Confinement Efficiency and Stability of a Toroidal Magnetized Plasma Device with Sheared Magnetic Field Lines using an Internal Ring Conductor

In a new toroidal laboratory plasma device including a poloidal magnetic field created by an internal circular conductor, the confinement efficiency of the magnetized plasma and the turbulence level are studied in different situations. The plasma density is greatly enhanced when a sufficient poloidal magnetic field is established. Moreover, the instabilities and the turbulence usually found in toroidal devices without shear of the magnetic field lines are suppressed when the rotational transform is present. The measurement of the plasma decay time allows to determine the confinement time of the particles which is compared to the Bohm diffusion time and to the value predicted by different diffusion models, especially the neoclassical diffusion.Comment: 3 figure

Spatial shape of avalanches in the Brownian force model

We study the Brownian force model (BFM), a solvable model of avalanche statistics for an interface, in a general discrete setting. The BFM describes the overdamped motion of elastically coupled particles driven by a parabolic well in independent Brownian force landscapes. Avalanches are defined as the collective jump of the particles in response to an arbitrary monotonous change in the well position (i.e. in the applied force). We derive an exact formula for the joint probability distribution of these jumps. From it we obtain the joint density of local avalanche sizes for stationary driving in the quasi-static limit near the depinning threshold. A saddle-point analysis predicts the spatial shape of avalanches in the limit of large aspect ratios for the continuum version of the model. We then study fluctuations around this saddle point, and obtain the leading corrections to the mean shape, the fluctuations around the mean shape and the shape asymmetry, for finite aspect ratios. Our results are finally confronted to numerical simulations.Comment: 41 pages, 16 figure

Using Users' Expectations to Adapt Business Intelligence Systems

This paper takes a look at the general characteristics of business or economic intelligence system. The role of the user within this type of system is emphasized. We propose two models which we consider important in order to adapt this system to the user. The first model is based on the definition of decisional problem and the second on the four cognitive phases of human learning. We also describe the application domain we are using to test these models in this type of system

Markov chains, R\mathscr R-trivial monoids and representation theory

We develop a general theory of Markov chains realizable as random walks on $\mathscr R$-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via M\"obius inversion along a lattice, a condition for diagonalizability of the transition matrix and some techniques for bounding the mixing time. In addition, we discuss several examples, such as Toom-Tsetlin models, an exchange walk for finite Coxeter groups, as well as examples previously studied by the authors, such as nonabelian sandpile models and the promotion Markov chain on posets. Many of these examples can be viewed as random walks on quotients of free tree monoids, a new class of monoids whose combinatorics we develop.Comment: Dedicated to Stuart Margolis on the occasion of his sixtieth birthday; 71 pages; final version to appear in IJA

Midpoint distribution of directed polymers in the stationary regime: exact result through linear response

We obtain an exact result for the midpoint probability distribution function (pdf) of the stationary continuum directed polymer, when averaged over the disorder. It is obtained by relating that pdf to the linear response of the stochastic Burgers field to some perturbation. From the symmetries of the stochastic Burgers equation we derive a fluctuation-dissipation relation so that the pdf gets given by the stationary two space-time points correlation function of the Burgers field. An analytical expression for the latter was obtained by Imamura and Sasamoto [2013], thereby rendering our result explicit. In the large length limit that implies that the pdf is nothing but the scaling function $f_{{\rm KPZ}}(y)$ introduced by Pr\"ahofer and Spohn [2004]. Using the KPZ-universality paradigm, we find that this function can therefore also be interpreted as the pdf of the position y of the maximum of the Airy process minus a parabola and a two-sided Brownian motion. We provide a direct numerical test of the result through simulations of the Log-Gamma polymer.Comment: 22 pages, 9 figures. v2: published version; minor changes and references added; v3: typos fixed and ref [53] update