1,263 research outputs found
A geometric study of Wasserstein spaces: Hadamard spaces
Optimal transport enables one to construct a metric on the set of
(sufficiently small at infinity) probability measures on any (not too wild)
metric space X, called its Wasserstein space W(X). In this paper we investigate
the geometry of W(X) when X is a Hadamard space, by which we mean that has
globally non-positive sectional curvature and is locally compact. Although it
is known that -except in the case of the line- W(X) is not non-positively
curved, our results show that W(X) have large-scale properties reminiscent of
that of X. In particular we define a geodesic boundary for W(X) that enables us
to prove a non-embeddablity result: if X has the visibility property, then the
Euclidean plane does not admit any isometric embedding in W(X).Comment: This second version contains only the first part of the preceeding
one. The visibility properties of W(X) and the isometric rigidity have been
split off to other articles after a referee's commen
Nernst quantum oscillations in bulk semi-metals
With a widely available magnetic field of 10 T, one can attain the quantum
limit in bismuth and graphite. At zero magnetic field, these two elemental
semi-metals host a dilute liquid of carriers of both signs. When the quantum
limit is attained, all quasi-particles are confined to a few Landau tubes. Each
time a Landau tube is squeezed before definitely leaving the Fermi surface, the
Nernst response sharply peaks. In bismuth, additional Nernst peaks, unexpected
in the non-interacting picture, are resolved beyond the quantum limit. The
amplitude of these unexpected Nernst peaks is larger in the samples with the
longest electron mean-free-path.Comment: Accepted for publication in Journal of Physics: Condensed Matter's
special issue on Strongly Correlated Electron Systems(SCES
Influence of blade aerodynamic model on the prediction of helicopter high-frequency airloads
Brownâs vorticity transport model has been used to investigate the inïŹuence of the blade aerodynamic model on the accuracy with which the high-frequency airloads associated with helicopter bladeâvortex interactions can be predicted. The model yields an accurate representation of the wake structure yet allows signiïŹcant ïŹexibility in the way that the blade loading can be represented. A simple lifting-line model and a somewhat more sophisticated liftingchord model, based on unsteady thin aerofoil theory, are compared. A marked improvement in the accuracy of the predicted high-frequency airloads of the higher harmonic control aeroacoustic rotor is obtained when the liftingchord model is used instead of the lifting-line approach, and the quality of the prediction is affected less by the computational resolution of the wake. The lifting-line model overpredicts the amplitude of the lift response to bladeâvortex interactions as the computational grid is reïŹned, exposing the fundamental deïŹciencies in this approach when modeling the aerodynamic response of the blade to interactions with vortices that are much smaller than its chord. The airloads that are predicted using the lifting-chord model are relatively insensitive to the resolution of the computation, and there are fundamental reasons to believe that properly converged numerical solutions may be attainable using this approach
Memory Effects and Scaling Laws in Slowly Driven Systems
This article deals with dynamical systems depending on a slowly varying
parameter. We present several physical examples illustrating memory effects,
such as metastability and hysteresis, which frequently appear in these systems.
A mathematical theory is outlined, which allows to show existence of hysteresis
cycles, and determine related scaling laws.Comment: 28 pages (AMS-LaTeX), 18 PS figure
Giant Magnons and Singular Curves
We obtain the giant magnon of Hofman-Maldacena and its dyonic generalisation
on R x S^3 < AdS_5 x S^5 from the general elliptic finite-gap solution by
degenerating its elliptic spectral curve into a singular curve. This alternate
description of giant magnons as finite-gap solutions associated to singular
curves is related through a symplectic transformation to their already
established description in terms of condensate cuts developed in
hep-th/0606145.Comment: 34 pages, 17 figures, minor change in abstrac
Random graph states, maximal flow and Fuss-Catalan distributions
For any graph consisting of vertices and edges we construct an
ensemble of random pure quantum states which describe a system composed of
subsystems. Each edge of the graph represents a bi-partite, maximally entangled
state. Each vertex represents a random unitary matrix generated according to
the Haar measure, which describes the coupling between subsystems. Dividing all
subsystems into two parts, one may study entanglement with respect to this
partition. A general technique to derive an expression for the average
entanglement entropy of random pure states associated to a given graph is
presented. Our technique relies on Weingarten calculus and flow problems. We
analyze statistical properties of spectra of such random density matrices and
show for which cases they are described by the free Poissonian
(Marchenko-Pastur) distribution. We derive a discrete family of generalized,
Fuss-Catalan distributions and explicitly construct graphs which lead to
ensembles of random states characterized by these novel distributions of
eigenvalues.Comment: 37 pages, 24 figure
Mathematical description of bacterial traveling pulses
The Keller-Segel system has been widely proposed as a model for bacterial
waves driven by chemotactic processes. Current experiments on {\em E. coli}
have shown precise structure of traveling pulses. We present here an
alternative mathematical description of traveling pulses at a macroscopic
scale. This modeling task is complemented with numerical simulations in
accordance with the experimental observations. Our model is derived from an
accurate kinetic description of the mesoscopic run-and-tumble process performed
by bacteria. This model can account for recent experimental observations with
{\em E. coli}. Qualitative agreements include the asymmetry of the pulse and
transition in the collective behaviour (clustered motion versus dispersion). In
addition we can capture quantitatively the main characteristics of the pulse
such as the speed and the relative size of tails. This work opens several
experimental and theoretical perspectives. Coefficients at the macroscopic
level are derived from considerations at the cellular scale. For instance the
stiffness of the signal integration process turns out to have a strong effect
on collective motion. Furthermore the bottom-up scaling allows to perform
preliminary mathematical analysis and write efficient numerical schemes. This
model is intended as a predictive tool for the investigation of bacterial
collective motion
Multifractal Analysis of inhomogeneous Bernoulli products
We are interested to the multifractal analysis of inhomogeneous Bernoulli
products which are also known as coin tossing measures. We give conditions
ensuring the validity of the multifractal formalism for such measures. On
another hand, we show that these measures can have a dense set of phase
transitions
A search for low-mass WIMPs with EDELWEISS-II heat-and-ionization detectors
We report on a search for low-energy (E < 20 keV) WIMP-induced nuclear
recoils using data collected in 2009 - 2010 by EDELWEISS from four germanium
detectors equipped with thermal sensors and an electrode design (ID) which
allows to efficiently reject several sources of background. The data indicate
no evidence for an exponential distribution of low-energy nuclear recoils that
could be attributed to WIMP elastic scattering after an exposure of 113 kg.d.
For WIMPs of mass 10 GeV, the observation of one event in the WIMP search
region results in a 90% CL limit of 1.0x10^-5 pb on the spin-independent
WIMP-nucleon scattering cross-section, which constrains the parameter space
associated with the findings reported by the CoGeNT, DAMA and CRESST
experiments.Comment: PRD rapid communication accepte
HQET at order : II. Spectroscopy in the quenched approximation
Using Heavy Quark Effective Theory with non-perturbatively determined
parameters in a quenched lattice calculation, we evaluate the splittings
between the ground state and the first two radially excited states of the
system at static order. We also determine the splitting between first excited
and ground state, and between the and ground states to order
. The Generalized Eigenvalue Problem and the use of all-to-all
propagators are important ingredients of our approach.Comment: (1+18) pages, 3 figures (4 pdf files); pdflatex; v2: corrections to
table 1, results unaffecte
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