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On the fractal characteristics of the η model

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  • Sánchez, Angel
  • Guinea, Francisco
  • Louis, Enrique
  • Hakim, Vincent

Abstract

Since the η or dielectric breakdown model was proposed, it has been generally accepted that the fractal characteristics of the so-grown clusters have a smooth behavior as η increases from 0 to infinity. On the basis of recent theoretical calculations on a related model, we conjecture that the aggregate can become effectively branchless for η larger than a critical value η1. A related possibility is that the value 1 for the fractal dimension might be reached at finite values of η. We have carried out a large simulation program to test these conjectures and we find evidence supporting their validity. This is a preliminary report of our work on this problem.

Suggested Citation

  • Sánchez, Angel & Guinea, Francisco & Louis, Enrique & Hakim, Vincent, 1992. "On the fractal characteristics of the η model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 123-127.
    • Handle: RePEc:eee:phsmap:v:191:y:1992:i:1:p:123-127
    DOI: 10.1016/0378-4371(92)90515-R
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