Speaker: Muhittin Mungan, Dept. of Physics, Boğaçizi University, Istanbul
Abstract: We consider the relationship between the lowest energy configurations of an infinite harmonic chain of particles in a periodic potential and the evolution of characteristics in a periodically-forced inviscid Burgers equation. The shock discontinuities in the Burgers evolution arise from thermodynamical considerations and play an important role as they separate out flows related to lowest energy configurations from those associated with higher energies containing defects. We will explicitly work out the flow patterns in the exactly solvable case of an external potential consisting of parabolic segments,and and show how the lowest energy configurations, as well as excited states exhibiting can be calculated analytically within this settings. The description of lowest energy configurations of a discrete mechanical model such as the Frenkel-Kontorowa model in terms of the characteristic flows of a periodically forced hyperbolic PDE also provides and interesting example for the interplay between thermodynamical arguments and the mathematical notion of weak solutions and convergence.