Publication: Wave Front Depinning Transition in Discrete One-Dimensional Reaction-Diffusion Systems
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2001
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American Physical Society
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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.
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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. Ponce
Dawson, 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 (Oxford
University Press, Oxford, 1967).
P. M. Chaikin and T. C. Lubensky, Principles of Condensed
Matter 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. MartÃnez, and
J. 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 Semiconductor
Nanostructures, edited by E. Schöll (Chapman
and 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 and
S. 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 1
un21 1 F 2 Agun and ln # ln11 2 2ln 1 ln21 1 F 2
Agln, then lnt # unt for all later times. lnt and
unt 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).