February 4, 2011
Location: Janskerkhof 15a (Utrecht), room 101
The parabolic Anderson model in dynamic random environments
The parabolic Anderson equation in dynamic random environment corresponds to the Cauchy problem for the heat equation with random time-dependent potential on the Zd lattice.
In the first part we will focus on the intermittent behavior of the model by analyzing the corresponding annealed Lyapunov exponents. The second part will be devoted to new results on the quenched Lyapunov exponents. It turns out that these exponents, annealed and quenched, exhibit an interesting dependence on the different parameters of the system.
This is mainly based on joint work with Jürgen Gärtner and Frank den Hollander.
Gradient models with non-convex potential
Recent efforts to link macroscopic nonlinear elasticity with microscopic gradient models at nonzero temperature will be discussed. In particular, we will be concerned with a microscopic derivation of the Cauchy–Born rule and nonlinear elastic free energies.