Name
Title | ||
|---|---|---|
Subsonic Phase Transition Waves in Bistable Lattice Models with Small Spinodal Region. |
Abstract | ||
|---|---|---|
Although phase transition waves in atomic chains with double-well potential play a fundamental role in materials science, very little is known about their mathematical properties. In particular, the only available results about waves with large amplitudes concern chains with piecewise-quadratic pair potential. In this paper we consider perturbations of a bi-quadratic potential and prove that the corresponding three-parameter family of waves persists as long as the perturbation is small and localized with respect to the strain variable. As a standard Lyapunov-Schmidt reduction cannot be used due to the presence of an essential spectrum, we characterize the perturbation of the wave as a fixed point of a nonlinear and nonlocal operator and show that this operator is contractive on a small ball in a suitable function space. Moreover, we derive a uniqueness result for phase transition waves with certain properties and discuss the kinetic relations. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1137/120877878 | SIAM JOURNAL ON MATHEMATICAL ANALYSIS |
Keywords | Field | DocType |
phase transitions in lattices,kinetic relations,heteroclinic traveling waves in Fermi-Pasta-Ulam chains | Uniqueness,Bistability,Essential spectrum,Pair potential,Phase transition,Spinodal,Quantum mechanics,Mathematical analysis,Operator (computer programming),Fixed point,Classical mechanics,Physics | Journal |
Volume | Issue | ISSN |
45 | 5 | 0036-1410 |
Citations | PageRank | References |
0 | 0.34 | 3 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Michael Herrmann | 1 | 4 | 2.41 |
| Karsten Matthies | 2 | 1 | 2.65 |
| Hartmut Schwetlick | 3 | 13 | 2.99 |
| Johannes Zimmer | 4 | 9 | 3.33 |