6,649 research outputs found
Complexity spectrum of some discrete dynamical systems
We first study birational mappings generated by the composition of the matrix
inversion and of a permutation of the entries of matrices. We
introduce a semi-numerical analysis which enables to compute the Arnold
complexities for all the possible birational transformations. These
complexities correspond to a spectrum of eighteen algebraic values. We then
drastically generalize these results, replacing permutations of the entries by
homogeneous polynomial transformations of the entries possibly depending on
many parameters. Again it is shown that the associated birational, or even
rational, transformations yield algebraic values for their complexities.Comment: 1 LaTex fil
Identification of the donor in GRS 1915+105
We report on the results of medium-resolution spectroscopy of GRS 1915+105 in
the H and K band using the 8m VLT at ESO. We clearly identify absorption
bandheads from CO12 and CO13. Together with other features this results in a
classification of the donor as a K-M III star.Comment: 4 pages, Kluwer style, to appear in Astrophys. Space Sci. Rev, Proc.
of 3rd Microquasar workshop, Granada, Sep. 2000, Eds. A.J. Castro-Tirado, J.
Greiner, J.M. Paredes; all proceedings contr. available at
http://www.aip.de/~jcg/granada.htm
Painleve versus Fuchs
The sigma form of the Painlev{\'e} VI equation contains four arbitrary
parameters and generically the solutions can be said to be genuinely
``nonlinear'' because they do not satisfy linear differential equations of
finite order. However, when there are certain restrictions on the four
parameters there exist one parameter families of solutions which do satisfy
(Fuchsian) differential equations of finite order. We here study this phenomena
of Fuchsian solutions to the Painlev{\'e} equation with a focus on the
particular PVI equation which is satisfied by the diagonal correlation function
C(N,N) of the Ising model. We obtain Fuchsian equations of order for
C(N,N) and show that the equation for C(N,N) is equivalent to the
symmetric power of the equation for the elliptic integral .
We show that these Fuchsian equations correspond to rational algebraic curves
with an additional Riccati structure and we show that the Malmquist Hamiltonian
variables are rational functions in complete elliptic integrals. Fuchsian
equations for off diagonal correlations are given which extend our
considerations to discrete generalizations of Painlev{\'e}.Comment: 18 pages, Dedicated to the centenary of the publication of the
Painleve VI equation in the Comptes Rendus de l'Academie des Sciences de
Paris by Richard Fuchs in 190
Fisher Zeroes and Singular Behaviour of the Two Dimensional Potts Model in the Thermodynamic Limit
The duality transformation is applied to the Fisher zeroes near the
ferromagnetic critical point in the q>4 state two dimensional Potts model. A
requirement that the locus of the duals of the zeroes be identical to the dual
of the locus of zeroes in the thermodynamic limit (i) recovers the ratio of
specific heat to internal energy discontinuity at criticality and the
relationships between the discontinuities of higher cumulants and (ii)
identifies duality with complex conjugation. Conjecturing that all zeroes
governing ferromagnetic singular behaviour satisfy the latter requirement gives
the full locus of such Fisher zeroes to be a circle. This locus, together with
the density of zeroes is then shown to be sufficient to recover the singular
form of the thermodynamic functions in the thermodynamic limit.Comment: 10 pages, 0 figures, LaTeX. Paper expanded and 2 references added
clarifying duality relationships between discontinuities in higher cumulant
The peculiar molecular envelope around the post-AGB star IRAS 08544--4431
Circumbinary disks have been hypothesized to exist around a number of binary
post-AGB stars. Although most of the circumbinary disks have been inferred
through the near IR excess, a few of them are strong emitters of molecular
emission. Here we present high angular resolution observations of the emission
of CO and its isotopomer CO J=2--1 line from the circumstellar
envelope around the binary post-AGB star IRAS 085444431, which is one of the
most prominent members of this class of objects. We find that the envelope is
resolved in our observations and two separate components can be identified: (a)
a central extended and strong component with very narrow linewidth between 2 -
6 \kms; (b) a weak bipolar outflow with expansion velocity up to 8 \kms. The
central compact component possesses low and variable CO/CO J=2--1
line ratio, indicating optically thick emission of the main isotope. We
estimate a molecular gas mass of 0.0047 M for this component based on
the optically thinner CO J=2--1 line. We discuss the relation of the
molecular envelope and the circumbinary disk inferred from near IR excess and
compare with other known cases where the distribution of molecular gas has been
imaged at high angular resolution.Comment: 14 pages, 4 figures. Accepted for publication in Astrophysical
Journa
The saga of the Ising susceptibility
We review developments made since 1959 in the search for a closed form for
the susceptibility of the Ising model. The expressions for the form factors in
terms of the nome and the modulus are compared and contrasted. The
generalized correlations are defined and explicitly
computed in terms of theta functions for .Comment: 19 pages, 1 figur
- …