let be a rationally connected three-dimensional algebraic variety and let
be an element of order two in the group of its birational selfmaps.
Suppose that there exists a non-uniruled divisorial component of the
-fixed point locus. Using the equivariant minimal model program we give a
rough classification of such elements.Comment: 24 pages, late
Confinement and diffusion time-scales of CR hadrons in AGN-inflated bubbles
While rich clusters are powerful sources of X-rays, gamma-ray emission from
these large cosmic structures has not been detected yet. X-ray radiative energy
losses in the central regions of relaxed galaxy clusters are so strong that one
needs to consider special sources of energy, likely AGN feedback, to suppress
catastrophic cooling of the gas. We consider a model of AGN feedback that
postulates that the AGN supplies the energy to the gas by inflating bubbles of
relativistic plasma, whose energy content is dominated by cosmic-ray (CR)
hadrons. If most of these hadrons can quickly escape the bubbles, then
collisions of CRs with thermal protons in the intracluster medium (ICM) should
lead to strong gamma-ray emission, unless fast diffusion of CRs removes them
from the cluster. Therefore, the lack of detections with modern gamma-ray
telescopes sets limits on the confinement time of CR hadrons in bubbles and CR
diffusive propagation in the ICM.Comment: 8 pages, 2 figures, accepted for publication in MNRA
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