Kalman Filtering in the Air Quality Monitoring

Data assimilation is a process where an improved prediction is obtained from a weighted combination between experimental measurements and mathematical model data. In the present work this procedure is applied to pollutant atmospheric dispersion by using a Kalman filter (KF). This is interesting approach, because the KF gives an output in which the balance between the data from the diffusion model and the experimental data is done automaticaly, through the Kalman gain. In addition, the Kalman filter computes the propagation of the error

Scaling and super-universality in the coarsening dynamics of the 3d random field Ising model

We study the coarsening dynamics of the three-dimensional random field Ising model using Monte Carlo numerical simulations. We test the dynamic scaling and super-scaling properties of global and local two-time observables. We treat in parallel the three-dimensional Edward-Anderson spin-glass and we recall results on Lennard-Jones mixtures and colloidal suspensions to highlight the common and different out of equilibrium properties of these glassy systems.Comment: 18 pages, 21 figure

Growing dynamical length, scaling and heterogeneities in the 3d Edwards-Anderson model

We study numerically spatio-temporal fluctuations during the out-of-equilibrium relaxation of the three-dimensional Edwards-Anderson model. We focus on two issues. (1) The evolution of a growing dynamical length scale in the glassy phase of the model, and the consequent collapse of the distribution of local coarse-grained correlations measured at different pairs of times on a single function using {\it two} scaling parameters, the value of the global correlation at the measuring times and the ratio of the coarse graining length to the dynamical length scale (in the thermodynamic limit). (2) The `triangular' relation between coarse-grained local correlations at three pairs of times taken from the ordered instants $t_3 \leq t_2 \leq t_1$. Property (1) is consistent with the conjecture that the development of time-reparametrization invariance asymptotically is responsible for the main dynamic fluctuations in aging glassy systems as well as with other mechanisms proposed in the literature. Property (2), we stress, is a much stronger test of the relevance of the time-reparametrization invariance scenario.Comment: 24 pages, 12 fig

Fluctuation-Dissipation relations far from Equilibrium

In this Article we review some recent progresses in the field of non-equilibrium linear response theory. We show how a generalization of the fluctuation-dissipation theorem can be derived for Markov processes, and discuss the Cugliandolo-Kurchan \cite{Cugliandolo93} fluctuation dissipation relation for aging systems and the theorem by Franz {\it et. al.} \cite{Franz98} relating static and dynamic properties. We than specialize the subject to phase-ordering systems examining the scaling properties of the linear response function and how these are determined by the behavior of topological defects. We discuss how the connection between statics and dynamics can be violated in these systems at the lower critical dimension or as due to stochastic instability.Comment: 18 pages, 10 figure