IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v364y2006icp190-196.html
   My bibliography  Save this article

Roughness fluctuations, roughness exponents and the universality class of ballistic deposition

Author

Listed:
  • Aarão Reis, F.D.A.

Abstract

In order to estimate roughness exponents of interface growth models, we propose the calculation of effective exponents from the roughness fluctuation σ in the steady state. We compare the finite-size behavior of these exponents and the ones calculated from the average roughness 〈w2〉 for two models in the 2+1-dimensional Kardar–Parisi–Zhang (KPZ) class and for a model in the 1+1-dimensional Villain–Lai–Das Sarma (VLDS) class. The values obtained from σ provide consistent asymptotic estimates, eventually with smaller finite-size corrections. For the VLDS (nonlinear molecular beam epitaxy) class, we obtain α=0.93±0.01, improving previous estimates. We also apply this method to two versions of the ballistic deposition model in two-dimensional substrates, in order to clarify the controversy in terms of its universality class raised by numerical results and a recent derivation of its continuous equation. Effective exponents calculated from σ suggest that both versions are in the KPZ class. Additional support for this conclusion is obtained by a comparison of the full-roughness distributions of these models and the distribution of other discrete KPZ models.

Suggested Citation

  • Aarão Reis, F.D.A., 2006. "Roughness fluctuations, roughness exponents and the universality class of ballistic deposition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 190-196.
    • Handle: RePEc:eee:phsmap:v:364:y:2006:i:c:p:190-196
    DOI: 10.1016/j.physa.2005.09.052
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437105010137
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2005.09.052?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Nogueira, Isadora R. & Alves, Sidiney G. & Ferreira, Silvio C., 2011. "Scaling laws in the diffusion limited aggregation of persistent random walkers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4087-4094.
    2. Disrattakit, P. & Chanphana, R. & Chatraphorn, P., 2016. "Roughness distribution of multiple hit and long surface diffusion length noise reduced discrete growth models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 619-629.
    3. Hao, Da-Peng & Tang, Gang & Xun, Zhi-Peng & Xia, Hui & Han, Kui, 2018. "Simulation of finite size effects of the fiber bundle model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 338-346.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:364:y:2006:i:c:p:190-196. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.