By Professor Oleg M. Braun, Professor Yuri S. Kivshar (auth.)
ISBN-10: 3642073972
ISBN-13: 9783642073977
ISBN-10: 3662103311
ISBN-13: 9783662103319
This publication offers an summary of the fundamental recommendations, tools and functions of nonlinear low-dimensional solid-state physics in accordance with the Frenkel--Kontorova version and its generalizations. It permits a nonspecialist to obtain foundations within the interdisciplinary techniques and strategies of either solid-state physics and nonlinear technology. It covers many very important issues akin to the nonlinear dynamics of discrete structures, the dynamics of solitons and their interplay, commensurate and incommensurate platforms, statistical mechanics of nonlinear structures, ratchets, and nonequilibrium dynamics of interacting many-body structures. additionally handled are the critical nonlinear equations in addition to the homes in their localized strategies and strategies for his or her analysis.
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Example text
26784 ... Comparing this exact result with the "bare" PN energy defined in Eq. 13 times. 5 10- 1 \\ \ \ 10-4 \ \ \ \ \ \ \ ;;,; 0.. 5 dla s == 10- 10 ,;g Fig. 2. Maximum of the PN potential relief, EPN, vs. the normalized width of the kink, d/ as == ,;g. Solid: numerical results of Joos [155] and Stancioff et al. [160]; dashed: the result of a weak-coupling approximation; dashed-dotted: the result of the continuous approximation. In the opposite case of a weak coupling, 9 « 1, the kink's parameters can be calculated in the lowest approximation if we neglect the atomic displacements from the bottoms of the substrate potential wells, for all the atoms except those in the kink's core.
Un-I, Un, Un+I,·. tr. 3) where the function f(x) describes the kink profile. e. 19) for the SG kink. In the discrete case, the function f(x) differs from the shape of the SG kink and it can be presented as the following, f(x) = u~SG)(X)+LlUad(X), where the function LlUad(X) is called "adiabatic dressing" of the kink. Using Eq. '(x-X)dx, where f'(x) = df(x)/dx. In numerical simulations of the system with an isolated kink, it is more convenient to define the coordinate X integrating Eq. , at n = 0).
For a FM chain with the so-called easy-plane anisotropy in the direction of the transverse magnetic field H at sufficiently low temperatures, there exists only one ground state with all spins being aligned in the direction of the magnetic field. A kink soliton in this case represents a 27r-twist of the ordered spin chain which can freely move along the chain without dispersion (see Fig. 9, top). e. the two sublattices, apart from a slight canting, are aligned antiparallel to each other and perpendicular to the field H.
The Frenkel-Kontorova Model: Concepts, Methods, and Applications by Professor Oleg M. Braun, Professor Yuri S. Kivshar (auth.)
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