Dynamics of chains with non-monotone stress-strain relations. II: Nonlinear waves and waves of phase transition. (English) Zbl 1005.74047
Summary: We investigate the dynamics of a one-dimensional mass-spring chain with non-monotone dependence of spring force vs. spring elongation. For this strongly nonlinear system, we find a family of exact solutions that represent nonlinear waves. We establish numerically that this system displays a dynamical phase transition from stationary phase (when all masses are at rest) to twinkling phase (when the masses oscillate in a wave motion). This transition has two fronts which propagate with different speeds. We study this phase transition analytically, and derive relations between its quantitative characteristics.
Keywords:
non-monotone stress-strain relations; waves of phase transition; variational principles; one-dimensional mass-spring chain; nonlinear waves; dynamical phase transition; twinkling phaseReferences:
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