Abstract
Since the pioneering work of Mandelbrot et al. demonstrating the self-affine nature of cracks in metals [1], a significant number of different methods were established and used to estimate the roughness exponent of self-affine interfaces, focusing in particular on fracture surfaces [2, 3]. In all of these methods, complete knowledge of the interface position is assumed, allowing the roughness exponent to be estimated, either indirectly by determining the fractal dimension or directly through dedicated self-affine analysis.
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Notes
- 1.
Using the fact that the 1D interface and the (\(1+1\)) directed polymer problems are exactly mappable one onto each other [5].
References
B.B. Mandelbrot, D.E. Passoja, A.J. Paullay, Fractal character of fracture surfaces of metals. Nature 308, 721 (1984)
K.J. Måløy, A. Hansen, E.L. Hinrichsen, S. Roux, Experimental measurements of the roughness of brittle cracks. Phys. Rev. Lett. 68, 213 (1992)
J. Schmittbuhl, F. Schmitt, C. Scholz, Scaling invariance of crack surfaces. J. Geophys. Res. 100, 5953 (1995)
J. Schmittbuhl, J.-P. Vilotte, S. Roux, Reliability of self-affine measurements. Phys. Rev. E 51, 131 (1995)
M. Mézard, G. Parisi, Manifolds in random media: two extreme cases. J. de Phys. I 2, 2231 (1992)
S. Santucci, K.J. Måløy, A. Delaplace, J. Mathiesen, A. Hansen, J.Ø.H. Bakke, J. Schmittbuhl, L. Vanel, R. Purusattam, Statistics of fracture surfaces. Phys. Rev. E 75, 016104 (2007)
S. Lemerle, J. Ferré, C. Chappert, V. Mathet, T. Giamarchi, P. Le Doussal, Domain wall creep in an Ising ultrathin magnetic film. Phys. Rev. Lett. 80, 849 (1998)
P. Paruch, T. Giamarchi, J.-M. Triscone, Nanoscale Studies of Domain Walls in Epitaxial Ferroelectric Thin Films, ed. by K. Rabe, C.H. Ahn, J.-M. Triscone. Physics of Ferroelectrics, a Modern Perspective (Springer, Berlin, 2007), p. 339
T. Natterman, S. Stepanow, L.-H. Tang, H. Leschhorn, Dynamics of interface depinning in a disordered medium. J. de Phys. II 2, 1483 (1992)
A. Rosso, A.K. Hartmann, W. Krauth, Depinning of elastic manifolds. Phys. Rev. Lett. 67, 021602 (2003)
H. Leschhorn, L.-H. Tang, Comment on “elastic string in a random potential”. Phys. Rev. 70, 2973 (1993)
J.M. López, M.A. Rodrìguez, R. Cuerno, Superroughening versus intrinsic anomalous scaling of surfaces. Phys. Rev. E 56, 56 (1997)
J.M. López, J. Schmittbuhl, Anomalous scaling of fracture surfaces. Phys. Rev. E 57, 6405 (1998)
J.J. Ramasco, J.M. López, M.A. Rodríguez, Generic dynamic scaling in kinetic roughening. Phys. Rev. Lett. 84, 2199 (2000)
S. Bustingorry, A.B. Kolton, T. Giamarchi, Thermal rounding of the depinning transition in ultrathin Pt/Co/Pt films. Phys. Rev. B 85, 214416 (2012)
V.V. Randoshkin, Magnetic-field dependence of the domain wall velocity in uniaxial films of iron garnets with various dampings. Sov. Phys. - Solid State 37, 355 (1995)
V.Ya. Shur, A. Gruverman, N.Yu. Ponomarev, E.L. Rumyantsev, N.A. Tonkacheva, Domain structure kinetics in ultrafast polarization switching in lead germanate. JETP Lett. 53, 615 (1991)
M. Dawber, A. Gruverman, J.F. Scott, Skyrmion model of nano-domain nucleation in ferroelectrics and ferromagnets. J. Phys.: Condens. Matter 18, L71 (2006)
B.J. Rodriguez, S. Jesse, A.P. Baddorf, S.-H. Kim, S.V. Kalinin, Controlling polarization dynamics in a liquid environment: from localized to macroscopic switching in ferroelectrics. Phys. Rev. Lett. 98, 247603 (2007)
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Guyonnet, J. (2014). Measuring the Roughness Exponent of One-Dimensional Interfaces. In: Ferroelectric Domain Walls. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-05750-7_7
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DOI: https://doi.org/10.1007/978-3-319-05750-7_7
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