13,367 research outputs found
Ergodic Transport Theory, periodic maximizing probabilities and the twist condition
The present paper is a follow up of another one by A. O. Lopes, E. Oliveira
and P. Thieullen which analyze ergodic transport problems. Our main focus will
a more precise analysis of case where the maximizing probability is unique and
is also a periodic orbit.
Consider the shift T acting on the Bernoulli space \Sigma={1, 2, 3,..,
d}^\mathbb{N} A:\Sigma \to \mathbb{R} a Holder potential.
Denote m(A)=max_{\nu is an invariant probability for T} \int A(x) \; d\nu(x)
and, \mu_{\infty,A}, any probability which attains the maximum value. We assume
this probability is unique (a generic property). We denote \T the bilateral
shift. For a given potential Holder A:\Sigma \to \mathbb{R}, we say that a
Holder continuous function W: \hat{\Sigma} \to \mathbb{R} is a involution
kernel for A, if there is a Holder function A^*:\Sigma \to \mathbb{R}, such
that, A^*(w)= A\circ \T^{-1}(w,x)+ W \circ \T^{-1}(w,x) - W(w,x). We say that
A^* is a dual potential of A. It is true that m(A)=m(A^*). We denote by V the
calibrated subaction for A, and, V^* the one for A^*. We denote by I^* the
deviation function for the family of Gibbs states for \beta A, when \beta \to
\infty.
For each x we get one (more than one) w_x such attains the supremum above.
That is, solutions of V(x) = W(w_x,x) - V^* (w_x)- I^*(w_x).
A pair of the form (x,w_x) is called an optimal pair. If \T is the shift
acting on (x,w) \in {1, 2, 3,.., d}^\mathbb{Z}, then, the image by \T^{-1} of
an optimal pair is also an optimal pair.
Theorem - Generically, in the set of Holder potentials A that satisfy
(i) the twist condition,
(ii) uniqueness of maximizing probability which is supported in a periodic
orbit, the set of possible optimal w_x, when x covers the all range of possible
elements x in \in \Sigma, is finite
Comment on Ricci Collineations of Static Spherically Symmetric Spacetimes
We present a counter example to a theorem given by Amir {\em et al.} J. Math.
Phys. {\bf 35}, 3005 (1994). We also comment on a misleading statements of the
same reference.Comment: 4 pages,LaTex fil
Radiative non-isothermal Bondi accretion onto a massive black hole
In this paper, we present the classical Bondi accretion theory for the case
of non-isothermal accretion processes onto a supermassive black hole (SMBH),
including the effects of X-ray heating and the radiation force due to electron
scattering and spectral lines. The radiation field is calculated by considering
an optically thick, geometrically thin, standard accretion disk as the emitter
of UV photons and a spherical central object as a source of X-ray emission. In
the present analysis, the UV emission from the accretion disk is assumed to
have an angular dependence, while the X-ray/central object radiation is assumed
to be isotropic. This allows us to build streamlines in any angular direction
we need to. The influence of both types of radiation is evaluated for different
flux fractions of the X-ray and UV emissions with and without the effects of
spectral line driving. We find that the radiation emitted near the SMBH
interacts with the infalling matter and modifies the accretion dynamics. In the
presence of line driving, a transition resembles from pure type 1 & 2 to type 5
solutions (see Fig2.1 of Frank etal. 2002), which takes place regardless of
whether or not the UV emission dominates over the X-ray emission. We compute
the radiative factors at which this transition occurs, and discard type 5
solution from all our models. Estimated values of the accretion radius and
accretion rate in terms of the classical Bondi values are also given. The
results are useful for the construction of proper initial conditions for
time-dependent hydrodynamical simulations of accretion flows onto SMBH at the
centre of galaxies.Comment: 10 pages, 10 figures, Accepted to be published in A&
A new determination of the Pomeron intercept in hard processes
A method allowing for a direct comparison of data with theoreticalpredictions is proposed for forward jet production at HERA. It avoids thereconstruction of multi-parton contributions by expressing the experimentalcuts directly as correction factors on the QCD forward jet cross-section. Anapplication to the determination of the {\it effective} Pomeron intercept inthe BFKL-LO parametrization from data at HERA leads to a good fitwith a significantly higher {\it effective} intercept, than for proton (total and diffractive)structure functions. It is however less than the value of the pomeron interceptusing dijets with large rapidity intervals obtained at Tevatron. We alsoevaluate the rapidity veto contribution to the higher order BFKL corrections.The method can be extended to other theoretical inputs
Variable stars in the globular cluster M28 (NGC 6626)
We present a new search for variable stars in the Galactic globular cluster
M28 (NGC 6626). The search is based on a series of BVI images obtained with the
SMARTS Consortium's 1.3m telescope at Cerro Tololo Inter-American Observatory,
Chile. The search was carried out using the ISIS v2.2 image subtraction
package. We find a total of 25 variable stars in the field of the cluster, 9
being new discoveries. Of the newly found variables, 1 is an ab-type RR Lyrae
star, 6 are c-type RR Lyrae, and 2 are long-period/semi-regular variables. V22,
previously classified as a type II Cepheid, appears as a bona-fide RRc in our
data. In turn, V20, previously classified as an ab-type RR Lyrae, could not be
properly phased with any reasonable period. The properties of the ab-type RR
Lyrae stars in M28 appear most consistent with an Oosterhoff-intermediate
classification, which is unusual for bona-fide Galactic globulars clusters.
However, the cluster's c-type variables do not clearly support such an
Oosterhoff type, and a hybrid Oosterhoff I/II system is accordingly another
possibility, thus raising the intriguing possibility of multiple populations
being present in M28. Coordinates, periods, and light curves in differential
fluxes are provided for all the detected variables.Comment: A&A, in pres
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