18,394 research outputs found
Equilibrium states and invariant measures for random dynamical systems
Random dynamical systems with countably many maps which admit countable
Markov partitions on complete metric spaces such that the resulting Markov
systems are uniformly continuous and contractive are considered. A
non-degeneracy and a consistency conditions for such systems, which admit some
proper Markov partitions of connected spaces, are introduced, and further
sufficient conditions for them are provided. It is shown that every uniformly
continuous Markov system associated with a continuous random dynamical system
is consistent if it has a dominating Markov chain. A necessary and sufficient
condition for the existence of an invariant Borel probability measure for such
a non-degenerate system with a dominating Markov chain and a finite (16) is
given. The condition is also sufficient if the non-degeneracy is weakened with
the consistency condition. A further sufficient condition for the existence of
an invariant measure for such a consistent system which involves only the
properties of the dominating Markov chain is provided. In particular, it
implies that every such a consistent system with a finite Markov partition and
a finite (16) has an invariant Borel probability measure. A bijective map
between these measures and equilibrium states associated with such a system is
established in the non-degenerate case. Some properties of the map and the
measures are given.Comment: The article is published in DCDS-A, but without the 3rd paragraph on
page 4 (the complete removal of the paragraph became the condition for the
publication in the DCDS-A after the reviewer ran out of the citation
suggestions collected in the paragraph
Element Abundance Determination in Hot Evolved Stars
The hydrogen-deficiency in extremely hot post-AGB stars of spectral class
PG1159 is probably caused by a (very) late helium-shell flash or a AGB final
thermal pulse that consumes the hydrogen envelope, exposing the usually-hidden
intershell region. Thus, the photospheric element abundances of these stars
allow us to draw conclusions about details of nuclear burning and mixing
processes in the precursor AGB stars. We compare predicted element abundances
to those determined by quantitative spectral analyses performed with advanced
non-LTE model atmospheres. A good qualitative and quantitative agreement is
found for many species (He, C, N, O, Ne, F, Si, Ar) but discrepancies for
others (P, S, Fe) point at shortcomings in stellar evolution models for AGB
stars. Almost all of the chemical trace elements in these hot stars can only be
identified in the UV spectral range. The Far Ultraviolet Spectroscopic Explorer
and the Hubble Space Telescope played a crucial role for this research.Comment: To appear in: Recent Advances in Spectroscopy: Theoretical,
Astrophysical, and Experimental Perspectives, Proceedings, Jan 28 - 31, 2009,
Kodaikanal, India (Springer
Local Hidden Variable Theories for Quantum States
While all bipartite pure entangled states violate some Bell inequality, the
relationship between entanglement and non-locality for mixed quantum states is
not well understood. We introduce a simple and efficient algorithmic approach
for the problem of constructing local hidden variable theories for quantum
states. The method is based on constructing a so-called symmetric
quasi-extension of the quantum state that gives rise to a local hidden variable
model with a certain number of settings for the observers Alice and Bob.Comment: 8 pages Revtex; v2 contains substantial changes, a strengthened main
theorem and more reference
Gas perturbations in cool cores of galaxy clusters: effective equation of state, velocity power spectra and turbulent heating
We present the statistical analysis of X-ray surface brightness and gas
density fluctuations in cool cores of ten, nearby and bright galaxy clusters
that have deep Chandra observations and show observational indications of
radio-mechanical AGN feedback. Within the central parts of cool cores the total
variance of fluctuations is dominated by isobaric and/or isothermal
fluctuations on spatial scales ~ 10-60 kpc, which are likely associated with
slow gas motions and bubbles of relativistic plasma. Adiabatic fluctuations
associated with weak shocks constitute less than 10 per cent of the total
variance in all clusters. The typical amplitude of density fluctuations is
small, ~ 10 per cent or less on scales of ~ 10-15 kpc. Subdominant contribution
of adiabatic fluctuations and small amplitude of density fluctuations support a
model of gentle AGN feedback as opposed to periodically explosive scenarios
which are implemented in some numerical simulations. Measured one-component
velocities of gas motions are typically below 100-150 km/s on scales < 50 kpc,
and can be up to ~ 300 km/s on ~ 100 kpc scales. The non-thermal energy is < 12
per cent of the thermal energy. Regardless of the source that drives these
motions the dissipation of the energy in such motions provides heat that is
sufficient to balance radiative cooling on average, albeit the uncertainties
are large. Presented results here support previous conclusions based on the
analysis of the Virgo and Perseus Clusters, and agree with the Hitomi
measurements. With next generation observatories like Athena and Lynx, these
techniques will be yet more powerful.Comment: 16 pages, 11 figures, submitted to MNRA
Chemical Treatment Methods Pilot (CTMP) System for Treatment of Urban Runoff – Phase I. Feasibility and Design
(pdf contains 418 pages
Random Aharonov-Bohm vortices and some funny families of integrals
A review of the random magnetic impurity model, introduced in the context of
the integer Quantum Hall effect, is presented. It models an electron moving in
a plane and coupled to random Aharonov-Bohm vortices carrying a fraction of the
quantum of flux. Recent results on its perturbative expansion are given. In
particular, some funny families of integrals show up to be related to the
Riemann and .Comment: 10 page
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