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We consider the weakly asymmetric exclusion process on the one dimensional lattice. It has been proven that, in the diiusive scaling limit, the density eld evolves according to the Burgers equation 8, 19, 14] and the uctuation eld converges to a generalized Ornstein-Uhlenbeck process 8, 10]. We analyze instead the density uctuations beyond the… (More)

We investigate a one dimensional chain of 2N harmonic oscillators in which neighboring sites have their energies redistributed randomly. The sites −N and N are in contact with thermal reservoirs at different temperature τ − and τ +. Kipnis, Marchioro, and Presutti [18] proved that this model satisfies Fourier's law and that in the hydrodynamical scaling… (More)

Stochastic lattice gases with degenerate rates, namely conservative particle systems where the exchange rates vanish for some configurations, have been introduced as simplified models for glassy dynamics. We introduce two particular models and consider them in a finite volume of size ℓ in contact with particle reservoirs at the boundary. We prove that, as… (More)

- LORENZO BERTINI
- 2006

We consider a stochastically perturbed reaction diffusion equation in a bounded interval, with boundary conditions imposing the two stable phases at the endpoints. We investigate the asymptotic behavior of the front separating the two stable phases, as the intensity of the noise vanishes and the size of the interval diverges. In particular, we prove that,… (More)

- Lorenzo Bertini, Stella Brassesco
- 2006

We consider the van der Waals free energy functional in a bounded interval with inhomogeneous Dirichlet boundary conditions imposing the two stable phases at the endpoints. We compute the asymptotic free energy cost, as the length of the interval diverges, of shifting the interface from the midpoint. We then discuss the effect of thermal fluctuations by… (More)

The purpose of this project was the modeling, optimization and prediction of a hybrid system composed of a fuel cell, a dc-dc converter and a supercapacitor in series. Lab tests were performed for each device to understand their behavior, and then each one was modeled using software (Simulink). The validation of the model was done by comparing its results… (More)

- Luca Fanucci, Sergio Saponara, Lorenzo Bertini
- Integration
- 2001

The Kuramoto model has been introduced in order to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc... We look at the Kuramoto model with white noise forces: in mathematical terms it is a set of N oscilla-tors, each driven by an independent Brownian motion with a constant drift, that is each oscillator has its own… (More)

- Luca Fanucci, Lorenzo Bertini, Sergio Saponara
- IEEE International Conference on Multimedia and…
- 2000

- Giovanni Bellettini, Lorenzo Bertini, Mauro Mariani, Matteo Novaga
- SIAM J. Math. Analysis
- 2012

We consider the Cahn-Hilliard equation in one space dimension with scaling parameter ε, i.e. ut = (W (u) − ε 2 uxx)xx, where W is a nonconvex potential. In the limit ε ↓ 0, under the assumption that the initial data are energetically well-prepared, we show the convergence to a Stefan problem. The proof is based on variational methods and exploits the… (More)