181,700 research outputs found
Height fluctuations of a contact line: a direct measurement of the renormalized disorder correlator
We have measured the center-of-mass fluctuations of the height of a contact
line at depinning for two different systems: liquid hydrogen on a rough cesium
substrate and isopropanol on a silicon wafer grafted with silanized patches.
The contact line is subject to a confining quadratic well, provided by gravity.
From the second cumulant of the height fluctuations, we measure the
renormalized disorder correlator Delta(u), predicted by the Functional RG
theory to attain a fixed point, as soon as the capillary length is large
compared to the Larkin length set by the microscopic disorder. The experiments
are consistent with the asymptotic form for Delta(u) predicted by Functional
RG, including a linear cusp at u=0. The observed small deviations could be used
as a probe of the underlying physical processes. The third moment, as well as
avalanche-size distributions are measured and compared to predictions from
Functional RG.Comment: 6 pages, 14 figure
Distribution of velocities in an avalanche
For a driven elastic object near depinning, we derive from first principles
the distribution of instantaneous velocities in an avalanche. We prove that
above the upper critical dimension, d >= d_uc, the n-times distribution of the
center-of-mass velocity is equivalent to the prediction from the ABBM
stochastic equation. Our method allows to compute space and time dependence
from an instanton equation. We extend the calculation beyond mean field, to
lowest order in epsilon=d_uc-d.Comment: 4 pages, 2 figure
Random real trees
We survey recent developments about random real trees, whose prototype is the
Continuum Random Tree (CRT) introduced by Aldous in 1991. We briefly explain
the formalism of real trees, which yields a neat presentation of the theory and
in particular of the relations between discrete Galton-Watson trees and
continuous random trees. We then discuss the particular class of self-similar
random real trees called stable trees, which generalize the CRT. We review
several important results concerning stable trees, including their branching
property, which is analogous to the well-known property of Galton-Watson trees,
and the calculation of their fractal dimension. We then consider spatial trees,
which combine the genealogical structure of a real tree with spatial
displacements, and we explain their connections with superprocesses. In the
last section, we deal with a particular conditioning problem for spatial trees,
which is closely related to asymptotics for random planar quadrangulations.Comment: 25 page
Ablation sensor Patent
Ablation sensor for measuring char layer recession rate using electric wire
Sticky Particles and Stochastic Flows
Gaw\c{e}dzki and Horvai have studied a model for the motion of particles
carried in a turbulent fluid and shown that in a limiting regime with low
levels of viscosity and molecular diffusivity, pairs of particles exhibit the
phenomena of stickiness when they meet. In this paper we characterise the
motion of an arbitrary number of particles in a simplified version of their
model
Permeability of a one-dimensional potential barrier
Permeability of one dimensional potential barrie
Bessel processes, the Brownian snake and super-Brownian motion
We prove that, both for the Brownian snake and for super-Brownian motion in
dimension one, the historical path corresponding to the minimal spatial
position is a Bessel process of dimension -5. We also discuss a spine
decomposition for the Brownian snake conditioned on the minimizing path.Comment: Submitted to the special volume of S\'eminaire de Probabilit\'es in
memory of Marc Yo
Structural Antennas for 3cm Radar Onboard Multi-Rotor UAV
A series of 3cm amateur band radar antennas suitable for installation on a cinematic grade multi-rotor UAV were considered. A wideband open waveguide mouth antenna was developed that can be made from the existing arms of a multi-rotor UAV without any increase in weight for side-looking wall detection ranging radar. For downward looking radio altimeter, cutting slots in the arms to form slotted waveguide antennas was shown in simulation to be possible both in terms of covering the entire 3cm band from 10 to 10.5GHz and without overly weakening the arms as structural members
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