Lorenzo Bertini

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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)
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)
Consider the viscous Burgers equation on a bounded interval with inhomogeneous Dirichlet boundary conditions. Following the variational framework introduced in [4], we analyze a Lyapunov functional for such equation which gives the large deviations asymptotics of a stochastic interacting particles model associated to the Burgers equation. We discuss the(More)
We consider the van der Waals' free energy functional, with scaling parameter ε, in the plane domain R + × R + , with inhomogeneous Dirich-let boundary conditions. We impose the two stable phases on the horizontal boundaries R + ×{0} and R + ×{∞}, and free boundary conditions on {∞}×R +. Finally, the datum on {0} × R + is chosen in such a way that the(More)
This paper presents an application based on a hot wire anemometric sensor in MEMS technology in the field of water flow monitoring. New generations of MEMS sensors feature remarkable savings in area, costs and power respect to conventional discrete devices, but as drawback, they require complex electronic interfaces for signal conditioning to achieve high(More)
We consider a two–dimensional Ising model with random i.i.d. nearest–neighbor fer-romagnetic couplings and no external magnetic field. We show that, if the probability of supercritical couplings is small enough, the system admits a convergent cluster expansion with probability one. The associated polymers are defined on a sequence of increasing scales; in(More)
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