By Günter Radons, Wolfram Just, Peter Häussler
Section transitions in disordered platforms and comparable dynamical phenomena are a subject of intrinsically excessive curiosity in theoretical and experimental physics. This ebook offers a unified view, adopting techniques from all of the disjoint fields of disordered structures and nonlinear dynamics. detailed realization is paid to the glass transition, from either experimental and theoretical viewpoints, to fashionable suggestions of development formation, and to the appliance of the recommendations of dynamical structures for knowing equilibrium and nonequilibrium houses of fluids and solids. The content material is on the market to graduate scholars, yet can also be of profit to experts, because the presentation extends so far as the themes of ongoing study paintings.
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Additional info for Collective Dynamics of Nonlinear and Disordered Systems
The exponent k in (30) is related to the diﬀusion kinetics on the vicinal surface8 . If diﬀusion on the terraces is fast compared to the attachment-detachment processes at the steps we have k = 1, while in the opposite limit k = 0 [95, 96]. In addition, it is assumed in  that the destabilising current j(m) can be represented by its leading order term in a gradient expansion, j(m) ≈ Bmρ , where Bρ > 0 to satisfy the condition dj/dm > 0 required for a linear instability (compare to Sect. 1). Then the scaling exponents α and z can be determined by requiring that (30) should be invariant under the scale transformation h(x, t) ⇒ b−α h(bx, bz t) 7 8 We take m > 0 without loss of generality.
442, 318 (1999) 92. S. Stoyanov, V. Tonchev: Phys. Rev. B 58, 1590 (1998) 93. K. Fujita, M. S. Stoyanov: Phys. Rev. B 60, 16006 (1999) 94. A. Pimpinelli, V. Tonchev, A. Videcoq, M. Vladimirova: Phys. Rev. Lett. 88, 206103 (2002) 95. P. Nozi`eres: J. Physique 48, 1605 (1987) 96. -J. S. D. D. D. Williams: J. Vac. Sci. Technol. B 14, 2799 (1996) 97. J. Krug, V. Tonchev, S. Stoyanov, A. Pimpinelli (submitted to Phys. Rev. B) 98. J. Krug: ‘Continuum Equations for Step Flow Growth’. In: Dynamics of Fluctuating Interfaces and Related Phenomena, ed.
Due to the slope selection property of the evolution equation, the lateral mound size has to increase at the same rate. Thus we have 11 Similar equations have been used to describe the faceting of thermodynamically unstable surfaces in the presence of a growth ﬂux [109, 110]. 32 Joachim Krug Fig. 15. 32. Conical mounds (right) form a cellular structure shown in gray-scale representation on the left dλ/dt ≈ /λ ⇒ λ ≈ √ t. (35) A model system for which the speedup of coarsening and the transition from coarsening to chaotic dynamics has been studied in detail is the onedimensional convective Cahn-Hilliard equation [110, 111] ∂m ∂2 ∂4m ∂m + 2 (m − m3 ) + =0.
Collective Dynamics of Nonlinear and Disordered Systems by Günter Radons, Wolfram Just, Peter Häussler