401 research outputs found
Correlated Gaussian systems exhibiting additive power-law entropies
We show, on purely statistical grounds and without appeal to any physical
model, that a power-law entropy , with , can be {\it
extensive}. More specifically, if the components of a vector are distributed according to a Gaussian probability distribution
, the associated entropy exhibits the extensivity property for
special types of correlations among the . We also characterize this kind
of correlation.Comment: 2 figure
Enigma of ultraluminous X-ray sources may be resolved by 3D-spectroscopy (MPFS data)
The ultraluminous X-ray sources (ULXs) were isolated in external galaxies for
the last 5 years. Their X-ray luminosities exceed 100-10000 times those of
brightest Milky Way black hole binaries and they are extremely variable. There
are two models for the ULXs, the best black hole candidates. 1. They are
supercritical accretion disks around a stellar mass black hole like that in
SS433, observed close to the disk axes. 2. They are Intermediate Mass Black
Holes (of 100-10000 solar masses). Critical observations which may throw light
upon the ULXs nature come from observations of nebulae around the ULXs. We
present results of 3D-spectroscopy of nebulae around several ULXs located in
galaxies at 3-6 Mpc distances. We found that the nebulae to be powered by their
central black holes. The nebulae are shocked and dynamically perturbed probably
by jets. The nebulae are compared with SS433 nebula (W50).Comment: Proceedings of the ESO and Euro3D Workshop "Science Perspectives for
3D Spectroscopy", Garching (Germany), October 10-14, 2005. M. Kissler-Patig,
M.M. Roth and J.R. Walsh (eds.
Thermodynamics with long-range interactions: from Ising models to black-holes
New methods are presented which enables one to analyze the thermodynamics of
systems with long-range interactions. Generically, such systems have entropies
which are non-extensive, (do not scale with the size of the system). We show
how to calculate the degree of non-extensivity for such a system. We find that
a system interacting with a heat reservoir is in a probability distribution of
canonical ensembles. The system still possesses a parameter akin to a global
temperature, which is constant throughout the substance. There is also a useful
quantity which acts like a {\it local temperatures} and it varies throughout
the substance. These quantities are closely related to counterparts found in
general relativity. A lattice model with long-range spin-spin coupling is
studied. This is compared with systems such as those encountered in general
relativity, and gravitating systems with Newtonian-type interactions. A
long-range lattice model is presented which can be seen as a black-hole analog.
One finds that the analog's temperature and entropy have many properties which
are found in black-holes. Finally, the entropy scaling behavior of a
gravitating perfect fluid of constant density is calculated. For weak
interactions, the entropy scales like the volume of the system. As the
interactions become stronger, the entropy becomes higher near the surface of
the system, and becomes more area-scaling.Comment: Corrects some typos found in published version. Title changed 22
pages, 2 figure
How fundamental is the character of thermal uncertainty relations?
We show that thermodynamic uncertainties do not preserve their form if the
underlying probability distribution is transformed into an escort one.
Heisenberg's relations, on the other hand, are not affected by such
transformation. We conclude therefore that the former uncertainty cannot be as
fundamental as the quantum one.Comment: 4 pages, no figure
Generalized thermodynamics and Fokker-Planck equations. Applications to stellar dynamics, two-dimensional turbulence and Jupiter's great red spot
We introduce a new set of generalized Fokker-Planck equations that conserve
energy and mass and increase a generalized entropy until a maximum entropy
state is reached. The concept of generalized entropies is rigorously justified
for continuous Hamiltonian systems undergoing violent relaxation. Tsallis
entropies are just a special case of this generalized thermodynamics.
Application of these results to stellar dynamics, vortex dynamics and Jupiter's
great red spot are proposed. Our prime result is a novel relaxation equation
that should offer an easily implementable parametrization of geophysical
turbulence. This relaxation equation depends on a single key parameter related
to the skewness of the fine-grained vorticity distribution. Usual
parametrizations (including a single turbulent viscosity) correspond to the
infinite temperature limit of our model. They forget a fundamental systematic
drift that acts against diffusion as in Brownian theory. Our generalized
Fokker-Planck equations may have applications in other fields of physics such
as chemotaxis for bacterial populations. We propose the idea of a
classification of generalized entropies in classes of equivalence and provide
an aesthetic connexion between topics (vortices, stars, bacteries,...) which
were previously disconnected.Comment: Submitted to Phys. Rev.
An optimization principle for deriving nonequilibrium statistical models of Hamiltonian dynamics
A general method for deriving closed reduced models of Hamiltonian dynamical
systems is developed using techniques from optimization and statistical
estimation. As in standard projection operator methods, a set of resolved
variables is selected to capture the slow, macroscopic behavior of the system,
and the family of quasi-equilibrium probability densities on phase space
corresponding to these resolved variables is employed as a statistical model.
The macroscopic dynamics of the mean resolved variables is determined by
optimizing over paths of these probability densities. Specifically, a cost
function is introduced that quantifies the lack-of-fit of such paths to the
underlying microscopic dynamics; it is an ensemble-averaged, squared-norm of
the residual that results from submitting a path of trial densities to the
Liouville equation. The evolution of the macrostate is estimated by minimizing
the time integral of the cost function. The value function for this
optimization satisfies the associated Hamilton-Jacobi equation, and it
determines the optimal relation between the statistical parameters and the
irreversible fluxes of the resolved variables, thereby closing the reduced
dynamics. The resulting equations for the macroscopic variables have the
generic form of governing equations for nonequilibrium thermodynamics, and they
furnish a rational extension of the classical equations of linear irreversible
thermodynamics beyond the near-equilibrium regime. In particular, the value
function is a thermodynamic potential that extends the classical dissipation
function and supplies the nonlinear relation between thermodynamics forces and
fluxes
Topological String Amplitudes, Complete Intersection Calabi-Yau Spaces and Threshold Corrections
We present the most complete list of mirror pairs of Calabi-Yau complete
intersections in toric ambient varieties and develop the methods to solve the
topological string and to calculate higher genus amplitudes on these compact
Calabi-Yau spaces. These symplectic invariants are used to remove redundancies
in examples. The construction of the B-model propagators leads to compatibility
conditions, which constrain multi-parameter mirror maps. For K3 fibered
Calabi-Yau spaces without reducible fibers we find closed formulas for all
genus contributions in the fiber direction from the geometry of the fibration.
If the heterotic dual to this geometry is known, the higher genus invariants
can be identified with the degeneracies of BPS states contributing to
gravitational threshold corrections and all genus checks on string duality in
the perturbative regime are accomplished. We find, however, that the BPS
degeneracies do not uniquely fix the non-perturbative completion of the
heterotic string. For these geometries we can write the topological partition
function in terms of the Donaldson-Thomas invariants and we perform a
non-trivial check of S-duality in topological strings. We further investigate
transitions via collapsing D5 del Pezzo surfaces and the occurrence of free Z2
quotients that lead to a new class of heterotic duals.Comment: 117 pages, 1 Postscript figur
Does Women's Preference for Highbrow Leisure Begin in the Family? Comparing Leisure Participation among Brothers and Sisters
Gamma-Ray Bursts: The Underlying Model
A pedagogical derivation is presented of the ``fireball'' model of gamma-ray
bursts, according to which the observable effects are due to the dissipation of
the kinetic energy of a relativistically expanding wind, a ``fireball.'' The
main open questions are emphasized, and key afterglow observations, that
provide support for this model, are briefly discussed. The relativistic outflow
is, most likely, driven by the accretion of a fraction of a solar mass onto a
newly born (few) solar mass black hole. The observed radiation is produced once
the plasma has expanded to a scale much larger than that of the underlying
``engine,'' and is therefore largely independent of the details of the
progenitor, whose gravitational collapse leads to fireball formation. Several
progenitor scenarios, and the prospects for discrimination among them using
future observations, are discussed. The production in gamma- ray burst
fireballs of high energy protons and neutrinos, and the implications of burst
neutrino detection by kilometer-scale telescopes under construction, are
briefly discussed.Comment: In "Supernovae and Gamma Ray Bursters", ed. K. W. Weiler, Lecture
Notes in Physics, Springer-Verlag (in press); 26 pages, 2 figure
Staffing and Training Aspects of Hospital Management: Some Issues for Research
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68624/2/10.1177_107755878904600205.pd
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