Period polynomials and Ihara brackets

Schneps [J. Lie Theory 16 (2006), 19--37] has found surprising links between Ihara brackets and even period polynomials. These results can be recovered and generalized by considering some identities relating Ihara brackets and classical Lie brackets. The period polynomials generated by this method are found to be essentially the Kohnen-Zagier polynomials.Comment: 12 pages, LaTE

A Promising Portable Tool for the Continuous, Online, and Field Monitoring of Pressured Processes

International audienceFirst reaction on B. Mizaikoff's article in the same issue

Free quasi-symmetric functions, product actions and quantum field theory of partitions

We examine two associative products over the ring of symmetric functions related to the intransitive and Cartesian products of permutation groups. As an application, we give an enumeration of some Feynman type diagrams arising in Bender's QFT of partitions. We end by exploring possibilities to construct noncommutative analogues.Comment: Submitted 28.11.0

Hyperdeterminantal computation for the Laughlin wave function

International audienceThe decomposition of the Laughlin wave function in the Slater orthogonal basis appears in the discussion on the second-quantized form of the Laughlin states and is straightforwardly equivalent to the decomposition of the even powers of the Vandermonde determinants in the Schur basis. Such a computation is notoriously difficult and the coefficients of the expansion have not yet been interpreted. In our paper, we give an expression of these coefficients in terms of hyperdeterminants of sparse tensors. We use this result to construct an algorithm allowing to compute one coefficient of the development without computing the others. Thanks to a program in {\tt C}, we performed the calculation for the square of the Vandermonde up to an alphabet of eleven lettres

Flow and fracture in water-saturated, unconstrained granular beds

International audienceSpecialty section: This article was submitted to Interdisciplinary Physics, a section of the journal Frontiers in Physics The injection of gas in a liquid-saturated granular bed gives rise to a wide variety of invasion patterns. Many studies have focused on constrained porous media, in which the grains are fixed in the bed and only the interstitial fluid flows when the gas invades the system. With a free upper boundary, however, the grains can be entrained by the ascending gas or fluid motion, and the competition between the upward motion of grains and sedimentation leads to new patterns. We propose a brief review of the experimental investigation of the dynamics of air rising through a water-saturated, unconstrained granular bed, in both two and three dimensions. After describing the invasion pattern at short and long time, a tentative regime-diagram is proposed. We report original results showing a dependence of the fluidized zone shape, at long times, on the injection flow rate and grain size. A method based on image analysis makes it possible to detect not only the fluidized zone profile in the stationary regime, but also to follow the transient dynamics of its formation. Finally, we describe the degassing dynamics inside the fluidized zone, in the stationary regime. Depending on the experimental conditions, regular bubbling, continuous degassing, intermittent regime or even spontaneous flow-to-fracture transition are observed

Gas-induced fluidization of mobile liquid-saturated grains

International audienceGas invasion in liquid-saturated sands exhibits different morphologies and dynamics. For mobile beds, the repeated rise of gas through the layer leads to the growth of a fluidized zone, which reaches a stationary shape. Here, we present experimental results characterizing the evolution of the fluidized region as a function of the gas-flow rate and grain size. We introduce a new observable, the flow density, which quantifies the motion of the grains in the system. The growth of the fluidized zone is characterized by a spatiotemporal analysis, which provides the stabilization time, τ_s. In the stationary regime, we report two main contributions to motion in the fluidized region: the central gas rise and a convective granular motion. Interestingly, a static model with a fixed porous network accounts for the final shape of the invasion zone. We propose an explanation where the initial gas invasion weakens the system and fixes since the early stage the morphology of the fluidized zone

Granular flow through an aperture: Pressure and flow rate are independent

We simultaneously measure the flow rate and the normal force on the base, near the outlet, during the discharge through an orifice of a dense packing of monosized disks driven by a conveyor belt. We find that the normal force on the base decreases even when a constant flow rate is measured. In addition, we show, by changing the mass of the disks, that pressure can be changed while the flow rate remains constant. Conversely, we are able, by changing the belt velocity, to set different flow rates for the same pressure. The experiment confirms that, contrary to what has been implicitly assumed in numerous works, the flow rate through an aperture is not controlled by the pressure in the outlet region.Fil: Aguirre, Maria Alejandra. Franco-Argentinian International Associated Laboratory in the Physics and Mechanics of Fluids; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Física. Grupo de Medios Porosos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Grande, Juan Gabriel. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Física. Grupo de Medios Porosos; Argentina. Franco-Argentinian International Associated Laboratory in the Physics and Mechanics of Fluids; ArgentinaFil: Calvo, Adriana. Franco-Argentinian International Associated Laboratory in the Physics and Mechanics of Fluids; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Física. Grupo de Medios Porosos; ArgentinaFil: Pugnaloni, Luis Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; ArgentinaFil: Géminard, Jean-Christophe. Universidad de Lyon 3; Franci