80,516 research outputs found
The Steiner tree problem revisited through rectifiable G-currents
The Steiner tree problem can be stated in terms of finding a connected set of
minimal length containing a given set of finitely many points. We show how to
formulate it as a mass-minimization problem for -dimensional currents with
coefficients in a suitable normed group. The representation used for these
currents allows to state a calibration principle for this problem. We also
exhibit calibrations in some examples
Tusnady's inequality revisited
Tusnady's inequality is the key ingredient in the KMT/Hungarian coupling of
the empirical distribution function with a Brownian bridge. We present an
elementary proof of a result that sharpens the Tusnady inequality, modulo
constants. Our method uses the beta integral representation of Binomial tails,
simple Taylor expansion and some novel bounds for the ratios of normal tail
probabilities.Comment: Published at http://dx.doi.org/10.1214/009053604000000733 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Quantization of the Nonlinear Sigma Model Revisited
We revisit the subject of perturbatively quantizing the nonlinear sigma model
in two dimensions from a rigorous, mathematical point of view. Our main
contribution is to make precise the cohomological problem of eliminating
potential anomalies that may arise when trying to preserve symmetries under
quantization. The symmetries we consider are twofold: (i) diffeomorphism
covariance for a general target manifold; (ii) a transitive group of isometries
when the target manifold is a homogeneous space. We show that there are no
anomalies in case (i) and that (ii) is also anomaly-free under additional
assumptions on the target homogeneous space, in agreement with the work of
Friedan. We carry out some explicit computations for the -model. Finally,
we show how a suitable notion of the renormalization group establishes the
Ricci flow as the one loop renormalization group flow of the nonlinear sigma
model.Comment: 51 page
The Cerenkov effect revisited: from swimming ducks to zero modes in gravitational analogs
We present an interdisciplinary review of the generalized Cerenkov emission
of radiation from uniformly moving sources in the different contexts of
classical electromagnetism, superfluid hydrodynamics, and classical
hydrodynamics. The details of each specific physical systems enter our theory
via the dispersion law of the excitations. A geometrical recipe to obtain the
emission patterns in both real and wavevector space from the geometrical shape
of the dispersion law is discussed and applied to a number of cases of current
experimental interest. Some consequences of these emission processes onto the
stability of condensed-matter analogs of gravitational systems are finally
illustrated.Comment: Lecture Notes at the IX SIGRAV School on "Analogue Gravity" in Como,
Italy from May 16th-21th, 201
A continuous model of transportation revisited
We review two models of optimal transport, where congestion effects during
the transport can be possibly taken into account. The first model is Beckmann's
one, where the transport activities are modeled by vector fields with given
divergence. The second one is the model by Carlier et al. (SIAM J Control Optim
47: 1330-1350, 2008), which in turn is the continuous reformulation of
Wardrop's model on graphs. We discuss the extensions of these models to their
natural functional analytic setting and show that they are indeed equivalent,
by using Smirnov decomposition theorem for normal 1-currents.Comment: 26 pages. Theorem A.20 of v1 was not correct: we removed it and
replaced it with the counterexample A.18 in v2. We also made some
improvements to the wording and corrected some typo
The Central Charge of the Warped AdS^3 Black Hole
The AdS/CFT conjecture offers the possibility of a quantum description for a
black hole in terms of a CFT. This has led to the study of general AdS^3 type
black holes with a view to constructing an explicit toy quantum black hole
model. Such a CFT description would be characterized by its central charge and
the dimensions of its primary fields. Recently the expression for the central
charges (C_L, C_R) of the CFT dual to the warped AdS^3 have been determined
using asymptotic symmetry arguments. The central charges depend, as expected,
on the warping factor. We show that topological arguments, used by Witten to
constrain central charges for the BTZ black hole, can be generalized to deal
with the warped AdS^3 case. Topology constrains the warped factor to be
rational numbers while quasinormal modes are conjectured to give the dimensions
of primary fields. We find that in the limit when warping is large or when it
takes special rational values the system tends to Witten's conjectured unique
CFT's with central charges that are multiples of 24.Comment: 6 pages, Latex fil
Unruh effect revisited
The vacuum energy density of free scalar quantum field phgr in a Rindler distributional space-time with distributional Levi-Cività connection is considered. It has been widely believed that, except in very extreme situations, the influence of acceleration on quantum fields should amount to just small, sub-dominant contributions. Here we argue that this belief is wrong by showing that in a Rindler distributional background space-time with distributional Levi-Cività connection the vacuum energy of free quantum fields is forced, by the very same background distributional space-time such the Rindler distributional background space-time, to become dominant over any classical energy density component. This semiclassical gravity effect finds its roots in the singular behavior of quantum fields on a Rindler distributional space-times with distributional Levi-Cività connection. In particular we obtain that the vacuum fluctuations 〈phgr2〉 has a singular behavior on a Rindler horizon. Therefore sufficiently strongly accelerated observer burns up near the Rindler horizon. Thus Polchinski's account doesn't violate of the Einstein equivalence principl
Interfaces endowed with non-constant surface energies revisited with the d'Alembert-Lagrange principle
The equation of motions and the conditions on surfaces and edges between
fluids and solids in presence of non-constant surface energies, as in the case
of surfactants attached to the fluid particles at the interfaces, are revisited
under the principle of virtual work. We point out that adequate behaviors of
surface concentrations may drastically modify the surface tension which
naturally appears in the Laplace and the Young-Dupr\'e equations. Thus, the
principle of virtual work points out a strong difference between the two
revisited concepts of surface energy and surface tension.Comment: 20 page
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