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

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

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

Topological relaxation of entangled flux lattices: Single vs collective line dynamics

A symbolic language allowing to solve statistical problems for the systems with nonabelian braid-like topology in 2+1 dimensions is developed. The approach is based on the similarity between growing braid and "heap of colored pieces". As an application, the problem of a vortex glass transition in high-T_c superconductors is re-examined on microscopic levelComment: 4 pages (revtex), 4 figure

Statistics of reduced words in locally free and braid groups: Abstract studies and application to ballistic growth model

We study numerically and analytically the average length of reduced (primitive) words in so-called locally free and braid groups. We consider the situations when the letters in the initial words are drawn either without or with correlations. In the latter case we show that the average length of the reduced word can be increased or lowered depending on the type of correlation. The ideas developed are used for analytical computation of the average number of peaks of the surface appearing in some specific ballistic growth modelComment: 29 pages, LaTeX, 7 separated Postscript figures (available on request), submitted to J. Phys. (A): Math. Ge

Radiation budget estimates over Africa and surrounding oceans: inter-annual comparisons

International audienceThree independent datasets of Radiation Budget at the top of the atmosphere (TOA) spanning two decades are compared: the Scanner Narrow Field of View data (from ERBE, ScaRaB, and CERES instruments, 1985–2005), the ERBS Nonscanner Wide Field of View data (1985–1998) and the simulated broadband fluxes from the International Satellite Cloud Climatology Project (ISCCP-FD, 1983–2004). The analysis concerns the shortwave (SW) reflected flux, the longwave (LW) emitted flux and the net flux at the Top Of the Atmosphere (TOA) over Africa and the surrounding oceans (45° S–45° N/60° W–60° E), a region particularly impacted by climate variability. For each month, local anomalies are computed with reference to the average over this large region, and their differences between the 2002–2005 and 1985–1989 periods are analysed. These anomalies are relative values and are mostly independent on the absolute observed trends (about 2.5 Wm-2 per decade) which may be affected by possible calibration drifts. Large inter-annual variations are observed locally. Over a part of the South East Atlantic (35°–10° S/10° W–10° E), including the marine low cloud area off Angola, there is a decrease of the yearly means of net flux estimated to 2.2, 3 and 6 Wm-2 respectively for the Scanner, Nonscanner and ISCPP-FD data. Over a narrow strip of the Sahel Zone, the net flux increases by about 5 Wm-2

Localization effects in a periodic quantum graph with magnetic field and spin-orbit interaction

A general technique for the study of embedded quantum graphs with magnetic fields and spin-orbit interaction is presented. The analysis is used to understand the contribution of Rashba constant to the extreme localization induced by magnetic field in the T3 shaped quantum graph. We show that this effect is destroyed at generic values of the Rashba constant. On the other hand, for certain combinations of the Rashba constant and the magnetic parameters another series of infinitely degenerate eigenvalues appears.Comment: 25 pages, typos corrected, references extende

Statistical Interparticle Potential of an Ideal Gas of Non-Abelian Anyons

We determine and study the statistical interparticle potential of an ideal system of non-Abelian Chern-Simons (NACS) particles, comparing our results with the corresponding results of an ideal gas of Abelian anyons. In the Abelian case, the statistical potential depends on the statistical parameter and it has a "quasi-bosonic" behaviour for statistical parameter in the range (0,1/2) (non-monotonic with a minimum) and a "quasi-fermionic" behaviour for statistical parameter in the range (1/2,1) (monotonically decreasing without a minimum). In the non-Abelian case the behavior of the statistical potential depends on the Chern- Simons coupling and the isospin quantum number: as a function of these two parameters, a phase diagram with quasi-bosonic, quasi-fermionic and bosonic-like regions is obtained and investigated. Finally, using the obtained expression for the statistical potential, we compute the second virial coefficient of the NACS gas, which correctly reproduces the results available in literature.Comment: 21 pages, 4 color figure

On the spectrum of the Laplace operator of metric graphs attached at a vertex -- Spectral determinant approach

We consider a metric graph $\mathcal{G}$ made of two graphs $\mathcal{G}_1$ and $\mathcal{G}_2$ attached at one point. We derive a formula relating the spectral determinant of the Laplace operator $S_\mathcal{G}(\gamma)=\det(\gamma-\Delta)$ in terms of the spectral determinants of the two subgraphs. The result is generalized to describe the attachment of $n$ graphs. The formulae are also valid for the spectral determinant of the Schr\"odinger operator $\det(\gamma-\Delta+V(x))$.Comment: LaTeX, 8 pages, 7 eps figures, v2: new appendix, v3: discussions and ref adde

Surgical treatment of large incisional hernias by intraperitoneal insertion of Parietex® composite mesh with an associated aponeurotic graft (280 cases)

AIMS OF THE STUDY: To evaluate post-operative complications and the recurrence rate after repair of large ventral incisional hernia with an open technique using intraperitoneal composite mesh and an associated aponeurotic overlay. PATIENTS AND METHODS: This prospective study included a total of 280 patients who underwent repair of large incisional hernia using Parietex(®) composite mesh. RESULTS: The post-operative mortality rate was 0.35%. Six patients (2%) developed subcutaneous surgical site infection without infection of the prosthesis. Six other patients (2%) developed a deep-seated infection; in three cases, the mesh had to be removed. Nine patients (3.2%) developed recurrent incisional hernia. CONCLUSION: Large ventral incisional hernias can be effectively treated by the intraperitoneal placement of Parietex(®) composite mesh overlaid by an aponeurotic graft; the incidence of complications in this prospective study was very low