Abstract
In this chapter we show how a new type of nonlinear lattice excitation is helping to understand the long-standing puzzle of unexplained dark lines in crystals of muscovite mica. In fact, it was the conjecture that some kind of quasi-one-dimensional lattice soliton was responsible for those lines which led to the discovery of this new family of lattice excitations: mobile localized breathers of longitudinal type.
We explore several properties of these moving breathers, both by numerical methods and by experimenting with analogue models. The results suggest a much broader application than just the mica problem.
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References
S. Aubry. Breathers in nonlinear lattices: existence, linear stability and quantization. Physica D, 103:201–250, 1997.
V.M. Burlakov, S.A. Kisilev, and V.N. Pyrkov. Computer simulation of intrinsic localized modes in one-dimensional and two-dimensional anharmonic lattices. Phys. Rev. B, 42:4921, 1990.
Jin-Ho Choy, Soon-Jae Kwon, and Gyeong-Su Park. High T c superconductors in the two-dimensional limit. Science, 280:1589–1592, 1998.
D.R. Collins. Computer simulations and netron scattering studies of layer silicates minerals.PhD thesis, University of Keele, 1990.
T. Cretegny and S. Aubry. Mobility and reactivity of discrete breathers. Physica D, 119:34–46, 1998.
T. Cretegny, S. Aubry, and J.L. Marín. Exchange of stability and mobility of discrete breathers. in preparation.
D.B. Duncan, J.C. Eilbeck, H. Feddersen, and J.A.D. Wattis. Solitons on lattices. Physica D, 68:1–11, 1993.
J.C. Eilbeck and R. Flesch. Calculation of families of solitary waves on discrete lattices. Phys. Lett. A, 149(4):200–202, 1990.
S. Flach and C.R. Willis. Discrete breathers. Physics Reports, 295:181–264, 1998.
K. Hori and S. Takeno. Low-frequency and high-frequency moving anharmonic localized modes in a one-dimensional lattice with quartic anharmonicity. J. Phys. Soc. Jpn., 61:4263, 1992.
R.S. MacKay and S. Aubry. Proof of existence of breathers for timereversible or Hamiltonian networks of weakly coupled oscillators. Nonlinearity, 7:1623–1643, 1994.
J.L. Marín, S. Aubry, and L.M. Floría. Intrinsic localized modes: discrete breathers. existence and linear stability. Physica D, 113:283–292, 1998.
J.L. Marín, J.C. Eilbeck, and F.M. Russell. Localized moving breathers in 2-d lattices. in preparation.
J.L. Marín, J.C. Eilbeck, and F.M. Russell. Localized moving breathers in a 2-d hexagonal lattice. Phys. Lett. A, 1998. to appear.
Yu V. Martynenko and P.G. Moscovkin. Solitons in radiation physics of crystals. Radiation Effects and Defects in Solids, 117:321–328, 1991.
E.W. Radoslovich. The structure of muscovite, KAl2(Si3Al)O10(OH)2. Acta Cryst., 13:919–930, 1960.
F.M. Russell. The observation in mica of charged particles from neutrino interactions. Phys. Lett. B, 25:298–300, 1967.
F.M. Russell. Identification and selection criteria for charged lepton tracks in mica. Nucl. Tracks Radiat. Meas., 15:41–44, 1988.
F.M. Russell. Positive charge transport in layered crystalline solids. Phys. Lett. A, 130:489–491, 1988.
F.M. Russell and D.R. Collins. Lattice-solitons in radiation damage. Nuclear instruments & methods in physics research B, 105:1–4, 1995.
F.M. Russell and D.R. Collins. Anharmonic excitations in high T c materials. Phys. Lett. A, 216:197–202, 1996.
F.M. Russell, Y. Zolotaryuk, and J.C. Eilbeck. Moving breathers in a chain of magnetic pendulums. Phys. Rev. B, 55:6304–6308, 1997.
D. Schlosser, K. Kroneberger, M. Schosnig, F.M. Russell, and K.O. Groeneveld. Search for solitons in solids. Radiat. Meas., 23:209–213, 1994.
A.J. Sievers and S. Takeno. Intrinsic localized modes in anharmonic crystals. Phys. Rev. Lett., 61:631–633, 1988.
J.W. Steeds, F.M. Russell, and W.J. Vine. Formation of epidote fossil positron tracks in mica. Optik, 92:149–154, 1993.
J.M. Tamga, M. Remoissenet, and J. Pouget. Breathing solitary waves in a sine-Gordon two-dimensional lattice. Phys. Rev. Lett., 75:357–361, 1995.
G.K. Wehner. Controlled sputtering of metals by low-energy Hg ions. Phys. Rev., 102:690–704, 1956.
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Marín, J.L., Eilbeck, J.C., Russell, F.M. (2000). 2-D Breathers and Applications. In: Christiansen, P.L., Sørensen, M.P., Scott, A.C. (eds) Nonlinear Science at the Dawn of the 21st Century. Lecture Notes in Physics, vol 542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46629-0_14
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DOI: https://doi.org/10.1007/3-540-46629-0_14
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