RT Journal Article T1 Wave Front Depinning Transition in Discrete One-Dimensional Reaction-Diffusion Systems A1 Carpio, Ana A1 Bonilla, L.L. AB Pinning and depinning of wave fronts are ubiquitous features of spatially discrete systems describing a host of phenomena in physics, biology, etc. A large class of discrete systems is described by overdamped chains of nonlinear oscillators with nearest-neighbor coupling and controlled by constant external forces. A theory of the depinning transition for these systems, including scaling laws and asymptotics of wave fronts, is presented and confirmed by numerical calculations. PB American Physical Society SN 0031-9007 YR 2001 FD 2001 LK https://hdl.handle.net/20.500.14352/57214 UL https://hdl.handle.net/20.500.14352/57214 LA eng NO J. P. Keener, SIAM J. Appl. Math. 47, 556 (1987). J. P. Keener and J. Sneyd, Mathematical Physiology(Springer, New York, 1998), Chap. 9. A. E. Bugrim, A. M. Zhabotinsky, and I. R. Epstein, Biophys.J. 73, 2897 (1997); J. Keizer, G.D. Smith, S. PonceDawson, and J. E. Pearson, Biophys. J. 75, 595 (1998). G. Grüner, Rev. Mod. Phys. 60, 1129 (1988); A. A.Middleton, Phys. Rev. Lett. 68, 670 (1992). H. S. J. van der Zant, T. P. Orlando, S. Watanabe, and S. H.Strogatz, Phys. Rev. Lett. 74, 174 (1995). F. R. N. Nabarro, Theory of Crystal Dislocations (OxfordUniversity Press, Oxford, 1967). P. M. Chaikin and T. C. Lubensky, Principles of CondensedMatter Physics (Cambridge University Press, Cambridge,UK, 1995), Chap. 10.] M. Löcher, G.A. Johnson, and E. R. Hunt, Phys. Rev. Lett.77, 4698 (1996). L. L. Bonilla, J. Galán, J. A. Cuesta, F. C. Martínez, andJ. M. Molera, Phys. Rev. B 50, 8644 (1994); L. L. Bonilla,G. Platero, and D. Sánchez, Phys. Rev. B 62, 2786 (2000);A. Wacker, in Theory and Transport Properties of SemiconductorNanostructures, edited by E. Schöll (Chapmanand Hall, New York, 1998), Chap. 10. A. Carpio, L. L. Bonilla, A. Wacker, and E. Schöll, Phys.Rev. E 61, 4866 (2000). K. Kladko, I. Mitkov, and A. R. Bishop, Phys. Rev. Lett.84, 4505 (2000). I. Mitkov, K. Kladko, and J. E. Pearson, Phys. Rev. Lett.81, 5453 (1998). J. R. King and S. J. Chapman (to be published). B. Zinner, J. Differ. Equ. 96, 1 (1992); A.-M. Filip andS. Venakides, Commun. Pure Appl. Math. 52, 693(1999). A. Carpio, S. J. Chapman, S. Hastings, and J. B. McLeod,Eur. J. Appl. Math. 11, 399 (2000). J. Frenkel and T. Kontorova, Phys. Z. Sowjetunion 13, 1(1938). If we have ln0 # un0, such that un $ un11 2 2un 1un21 1 F 2 Agun and ln # ln11 2 2ln 1 ln21 1 F 2Agln, then lnt # unt for all later times. lnt andunt are called subsolutions and supersolutions, respectively(see Ref. [15]). R. Hobart, J. Appl. Phys. 36, 1948 (1965). V. L. Indenbom, Sov. Phys. Crystallogr. 3, 193 (1958). J. B. McLeod (private communication). L. L. Bonilla, J. Stat. Phys. 46, 659 (1987). A. Carpio, L. L. Bonilla, and G. Dell’Acqua, Phys.Rev. E (to be published); A. Carpio and L. L. Bonilla(unpublished). DS Docta Complutense RD 6 may 2024