By Günter Radons, Wolfram Just, Peter Häussler
ISBN-10: 354021383X
ISBN-13: 9783540213833
ISBN-10: 3540268693
ISBN-13: 9783540268697
Section transitions in disordered platforms and similar dynamical phenomena are a subject matter of intrinsically excessive curiosity in theoretical and experimental physics. This e-book offers a unified view, adopting options from all the disjoint fields of disordered structures and nonlinear dynamics. targeted recognition is paid to the glass transition, from either experimental and theoretical viewpoints, to trendy suggestions of development formation, and to the applying of the recommendations of dynamical structures for figuring out equilibrium and nonequilibrium homes of fluids and solids. The content material is available to graduate scholars, yet may also be of gain to experts, because the presentation extends so far as the subjects of ongoing study paintings.
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Additional info for Collective Dynamics of Nonlinear and Disordered Systems
Example text
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. In [94], only the case k = 0 was considered. (31) 28 Joachim Krug for an arbitrary scale factor b. Comparing the three terms on the right hand side of (30) yields two conditions for the unknown exponents α and z, which are solved by the expressions α=1+ 2 2(1 + n − k − 2ρ) 2 , γ= , z= . n−k−ρ 2+n−k−ρ n−k−ρ (32) The authors of [94] argue that all known examples of step bunching are covered by three universality classes corresponding to ρ = 1, ρ = −1 and ρ = −2.
Stiles, A. M. Sander: Phys. Rev. Lett. 75, 4246 (1995) 77. J. Krug: J. Stat. Phys. 87, 505 (1997) 36 Joachim Krug 78. J. Krug, P. Kuhn: ‘Second Layer Nucleation and the Shape of Wedding Cakes’ In: Atomistic Aspects of Epitaxial Growth, ed. by M. I. D. T. Wille (Kluwer, Dordrecht 2002) pp. 145–163 79. J. Krug, P. Politi, T. Michely: Phys. Rev. B 61, 14037 (2000) 80. T. Michely, M. Kalff, G. Comsa, M. -H. Heinig: ‘Coarsening Mechanisms in Surface Morphological Evolution’. In: Atomistic Aspects of Epitaxial Growth, ed.
72, 116 (1994) 70. J. Krug, M. Plischke, M. Siegert: Phys. Rev. Lett. 70, 3271 (1993) 71. M. Siegert, M. Plischke: Phys. Rev. Lett. 73, 1517 (1994) 72. V. Kohn, X. Yan: Comm. Pure Appl. Math. 56 1549 (2003) 73. M. Siegert: Phys. Rev. Lett. 81, 5481 (1998) ˇ 74. -H. Tang, P. D. Vvedensky: Eur. Phys. J. B 2, 409 (1998) ˇ 75. P. Smilauer, M. Rost, J. Krug: Phys. Rev. E 59, R6263 (1999) 76. A. T. D. Stiles, A. M. Sander: Phys. Rev. Lett. 75, 4246 (1995) 77. J. Krug: J. Stat. Phys. 87, 505 (1997) 36 Joachim Krug 78.
Collective Dynamics of Nonlinear and Disordered Systems by Günter Radons, Wolfram Just, Peter Häussler
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