2,077 research outputs found
A Bose-Einstein Approach to the Random Partitioning of an Integer
Consider N equally-spaced points on a circle of circumference N. Choose at
random n points out of on this circle and append clockwise an arc of
integral length k to each such point. The resulting random set is made of a
random number of connected components. Questions such as the evaluation of the
probability of random covering and parking configurations, number and length of
the gaps are addressed. They are the discrete versions of similar problems
raised in the continuum. For each value of k, asymptotic results are presented
when n,N both go to infinity according to two different regimes. This model may
equivalently be viewed as a random partitioning problem of N items into n
recipients. A grand-canonical balls in boxes approach is also supplied, giving
some insight into the multiplicities of the box filling amounts or spacings.
The latter model is a k-nearest neighbor random graph with N vertices and kn
edges. We shall also briefly consider the covering problem in the context of a
random graph model with N vertices and n (out-degree 1) edges whose endpoints
are no more bound to be neighbors
Black Holes and Wormholes in 2+1 Dimensions
A large variety of spacetimes---including the BTZ black holes---can be
obtained by identifying points in 2+1 dimensional anti-de Sitter space by means
of a discrete group of isometries. We consider all such spacetimes that can be
obtained under a restriction to time symmetric initial data and one asymptotic
region only. The resulting spacetimes are non-eternal black holes with
collapsing wormhole topologies. Our approach is geometrical, and we discuss in
detail: The allowed topologies, the shape of the event horizons, topological
censorship and trapped curves.Comment: 23 pages, LaTeX, 11 figure
A Spinning Anti-de Sitter Wormhole
We construct a 2+1 dimensional spacetime of constant curvature whose spatial
topology is that of a torus with one asymptotic region attached. It is also a
black hole whose event horizon spins with respect to infinity. An observer
entering the hole necessarily ends up at a "singularity"; there are no inner
horizons.
In the construction we take the quotient of 2+1 dimensional anti-de Sitter
space by a discrete group Gamma. A key part of the analysis proceeds by
studying the action of Gamma on the boundary of the spacetime.Comment: Latex, 28 pages, 7 postscript figures included in text, a Latex file
without figures can be found at http://vanosf.physto.se/~stefan/spinning.html
Replaced with journal version, minor change
Making Anti-de Sitter Black Holes
It is known from the work of Banados et al. that a space-time with event
horizons (much like the Schwarzschild black hole) can be obtained from 2+1
dimensional anti-de Sitter space through a suitable identification of points.
We point out that this can be done in 3+1 dimensions as well. In this way we
obtain black holes with event horizons that are tori or Riemann surfaces of
genus higher than one. They can have either one or two asymptotic regions.
Locally, the space-time is isometric to anti-de Sitter space.Comment: LaTeX, 10 pages, 6 postscript figures, uses epsf.te
Electronic transport coefficients from ab initio simulations and application to dense liquid hydrogen
Using Kubo's linear response theory, we derive expressions for the
frequency-dependent electrical conductivity (Kubo-Greenwood formula),
thermopower, and thermal conductivity in a strongly correlated electron system.
These are evaluated within ab initio molecular dynamics simulations in order to
study the thermoelectric transport coefficients in dense liquid hydrogen,
especially near the nonmetal-to-metal transition region. We also observe
significant deviations from the widely used Wiedemann-Franz law which is
strictly valid only for degenerate systems and give an estimate for its valid
scope of application towards lower densities
Gott Time Machines, BTZ Black Hole Formation, and Choptuik Scaling
We study the formation of BTZ black holes by the collision of point
particles. It is shown that the Gott time machine, originally constructed for
the case of vanishing cosmological constant, provides a precise mechanism for
black hole formation. As a result, one obtains an exact analytic understanding
of the Choptuik scaling.Comment: 6 pages, Late
Toward detailed prominence seismology - I. Computing accurate 2.5D magnetohydrodynamic equilibria
Context. Prominence seismology exploits our knowledge of the linear
eigenoscillations for representative magnetohydro- dynamic models of filaments.
To date, highly idealized models for prominences have been used, especially
with respect to the overall magnetic configurations.
Aims. We initiate a more systematic survey of filament wave modes, where we
consider full multi-dimensional models with twisted magnetic fields
representative of the surrounding magnetic flux rope. This requires the ability
to compute accurate 2.5 dimensional magnetohydrodynamic equilibria that balance
Lorentz forces, gravity, and pressure gradients, while containing density
enhancements (static or in motion).
Methods. The governing extended Grad-Shafranov equation is discussed, along
with an analytic prediction for circular flux ropes for the Shafranov shift of
the central magnetic axis due to gravity. Numerical equilibria are computed
with a finite element-based code, demonstrating fourth order accuracy on an
explicitly known, non-trivial test case.
Results. The code is then used to construct more realistic prominence
equilibria, for all three possible choices of a free flux-function. We quantify
the influence of gravity, and generate cool condensations in hot cavities, as
well as multi- layered prominences.
Conclusions. The internal flux rope equilibria computed here have the
prerequisite numerical accuracy to allow a yet more advanced analysis of the
complete spectrum of linear magnetohydrodynamic perturbations, as will be
demonstrated in the companion paper.Comment: Accepted by Astronomy & Astrophysics, 15 pages, 15 figure
Toward detailed prominence seismology - II. Charting the continuous magnetohydrodynamic spectrum
Starting from accurate MHD flux rope equilibria containing prominence
condensations, we initiate a systematic survey of their linear
eigenoscillations. To quantify the full spectrum of linear MHD eigenmodes, we
require knowledge of all flux-surface localized modes, charting out the
continuous parts of the MHD spectrum. We combine analytical and numerical
findings for the continuous spectrum for realistic prominence configurations.
The equations governing all eigenmodes for translationally symmetric,
gravitating equilibria containing an axial shear flow, are analyzed, along with
their flux-surface localized limit. The analysis is valid for general 2.5D
equilibria, where either density, entropy, or temperature vary from one flux
surface to another. We analyze the mode couplings caused by the poloidal
variation in the flux rope equilibria, by performing a small gravity parameter
expansion. We contrast the analytical results with continuous spectra obtained
numerically. For equilibria where the density is a flux function, we show that
continuum modes can be overstable, and we present the stability criterion for
these convective continuum instabilities. Furthermore, for all equilibria, a
four-mode coupling scheme between an Alfvenic mode of poloidal mode number m
and three neighboring (m-1, m, m+1) slow modes is identified, occurring in the
vicinity of rational flux surfaces. For realistically prominence equilibria,
this coupling is shown to play an important role, from weak to stronger gravity
parameter g values. The analytic predictions for small g are compared with
numerical spectra, and progressive deviations for larger g are identified. The
unstable continuum modes could be relevant for short-lived prominence
configurations. The gaps created by poloidal mode coupling in the continuous
spectrum need further analysis, as they form preferred frequency ranges for
global eigenoscillations.Comment: Accepted by Astronmy & Astrophysics, 21 pages, 15 figure
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