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The role of spinodal region in the kinetics of lattice phase transitions. (English) Zbl 1193.82042
Summary: We consider a one-dimensional chain of phase-transforming springs with harmonic long-range interactions. The nearest-neighbor interactions are assumed to be trilinear, with a spinodal region separating two material phases. We derive the traveling wave solutions governing the motion of an isolated phase boundary through the chain and obtain the functional relation between the driving force and the velocity of a phase boundary which can be used as the closing kinetic relation for the classical continuum theory. We show that a sufficiently wide spinodal region substantially alters the phase boundary kinetics at low velocities and results in a richer solution structure, with phase boundaries emitting short-length lattice waves in both direction. Numerical simulations suggest that solutions of the Riemann problem for the discrete system converge to the obtained traveling waves near the phase boundary.

82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
70F45 The dynamics of infinite particle systems
65L99 Numerical methods for ordinary differential equations
Full Text: DOI
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