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Dynamics of Phase Transitions in a Piecewise Linear Diatomic Chain

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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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Authors and Affiliations

  1. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15260, USA

    Anna Vainchtein

  2. Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA, 01003, USA

    Panayotis G. Kevrekidis

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  1. Anna Vainchtein
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  2. Panayotis G. Kevrekidis
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Correspondence to Anna Vainchtein.

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Communicated by P. Newton.

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Vainchtein, A., Kevrekidis, P.G. Dynamics of Phase Transitions in a Piecewise Linear Diatomic Chain. J Nonlinear Sci 22, 107–134 (2012). https://doi.org/10.1007/s00332-011-9110-5

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  • DOI: https://doi.org/10.1007/s00332-011-9110-5

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