Arithmetic area for m planar Brownian paths

We pursue the analysis made in [1] on the arithmetic area enclosed by m closed Brownian paths. We pay a particular attention to the random variable S{n1,n2, ...,n} (m) which is the arithmetic area of the set of points, also called winding sectors, enclosed n1 times by path 1, n2 times by path 2, ...,nm times by path m. Various results are obtained in the asymptotic limit m->infinity. A key observation is that, since the paths are independent, one can use in the m paths case the SLE information, valid in the 1-path case, on the 0-winding sectors arithmetic area.Comment: 12 pages, 2 figure

The Local Time Distribution of a Particle Diffusing on a Graph

We study the local time distribution of a Brownian particle diffusing along the links on a graph. In particular, we derive an analytic expression of its Laplace transform in terms of the Green's function on the graph. We show that the asymptotic behavior of this distribution has non-Gaussian tails characterized by a nontrivial large deviation function.Comment: 8 pages, two figures (included

Structures observed on the spot radiance fields during the FIRE experiment

Three Spot images taken during the FIRE experiment on stratocumulus are analyzed. From this high resolution data detailed observations of the true cloud radiance field may be made. The structure and inhomogeneity of these radiance fields hold important implications for the radiation budget, while the fine scale structure in radiance field provides information on cloud dynamics. Wieliki and Welsh, and Parker et al., have quantified the inhomogeneities of the cumulus clouds through a careful examination of the distribution of cloud (and hole) size as functions of an effective cloud diameter and radiance threshold. Cahalan (1988) has compared for different cloud types of (stratocumulus, fair weather cumulus, convective clouds in the ITCZ) the distributions of clouds (and holes) sizes, the relation between the size and the perimeter of these clouds (and holes), and examining the possibility of scale invariance. These results are extended from LANDSAT resolution (57 m and 30 m) to the Spot resolution (10 m) resolution in the case of boundary layer clouds. Particular emphasis is placed on the statistics of zones of high and low reflectivity as a function of a threshold reflectivity

Analyse de la variabilité spatiale et temporelle du partage ruissellement-infiltration pour le système sol-bananier à la surface d'un andosol de Guadeloupe à l'échelle locale du bananier

Ce mémoire s'intéresse au partage ruissellement - infiltration à l'échelle locale de la plante et de son environnement immédiat pour le système sol - bananier sur andosols de Guadeloupe. Il repose sur l'analyse des données pluie - flux de ruissellement complétée par l'analyse des vidéos du ruissellement. Celles-ci montrent que la genèse du ruissellement présente une variabilité spatiale caractérisée par certaines zones contributives au ruissellement tandis que d'autres zones infiltrent la pluie incidente. Les zones contributives peuvent être reliées aux zones de concentration de la pluie incidente par le bananier (stemflow, zones d'égouttages des feuilles). Le ruissellement présente également une évolution temporelle à l'échelle de l'évènement pluvieux qui est liée aux intensités pluviométriques. L'analyse approfondie de données de pluies et de ruissellement recueillies au cours de l'été 2004 permet de différencier plusieurs phases successives dans la dynamique du ruissellement. Elles sont marquées par un coefficient de ruissellement (CR) constant par morceaux avec une rupture nette entre les deux premières phases. Cette rupture est régie par les intensités pluviométriques. Nous concluons que le ruissellement est de type hortonien par dépassement de la conductivité hydraulique à saturation Ks mesurée (Ks=60mm/h). Mais dans ce cas et en l'absence de concentration de la pluie par le bananier, les intensités pluviométriques mesurées ne permettent pas d'expliquer un tel ruissellement. Notre hypothèse est donc que la redistribution des pluies par le bananier permet, par apports concentrés en certaines zones, d'expliquer nos observations. Cette hypothèse est testée en créant un modèle pluie débit incluant une fonction de redistribution de la pluie. Les résultats de la modélisation valident cette hypothèse et confirment donc l'influence prépondérante de la redistribution des pluies dans le fonctionnement hydrologique du système sol - bananier à l'échelle locale de la plante. (Résumé d'auteur

Localization Properties in One Dimensional Disordered Supersymmetric Quantum Mechanics

A model of localization based on the Witten Hamiltonian of supersymmetric quantum mechanics is considered. The case where the superpotential $\phi(x)$ is a random telegraph process is solved exactly. Both the localization length and the density of states are obtained analytically. A detailed study of the low energy behaviour is presented. Analytical and numerical results are presented in the case where the intervals over which $\phi(x)$ is kept constant are distributed according to a broad distribution. Various applications of this model are considered.Comment: 43 pages, plain TEX, 8 figures not included, available upon request from the Authors

Persistent Currents and Magnetization in two-dimensional Magnetic Quantum Systems

Persistent currents and magnetization are considered for a two-dimensional electron (or gas of electrons) coupled to various magnetic fields. Thermodynamic formulae for the magnetization and the persistent current are established and the ``classical'' relationship between current and magnetization is shown to hold for systems invariant both by translation and rotation. Applications are given, including the point vortex superposed to an homogeneous magnetic field, the quantum Hall geometry (an electric field and an homogeneous magnetic field) and the random magnetic impurity problem (a random distribution of point vortices).Comment: 27 pages latex, 1 figur

Hall Conductivity for Two Dimensional Magnetic Systems

A Kubo inspired formalism is proposed to compute the longitudinal and transverse dynamical conductivities of an electron in a plane (or a gas of electrons at zero temperature) coupled to the potential vector of an external local magnetic field, with the additional coupling of the spin degree of freedom of the electron to the local magnetic field (Pauli Hamiltonian). As an example, the homogeneous magnetic field Hall conductivity is rederived. The case of the vortex at the origin is worked out in detail. This system happens to display a transverse Hall conductivity ($P$ breaking effect) which is subleading in volume compared to the homogeneous field case, but diverging at small frequency like $1/\omega^2$. A perturbative analysis is proposed for the conductivity in the random magnetic impurity problem (Poissonian vortices in the plane). At first order in perturbation theory, the Hall conductivity displays oscillations close to the classical straight line conductivity of the mean magnetic field.Comment: 28 pages, latex, 2 figure