The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: II. Numerical Treatment

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Scheidsteger, T.; Urbschat, H.; Griffiths, R. B.; Schellnhuber, H. J.;
(1997)
  • Related identifiers: doi: 10.1103/PhysRevB.56.8631
  • Subject: Nonlinear Sciences - Chaotic Dynamics | Nonlinear Sciences - Exactly Solvable and Integrable Systems | Condensed Matter - Statistical Mechanics

A procedure is described for efficiently finding the ground state energy and configuration for a Frenkel-Kontorova model in a periodic potential, consisting of N parabolic segments of identical curvature in each period, through a numerical solution of the convex minimiz... View more
  • References (7)

    [1] R.B.Griffiths, H.J.Schellnhuber, H.Urbschat (preceding paper).

    [2] R. B. Griffiths, H. J. Schellnhuber and H. Urbschat, Phys.Rev.Lett. 65, 2551 (1990).

    [3] P. Delaly, Ph.D. Thesis, Carnegie-Mellon University, 1995 (unpublished).

    [4] H. C. Kao, S.-C. Lee, and W.-J. Tzeng, Preprint (solv-int/9607001).

    [5] R. T. Rockafellar, Convex Analysis (Princeton University Press, Princeton, N. J., 1970) Part V.

    [6] See p. 223 of [5].

    [7] W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge University Press, Cambridge, U.K., 1988), Sec. 10.8.

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