@article{FernandezBrunoGarcesetal.2020,
  author    = {Fernandez, Ricardo and Bruno, Giovanni and Garces, Gerardo and Nieto-Luis, H. and Gonzalez-Doncel, Gaspar},
  title     = {Fractional brownian motion of dislocations during creep deformation of metals},
  series = {Materials science \& engineering. A, Structural materials},
  volume    = {796},
  journal   = {Materials science \& engineering. A, Structural materials},
  publisher = {Elsevier},
  address   = {Lausanne},
  issn      = {0921-5093},
  doi       = {10.1016/j.msea.2020.140013},
  pages     = {8},
  year      = {2020},
  abstract  = {The present work offers an explanation on how the long-range interaction of dislocations influences their movement, and therefore the strain, during creep of metals. It is proposed that collective motion of dislocations can be described as a fractional Brownian motion. This explains the noisy appearance of the creep strain signal as a function of time. Such signal is split into a deterministic and a stochastic part. These terms can be related to two kinds of dislocation motions: individual and collective, respectively. The description is consistent with the fractal nature of strain-induced dislocation structures predicated in previous works. Moreover, it encompasses the evolution of the strain rate during all stages of creep, including the tertiary one. Creep data from Al99.8\% and Al3.85\%Mg tested at different temperatures and stresses are used to validate the proposed ideas: it is found that different creep stages present different diffusion characters, and therefore different dislocation motion character.},
  language  = {en}
}
@article{GaciZaourarBriqueuetal.2011,
  author    = {Gaci, Said and Zaourar, Naima and Briqueu, Louis and Holschneider, Matthias},
  title     = {Regularity analysis applied to sonic logs data a case study from KTB borehole site},
  series = {Arabian journal of geosciences},
  volume    = {4},
  journal   = {Arabian journal of geosciences},
  number    = {1-2},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {1866-7511},
  doi       = {10.1007/s12517-010-0129-y},
  pages     = {221 -- 227},
  year      = {2011},
  abstract  = {Borehole logs provide in situ information about the fluctuations of petrophysical properties with depth and thus allow the characterization of the crustal heterogeneities. A detailed investigation of these measurements may lead to extract features of the geological media. In this study, we suggest a regularity analysis based on the continuous wavelet transform to examine sonic logs data. The description of the local behavior of the logs at each depth is carried out using the local Hurst exponent estimated by two (02) approaches: the local wavelet approach and the average-local wavelet approach. Firstly, a synthetic log, generated using the random midpoints displacement algorithm, is processed by the regularity analysis. The obtained Hurst curves allowed the discernment of the different layers composing the simulated geological model. Next, this analysis is extended to real sonic logs data recorded at the Kontinentales Tiefbohrprogramm (KTB) pilot borehole (Continental Deep Drilling Program, Germany). The results show a significant correlation between the estimated Hurst exponents and the lithological discontinuities crossed by the well. Hence, the Hurst exponent can be used as a tool to characterize underground heterogeneities.},
  language  = {en}
}