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

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

Design Studies for a High Current Bunching System for CLIC Test Facility (CTF3) Drive Beam

A bunching system is proposed for the initial stage of CTF3 which consists of one (two) 3 GHz prebunchers and one 3 GHz travelling wave (TW) buncher with variable phase velocities. The electron beam is emitted from a 140 KV DC gun. Since the macropulse beam current (3.5 A) at the exit of the TW buncher is rather high, inside the TW buncher one has to take the beam loading effect into consideration. By using PARMELA, it is shown numerically that the bunching system can provide the bunches whose properties satisfy the design requirement of CTF3. The 0.8 m long TW buncher working at 2pi/3 mode has two phase velocities, 0.75 and 1. The dimensions of the caities in the two phase velocity regions are proposed considering the beam loading effect. The transient beam loading effect and the multibunch transverse instabilities are studied numerically, and it is concluded that higher order mode couplers should be installed in the TW buncher with the loaded quality factor of the dipole mode lower than 80.Comment: 5 figures, presented at the Linear Accelerator Conference 2000, August 2000, US

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

Onset of the nonlinear dielectric response of glasses in the two-level system model

We have calculated the real part $\chi'$ of the nonlinear dielectric susceptibility of amorphous insulators in the kHz range, by using the two-level system model and a nonperturbative numerical quantum approach. At low temperature $T$, it is first shown that the standard two-level model should lead to a \textit{decrease} of $\chi'$ when the measuring field $E$ is raised, since raising $E$ increases the population of the upper level and induces Rabi oscillations canceling the ones induced from the ground level. This predicted $E$-induced decrease of $\chi'$ is at \textit{odds} with experiments. However, a \textit{good agreement} with low-frequency experimental nonlinear data is achieved if, in our fully quantum simulations, interactions between defects are taken into account by a new relaxation rate whose efficiency increases as $\sqrt{E}$, as was proposed recently by Burin \textit{et al.} (Phys. Rev. Lett. {\bf 86}, 5616 (2001)). In this approach, the behavior of $\chi'$ at low $T$ is mainly explained by the efficiency of this new relaxation channel. This new relaxation rate could be further tested since it is shown that it should lead: \textit{i)} to a completely new nonlinear behavior for samples whose thickness is $\simeq 10$ nm; \textit{ii)} to a decrease of nonequilibrium effects when $E$ is increased.Comment: latex Sept02.tex, 5 files, 4 figures, 17 pages, submitted to Eur. Phys. J. B. Text change