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Kinetic roughening in the nonlocal Kardar–Parisi–Zhang growth: Pseudospectral versus finite difference schemes

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  • Lu, Xinyu
  • Hao, Dapeng
  • Xia, Hui

Abstract

To investigate the effects of nonlocal interaction in kinetic roughening, we adopt two independent numerical methods including pseudospectral (PS) and finite difference (FD) schemes to simulate the nonlocal Kardar–Parisi–Zhang (NKPZ) equation in (1+1)-dimensions. We find that the values of growth exponent β increase gradually with the spatial decay exponent ρ, indicating that the scaling properties are dependence on nonlocal interactions within the effective spatial decay region. However, our simulations also imply that both the local roughness exponent αloc and the spectral roughness exponent αs decrease slightly with ρ. Our results could be consistent with each other using these two numerical methods, and the comparisons and differences among the existing analytical predictions and numerical results are also discussed.

Suggested Citation

  • Lu, Xinyu & Hao, Dapeng & Xia, Hui, 2022. "Kinetic roughening in the nonlocal Kardar–Parisi–Zhang growth: Pseudospectral versus finite difference schemes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    • Handle: RePEc:eee:phsmap:v:603:y:2022:i:c:s0378437122005350
    DOI: 10.1016/j.physa.2022.127819
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    References listed on IDEAS

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    1. Katzav, Eytan, 2002. "Exact result vs. dynamic renormalization group analysis for the nonlocal molecular-beam-epitaxy equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 308(1), pages 25-28.
    2. E. Katzav, 2006. "Effect of long range interactions on the growth of compact clusters under deposition," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 54(2), pages 137-140, November.
    3. Katzav, Eytan, 2002. "Exact result vs. dynamic renormalization group analysis for the non-local Kardar–Parisi–Zhang equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 309(1), pages 79-84.
    4. Tang, Gang & Ma, Benkun, 2001. "Scaling approach to the nonlocal surface growth equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 298(3), pages 257-265.
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