Andreas Minne: Mathematical analysis of a homogenization model for molecular motors

Homogenization is a mathematical tool widely used in different parts of applied mathematics. Here I compare two different articles, Asymmetric potentials and motor effect: a homogenization approach, [1], and Homogenization of a neutronic critical diffusion problem with drift, [2], that both
describe an exponential drift that occurs to the solution of a PDE eigenvalue problem, as the periods become smaller. I shed some light over a subtle but interesting difference between them, namely that the zeros of the effective Hamiltonian H‍̅ to the problem are key to the solutions in [1] while it is the maximum of H‍̅ in [2] that is important. Emphasis is put on presenting and analyzing [1] that models molecular motors.