Dynamics of Phase Transitions in a Piecewise Linear Diatomic Chain |
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Authors: | Anna Vainchtein Panayotis G Kevrekidis |
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Institution: | 1. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15260, USA 2. Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA, 01003, USA
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Abstract: | We consider a diatomic chain with nearest neighbors connected by phase-transforming springs. Assuming a piecewise linear interaction
force, we use the Fourier transform to construct exact traveling wave solutions representing a moving phase-transition front
and examine their stability through numerical experiments. We find that the identified traveling wave solutions may be stable
in some velocity intervals. We show that the kinetic relation between the driving force on the phase boundary and its velocity
is significantly affected by the ratio of the two masses. When the ratio is small enough, the relation may become multivalued
at some velocities, with the two solutions corresponding to the different orders in which the two springs in a dimer cell
change phase. The model bears additional interesting waveforms such as the so-called twinkling phase, which is also briefly
discussed and compared to its monatomic analog. |
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Keywords: | |
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