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Roughness at the depinning threshold for a long-range elastic string.

Alberto Rosso1, Werner Krauth

  • 1CNRS-Laboratoire de Physique Statistique, Ecole Normale Supérieure, 24, rue Lhomond, 75231 Paris Cedex 05, France. rosso@lps.ens.fr

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 28, 2002
PubMed
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We precisely calculated the roughness exponent (zeta) for elastic strings in random media. Our findings differ from prior simulations and experiments, suggesting limitations in current elasticity models.

Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Materials Science

Background:

  • The roughness exponent (zeta) characterizes the interface width of elastic systems in disordered environments.
  • Previous studies on long-range elastic strings at the depinning threshold yielded varying results.
  • Experimental observations in crack propagation and liquid helium (4He) have been linked to this exponent.

Purpose of the Study:

  • To compute the roughness exponent (zeta) of a long-range elastic string at the depinning threshold in a random medium with high precision.
  • To compare the computed value with results from previous simulations, renormalization-group calculations, and experiments.
  • To assess the validity of pure harmonic long-range elasticity models in describing experimental phenomena.

Main Methods:

Related Experiment Videos

  • A novel numerical method exploiting the analytic structure of the problem (no-passing theorem).
  • Avoidance of direct simulation of the evolution equations for efficiency and accuracy.
  • High-precision computation of the roughness exponent zeta.

Main Results:

  • The computed roughness exponent is zeta = 0.388 +/- 0.002.
  • This value is significantly larger than those reported in previous simulations.
  • The results are incompatible with experimental data from crack propagation in solids and 4He liquid meniscus experiments.

Conclusions:

  • The precise calculation of zeta provides a new benchmark for theoretical and experimental studies.
  • Discrepancies with previous simulations suggest limitations in earlier computational approaches.
  • The incompatibility with experimental data indicates that pure harmonic long-range elasticity in the quasistatic limit is insufficient to describe these phenomena.