Moving interfaces in solids: from conservative lattice models to macroscopic dissipation

Johannes Zimmer (University of Bath)

Friday 27th February, 2009 14:00-15:00 204

Abstract

Moving interfaces in solids can dissipate energy, but are commony described by conservative (Hamiltonian) equations on the lattice scale. How can conservative lattice models generate dissipation on the continuum scale? To understand this, we consider a model problem, namely travelling waves in a one-dimensional chain of atoms with nearest neighbour interaction. The elastic potential is piecewise quadratic and the model is thus capable of describing phase transitions. (The talk will start with a short survey on phase transitions.) A solution which explores both wells of the energy will then have an interface, moving with the speed of the wave. We show that for suitable fixed subsonic velocities, there is a family of ``heteroclinic" travelling waves (heteroclinic means here that they connect both wells of the energy). Though the microscopic picture is Hamiltonian, we derive non-trivial so-called kinetic relations on the continuum scale; they can be related to the dissipation generated by a moving phase boundary. We then investigate the question of when the kinetic relation does not vanish (dissipation is generated). It turns out that a microscopic asymmety determines here the macroscopic dissipation.

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