532 research outputs found
Thermodynamic formalism for contracting Lorenz flows
We study the expansion properties of the contracting Lorenz flow introduced
by Rovella via thermodynamic formalism. Specifically, we prove the existence of
an equilibrium state for the natural potential for the contracting Lorenz flow and for in an interval
containing . We also analyse the Lyapunov spectrum of the flow in terms
of the pressure
Lyapunov spectrum of asymptotically sub-additive potentials
For general asymptotically sub-additive potentials (resp. asymptotically
additive potentials) on general topological dynamical systems, we establish
some variational relations between the topological entropy of the level sets of
Lyapunov exponents, measure-theoretic entropies and topological pressures in
this general situation. Most of our results are obtained without the assumption
of the existence of unique equilibrium measures or the differentiability of
pressure functions. Some examples are constructed to illustrate the
irregularity and the complexity of multifractal behaviors in the sub-additive
case and in the case that the entropy map that is not upper-semi continuous.Comment: 44 page
The Ring Imaging Cherenkov detector (RICH) of the AMS experiment
The Alpha Magnetic Spectrometer (AMS) experiment to be installed on the
International Space Station (ISS) will be equipped with a proximity focusing
Ring Imaging Cherenkov (RICH) detector for measuring the electric charge and
velocity of the charged cosmic particles. A RICH prototype consisting of 96
photomultiplier units, including a piece of the conical reflector, was built
and its performance evaluated with ion beam data. Preliminary results of the
in-beam tests performed with ion fragments resulting from collisions of a 158
GeV/c/nuc primary beam of Indium ions (CERN SPS) on a Pb target are reported.
The collected data included tests to the final front-end electronics and to
different aerogel radiators. Cherenkov rings for a large range of charged
nuclei and with reflected photons were observed. The data analysis confirms the
design goals. Charge separation up to Fe and velocity resolution of the order
of 0.1% for singly charged particles are obtained.Comment: 29th International Conference on Cosmic Rays (Pune, India
The Hausdorff and dynamical dimensions of self-affine sponges : a dimension gap result
We construct a self-affine sponge in R 3 whose dynamical dimension, i.e. the supremum of the Hausdorff dimensions of its invariant measures, is strictly less than its Hausdorff dimension. This resolves a long-standing open problem in the dimension theory of dynamical systems, namely whether every expanding repeller has an ergodic invariant measure of full Hausdorff dimension. More generally we compute the Hausdorff and dynamical dimensions of a large class of self-affine sponges, a problem that previous techniques could only solve in two dimensions. The Hausdorff and dynamical dimensions depend continuously on the iterated function system defining the sponge, implying that sponges with a dimension gap represent a nonempty open subset of the parameter space
Black Hole Thermodynamics: Entropy, Information and Beyond
We review some recent advances in black hole thermodynamics, including
statistical mechanical origins of black hole entropy and its leading order
corrections, from the viewpoints of various quantum gravity theories. We then
examine the information loss problem and some possible approaches to its
resolution. Finally, we study some proposed experiments which may be able to
provide experimental signatures of black holes.Comment: Plenary talk given at the Fifth International Conference on
Gravitation and Cosmology, Cochin, 7 January 2004. 13 pages, Revte
Invariant elliptic curves as attractors in the projective plane
Let f be a rational self-map of P^2 which leaves invariant an elliptic curve
C with strictly negative transverse Lyapunov exponent. We show that C is an
attractor, i.e. it possesses a dense orbit and its basin is of strictly
positive measure
How does Inflation Depend Upon the Nature of Fluids Filling Up the Universe in Brane World Scenario
By constructing different parameters which are able to give us the
information about our universe during inflation,(specially at the start and the
end of the inflationary universe) a brief idea of brane world inflation is
given in this work. What will be the size of the universe at the end of
inflation,i.e.,how many times will it grow than today's size is been speculated
and analysed thereafter. Different kinds of fluids are taken to be the matter
inside the brane. It is observed that in the case of highly positive pressure
grower gas like polytropic,the size of the universe at the end of inflation is
comparitively smaller. Whereas for negative pressure creators (like chaplygin
gas) this size is much bigger. Except thse two cases, inflation has been
studied for barotropic fluid and linear redshift parametrization too. For them the size of the universe after
inflation is much more high. We also have seen that this size does not depend
upon the potential energy at the end of the inflation. On the contrary, there
is a high impact of the initial potential energy upon the size of inflation.Comment: 20 page
Loop Quantum Gravity
The problem of finding the quantum theory of the gravitational field, and
thus understanding what is quantum spacetime, is still open. One of the most
active of the current approaches is loop quantum gravity. Loop quantum gravity
is a mathematically well-defined, non-perturbative and background independent
quantization of general relativity, with its conventional matter couplings. The
research in loop quantum gravity forms today a vast area, ranging from
mathematical foundations to physical applications. Among the most significative
results obtained are: (i) The computation of the physical spectra of
geometrical quantities such as area and volume; which yields quantitative
predictions on Planck-scale physics. (ii) A derivation of the
Bekenstein-Hawking black hole entropy formula. (iii) An intriguing physical
picture of the microstructure of quantum physical space, characterized by a
polymer-like Planck scale discreteness. This discreteness emerges naturally
from the quantum theory and provides a mathematically well-defined realization
of Wheeler's intuition of a spacetime ``foam''. Long standing open problems
within the approach (lack of a scalar product, overcompleteness of the loop
basis, implementation of reality conditions) have been fully solved. The weak
part of the approach is the treatment of the dynamics: at present there exist
several proposals, which are intensely debated. Here, I provide a general
overview of ideas, techniques, results and open problems of this candidate
theory of quantum gravity, and a guide to the relevant literature.Comment: Review paper written for the electronic journal `Living Reviews'. 34
page
Background Independent Quantum Gravity: A Status Report
The goal of this article is to present an introduction to loop quantum
gravity -a background independent, non-perturbative approach to the problem of
unification of general relativity and quantum physics, based on a quantum
theory of geometry. Our presentation is pedagogical. Thus, in addition to
providing a bird's eye view of the present status of the subject, the article
should also serve as a vehicle to enter the field and explore it in detail. To
aid non-experts, very little is assumed beyond elements of general relativity,
gauge theories and quantum field theory. While the article is essentially
self-contained, the emphasis is on communicating the underlying ideas and the
significance of results rather than on presenting systematic derivations and
detailed proofs. (These can be found in the listed references.) The subject can
be approached in different ways. We have chosen one which is deeply rooted in
well established physics and also has sufficient mathematical precision to
ensure that there are no hidden infinities. In order to keep the article to a
reasonable size, and to avoid overwhelming non-experts, we have had to leave
out several interesting topics, results and viewpoints; this is meant to be an
introduction to the subject rather than an exhaustive review of it.Comment: 125 pages, 5 figures (eps format), the final version published in CQ
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