Kinetic Relations for a Lattice Model of Phase Transitions

Archive for Rational Mechanics and Analysis - Tập 206 - Trang 707-724 - 2012
Hartmut Schwetlick1, Johannes Zimmer1
1Mathematical Sciences, University of Bath, Bath, UK

Tóm tắt

The aim of this article is to analyse travelling waves for a lattice model of phase transitions, specifically the Fermi–Pasta–Ulam chain with piecewise quadratic interaction potential. First, for fixed, sufficiently large subsonic wave speeds, we rigorously prove the existence of a family of travelling wave solutions. Second, it is shown that this family of solutions gives rise to a kinetic relation which depends on the jump in the oscillatory energy in the solution tails. Third, our constructive approach provides a very good approximate travelling wave solution.

Tài liệu tham khảo

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Slepyan L.I.: Feeding and dissipative waves in fracture and phase transition. I. Some 1D structures and a square-cell lattice. J. Mech. Phys. Solids 49(3), 469–511 (2001)