247 research outputs found
A measure of non-convexity in the plane and the Minkowski sum
In this paper a measure of non-convexity for a simple polygonal region in the
plane is introduced. It is proved that for "not far from convex" regions this
measure does not decrease under the Minkowski sum operation, and guarantees
that the Minkowski sum has no "holes".Comment: 5 figures; Discrete and Computational Geometry, 201
Gain properties of dye-doped polymer thin films
Hybrid pumping appears as a promising compromise in order to reach the much
coveted goal of an electrically pumped organic laser. In such configuration the
organic material is optically pumped by an electrically pumped inorganic device
on chip. This engineering solution requires therefore an optimization of the
organic gain medium under optical pumping. Here, we report a detailed study of
the gain features of dye-doped polymer thin films. In particular we introduce
the gain efficiency , in order to facilitate comparison between different
materials and experimental conditions. The gain efficiency was measured with
various setups (pump-probe amplification, variable stripe length method, laser
thresholds) in order to study several factors which modify the actual gain of a
layer, namely the confinement factor, the pump polarization, the molecular
anisotropy, and the re-absorption. For instance, for a 600 nm thick 5 wt\% DCM
doped PMMA layer, the different experimental approaches give a consistent value
80 cm.MW. On the contrary, the usual model predicting the gain
from the characteristics of the material leads to an overestimation by two
orders of magnitude, which raises a serious problem in the design of actual
devices. In this context, we demonstrate the feasibility to infer the gain
efficiency from the laser threshold of well-calibrated devices. Besides,
temporal measurements at the picosecond scale were carried out to support the
analysis.Comment: 15 pages, 17 figure
Monge's transport problem in the Heisenberg group
We prove the existence of solutions to Monge transport problem between two
compactly supported Borel probability measures in the Heisenberg group equipped
with its Carnot-Caratheodory distance assuming that the initial measure is
absolutely continuous with respect to the Haar measure of the group
Symbolic approach and induction in the Heisenberg group
We associate a homomorphism in the Heisenberg group to each hyperbolic
unimodular automorphism of the free group on two generators. We show that the
first return-time of some flows in "good" sections, are conjugate to
niltranslations, which have the property of being self-induced.Comment: 18 page
Buckling Instabilities of a Confined Colloid Crystal Layer
A model predicting the structure of repulsive, spherically symmetric,
monodisperse particles confined between two walls is presented. We study the
buckling transition of a single flat layer as the double layer state develops.
Experimental realizations of this model are suspensions of stabilized colloidal
particles squeezed between glass plates. By expanding the thermodynamic
potential about a flat state of confined colloidal particles, we derive
a free energy as a functional of in-plane and out-of-plane displacements. The
wavevectors of these first buckling instabilities correspond to three different
ordered structures. Landau theory predicts that the symmetry of these phases
allows for second order phase transitions. This possibility exists even in the
presence of gravity or plate asymmetry. These transitions lead to critical
behavior and phases with the symmetry of the three-state and four-state Potts
models, the X-Y model with 6-fold anisotropy, and the Heisenberg model with
cubic interactions. Experimental detection of these structures is discussed.Comment: 24 pages, 8 figures on request. EF508
Sub-Riemannian Calculus on Hypersurfaces in Carnot Groups
We develope basic geometric quantities and properties of hypersurfaces in
Carnot groups
Quenching dynamics in CdSe nanoparticles: surface-induced defects upon dilution
International audienceWe have analyzed the decays of the fluorescence of colloidal CdSe quantum dots (QDs) suspensions during dilution and titration by the ligands. A ligand shell made of a combination of trioctylphosphine (TOP), oleylamine (OA), and stearic acid (SA) stabilizes the as-synthesized QDs. The composition of the shell was analyzed and quantified using high resolution liquid state 1H nuclear magnetic resonance (NMR) spectroscopy. A quenching of the fluorescence of the QDs is observed upon removal of the ligands by diluting the stock solution of the QDs. The fluorescence is restored by the addition of TOP. We analyze the results by assuming a binomial distribution of quenchers among the QDs and predict a linear trend in the time-resolved fluorescence decays. We have used a nonparametric analysis to show that for our QDs, 3.0 0.1 quenching sites per QD on average are revealed by the removal of TOP. We moreover show that the quenching rates of the quenching sites add up. The decay per quenching site can be compared with the decay at saturation of the dilution effect. This provides a value of 2.88 0.02 for the number of quenchers per QD. We extract the quenching dynamics of one site. It appears to be a process with a distribution of rates that does not involve the ligands
Order and Frustration in Chiral Liquid Crystals
This paper reviews the complex ordered structures induced by chirality in
liquid crystals. In general, chirality favors a twist in the orientation of
liquid-crystal molecules. In some cases, as in the cholesteric phase, this
favored twist can be achieved without any defects. More often, the favored
twist competes with applied electric or magnetic fields or with geometric
constraints, leading to frustration. In response to this frustration, the
system develops ordered structures with periodic arrays of defects. The
simplest example of such a structure is the lattice of domains and domain walls
in a cholesteric phase under a magnetic field. More complex examples include
defect structures formed in two-dimensional films of chiral liquid crystals.
The same considerations of chirality and defects apply to three-dimensional
structures, such as the twist-grain-boundary and moire phases.Comment: 39 pages, RevTeX, 14 included eps figure
Isometric group actions on Banach spaces and representations vanishing at infinity
Our main result is that the simple Lie group acts properly
isometrically on if . To prove this, we introduce property
({\BP}_0^V), for be a Banach space: a locally compact group has
property ({\BP}_0^V) if every affine isometric action of on , such
that the linear part is a -representation of , either has a fixed point
or is metrically proper. We prove that solvable groups, connected Lie groups,
and linear algebraic groups over a local field of characteristic zero, have
property ({\BP}_0^V). As a consequence for unitary representations, we
characterize those groups in the latter classes for which the first cohomology
with respect to the left regular representation on is non-zero; and we
characterize uniform lattices in those groups for which the first -Betti
number is non-zero.Comment: 28 page
First and second variation formulae for the sub-Riemannian area in three-dimensional pseudo-hermitian manifolds
We calculate the first and the second variation formula for the
sub-Riemannian area in three dimensional pseudo-hermitian manifolds. We
consider general variations that can move the singular set of a C^2 surface and
non-singular variation for C_H^2 surfaces. These formulas enable us to
construct a stability operator for non-singular C^2 surfaces and another one
for C2 (eventually singular) surfaces. Then we can obtain a necessary condition
for the stability of a non-singular surface in a pseudo-hermitian 3-manifold in
term of the pseudo-hermitian torsion and the Webster scalar curvature. Finally
we classify complete stable surfaces in the roto-traslation group RT .Comment: 36 pages. Misprints corrected. Statement of Proposition 9.8 slightly
changed and Remark 9.9 adde
- âŠ