Surface super-roughening driven by spatiotemporally correlated noise

Alés, Alejandro; López, Juan M.

doi:10.1088/1742-5468/ab74c9

Cited by 6 publications

(5 citation statements)

References 38 publications

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“…We use the label 'EW' to emphasize that these are the exponents in the Laplacian (harmonic elasticity) regime. These, indeed, correspond to the exact exponents for the purely Laplacian model, also known as the Edwards-Wilkinson equation, in the case of time correlated noise [51].…”

Section: A Theoretical Resultssupporting

confidence: 68%

“…The temporally correlated noise was generated by using the Mandelbrot fractional noise algorithm [52] that produces high quality Gaussian distributed random numbers with the desired correlation index θ. This technique has proven to be very efficient and precise [51,53,54] for systems similar to ours.…”

Section: Numerical Results In D =mentioning

confidence: 82%

“…Specifically, all models share in common the existence of a threshold value θ c = 1/4 for anomalous behavior, which seems to be robust across different universal-ity classes in d = 1. For EW, the interface shows anomalous scaling of the super-rough (non faceted) type [51] with α s (θ) = α(θ) > 1 and α loc = 1, while for KPZ the scaling is anomalous faceted type [53], with α s (θ) = α(θ) and α loc = 1, in both cases for θ > 1/4. The addition of anharmonic corrections to the EW equation studied here produces anomalous faceted scaling for a noise correlation index θ > θ c = d/4 suggesting that facet formation is a nonlinear effect.…”

Section: Discussionmentioning

confidence: 99%

“…Despite its simplicity the Larkin model is a good starting point to study the effects of disorder on kinetic roughening while, at the same time, it is related to other models of interface roughening. In fact, the model can also be seen as the limit of the EW model with temporally correlated noise as θ → 1/2, which was recently studied in detail [51]. A long standing question is whether the model is physically meaningful in d = 1 since it leads to a roughness exponent α = 3/2 so that the elastic string is characterized by local deformations that diverge as W (L)/L ∼ L 1/2 in the thermodynamic limit.…”

Section: Discussionmentioning

confidence: 99%

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Roughening of the Anharmonic Elastic Interface in Correlated Random Media

Alés,

López

2021

Preprint

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We study the roughening properties of the anharmonic elastic interface in the presence of temporally correlated noise. The model can be seen as a generalization of the anharmonic Larkin model, recently introduced by Purrello, Iguain, and Kolton [Phys. Rev. E 99, 032105 (2019)], to investigate the effect of higher-order corrections to linear elasticity in the fate of interfaces. We find analytical expressions for the critical exponents as a function of the anharmonicity index n, the noise correlator range θ ∈ [0, 1/2], and dimension d. In d = 1 we find that the interface becomes faceted and exhibits anomalous scaling for θ > 1/4 for any degree of anharmonicity n > 1. Analytical expressions for the anomalous exponents α loc and κ are obtained and compared with a numerical integration of the model. Our theoretical results show that anomalous roughening cannot exist for this model in dimensions d > 1.

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Section: A Theoretical Resultssupporting

confidence: 68%

Section: Numerical Results In D =mentioning

confidence: 82%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Roughening of the Anharmonic Elastic Interface in Correlated Random Media

Alés,

López

2021

Preprint

Self Cite

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“…However, most of previous study are conducted by Langevin thermostats [2,26] or Nose-Hoover thermostats [27,28], little has been done on the spatiotemporal effect. In fact, in numerous physical and biological systems, the spatiotemporal noises play a significant role in the dynamics [29][30][31][32][33][34], such as spatial variance and skewness [35], spatiotemporal order out of noise [36] and chirped-pulse amplification systems [37]. Simultaneously, some low-dimensional materials can form a variety of complex networks [38][39][40][41][42][43] through different junctions.…”

Section: Introductionmentioning

confidence: 99%

Energy diffusion of simple networks under the spatiotemporal thermostats

et al. 2021

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We investigate the energy transport in simple networks consisting of one-dimensional nonlinear chain with self-coupled loop. The impacts of the loop length and coupling strength on the heat flux and spatiotemporal correlation functions of energy-momentum fluctuations are discussed via Langevin thermostats generated by spatiotemporal noise. For thermostats at different temperatures, the spatiotemporal ones can weaken the total heat flux of the system in comparison with the normal Langevin ones. The total heat flux will increase when the dispersal kernel or the loop length or the coupling strength increases, while the heat flux in the loop does not change as the dispersal kernel or the loop length increases, and decrease as the coupling strength increases. Then the underlying mechanism of heat flux can be well explained by the phonon spectra and Fourier's law. For the thermostats at the same temperatures, it is shown that the peak of the propagating front for the trunk (PT) and the peak of the propagating front from the coupling position to the outer trunk (PC) do not change almost for the normal Langevin and spatiotemporal thermostats. The PT decreases and PC increases when the loop length or coupling strength increases. Our results may contribute to further understanding of thermal information appearing in coupled nanotubes, polymer chains and biological networks.

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Kinetic roughening and nontrivial scaling in the Kardar–Parisi–Zhang growth with long-range temporal correlations

Song¹,

Xia²

2021

J. Stat. Mech.

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Long-range spatiotemporal correlations may play important roles in nonequilibrium surface growth process. In order to explore the effects of long-range temporal correlation on dynamic scaling of growing surfaces, we carry out extensive numerical simulations of the (1+1)-and (2+1)-dimensional Kardar-Parisi-Zhang (KPZ) growth system in the presence of temporally correlated noise, and compare our results with previous theoretical predictions and numerical simulations. We find that surface morphologies are obviously affected with long-range temporal correlations, and as the temporal correlation exponent increases, the KPZ surfaces develop gradually faceted patterns in the saturated growth regimes. Our results show that the temporal correlated KPZ system displays evidently nontrivial dynamic properties when 0 0.5   , the characteristic roughness exponents satisfy s    , and loc  exhibiting non-universal scaling within local window sizes, which differs with the existing dynamic scaling hypotheses, both in the (1+1)-and (2+1)-dimensions.

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Surface super-roughening driven by spatiotemporally correlated noise

Cited by 6 publications

References 38 publications

Roughening of the Anharmonic Elastic Interface in Correlated Random Media

Roughening of the Anharmonic Elastic Interface in Correlated Random Media

Energy diffusion of simple networks under the spatiotemporal thermostats

Kinetic roughening and nontrivial scaling in the Kardar–Parisi–Zhang growth with long-range temporal correlations

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