Talk

On the optimal way to displace a stationary front

  • Errico Presutti (Università di Roma "Tor Vergata")
A3 01 (Sophus-Lie room)

Abstract

The stationary front in the title represents a planar interface which separates the two stable phases of a fluid. Due to stochastic forces, its position fluctuates and we would like to determine the most probable way in which a macroscopic displacement R may occur in a given macroscopic time interval T.

Supposing planar symmetry, the problem becomes one dimensional and it is modelled by introducing a non local cost functional which must then be minimized over orbits which exhibit the desired displacement in the given time.

It is found that in a "sharp interface limit" the optimal behavior for R small enough, is when the front moves with constant velocity V=R/T, the corresponding cost being cV2T, c a positive constant. However when R increases past a critical value, the cost becomes smaller than cV2T. The effect is caused by nucleations ahead of the moving front; there are critical values Rn, n1, so that, if R(Rn,Rn+1) then there are n nucleations.

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