Abstract:
One-dimensional solid crystals are modelled through a chain of oscillators called Fermi-Pasta-Ulam chain. When atoms in the crystal are assumed to interact through a quartic potential, we prove that the macroscopic equation describing energy transport corresponds to a fractional heat equation rather than the standard heat equation. The proof uses an intermediate step between the discrete chain model and the macroscopic one; the phonon-Boltzmann equation, which describes vibrations through the chain. (This is a joint work with Dr Mellet from the University of Maryland). |