On classical finite and affine W-algebras

This paper is meant to be a short review and summary of recent results on the structure of finite and affine classical W-algebras, and the application of the latter to the theory of generalized Drinfeld-Sokolov hierarchies.Comment: 12 page

Bihamiltonian Cohomologies and Integrable Hierarchies I: A Special Case

We present some general results on properties of the bihamiltonian cohomologies associated to bihamiltonian structures of hydrodynamic type, and compute the third cohomology for the bihamiltonian structure of the dispersionless KdV hierarchy. The result of the computation enables us to prove the existence of bihamiltonian deformations of the dispersionless KdV hierarchy starting from any of its infinitesimal deformations.Comment: 43 pages. V2: the accepted version, to appear in Comm. Math. Phy

Macroscopic fluctuations theory of aerogel dynamics

We consider the thermodynamic potential describing the macroscopic fluctuation of the current and local energy of a general class of Hamiltonian models including aerogels. We argue that this potential is neither analytic nor strictly convex, a property that should be expected in general but missing from models studied in the literature. This opens the possibility of describing in terms of a thermodynamic potential non-equilibrium phase transitions in a concrete physical context. This special behaviour of the thermodynamic potential is caused by the fact that the energy current is carried by particles which may have arbitrary low speed with sufficiently large probability.Comment: final versio

Dirac operators and the Very Strange Formula for Lie superalgebras

Using a super-affine version of Kostant's cubic Dirac operator, we prove a very strange formula for quadratic finite-dimensional Lie superalgebras with a reductive even subalgebra.Comment: Latex file, 25 pages. A few misprints corrected. To appear in the forthcoming volume "Advances in Lie Superalgebras", Springer INdAM Serie

From waves to avalanches: two different mechanisms of sandpile dynamics

Time series resulting from wave decomposition show the existence of different correlation patterns for avalanche dynamics. For the d=2 Bak-Tang-Wiesenfeld model, long range correlations determine a modification of the wave size distribution under coarse graining in time, and multifractal scaling for avalanches. In the Manna model, the distribution of avalanches coincides with that of waves, which are uncorrelated and obey finite size scaling, a result expected also for the d=3 Bak et al. model.Comment: 5 pages, 4 figure

Caracterização genética de ostras nativas do gênero Crassostrea no Brasil: base para o estabelecimento de um programa nacional de melhoramento.

bitstream/item/80696/1/documento-192.pd

Fluctuations in Stationary non Equilibrium States

In this paper we formulate a dynamical fluctuation theory for stationary non equilibrium states (SNS) which covers situations in a nonlinear hydrodynamic regime and is verified explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Our results include the modification of the Onsager-Machlup theory in the SNS, a general Hamilton-Jacobi equation for the macroscopic entropy and a non equilibrium, non linear fluctuation dissipation relation valid for a wide class of systems

Energy flux distribution in a two-temperature Ising model

The nonequilibrium steady state of an infinite-range Ising model is studied. The steady state is obtained by dividing the spins into two groups and attaching them to two heat baths generating spin flips at different temperatures. In the thermodynamic limit, the resulting dynamics can be solved exactly, and the probability flow in the phase space can be visualized. We can calculate the steady state fluctuations far from equilibrium and, in particular, we find the exact probability distribution of the energy current in both the high- and low-temperature phase.Comment: 19 pages, 4 figure

Non equilibrium current fluctuations in stochastic lattice gases

We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach for density fluctuations developed in previous articles. More precisely, we establish a large deviation principle for a space-time fluctuation $j$ of the empirical current with a rate functional \mc I (j). We then estimate the probability of a fluctuation of the average current over a large time interval; this probability can be obtained by solving a variational problem for the functional \mc I . We discuss several possible scenarios, interpreted as dynamical phase transitions, for this variational problem. They actually occur in specific models. We finally discuss the time reversal properties of \mc I and derive a fluctuation relationship akin to the Gallavotti-Cohen theorem for the entropy production.Comment: 36 Pages, No figur