Dynamics of surface roughening in disordered media

Z. Csahók, K. Honda, E. Somfai, M. Vicsek, T. Vicsek

Research output: Contribution to journalArticle

44 Citations (Scopus)

Abstract

In this paper the roughening of interfaces moving in inhomogeneous media is investigated by examining the corresponding stochastic differential equations using (i) numerical methods and (ii) dimensional analysis. We consider interface evolution equations where disorder is represented by quenched noise which can be both additive and multiplicative. Our main finding is that quenched noise leads to a new universality class as concerning the exponents δ and β describing respectively the spatial and temporal scaling of surface roughness. In particular, additive noise close to the pinning transition results in a behaviour with δ = 0.71 ± 0.08 and β = 0.61±0.06 up to a crossover time. These estimates are in very good agreement with the theoretical prediction β = 3 5 and δ = 3 4 that we derive from a dimensional analysis of the equation. Furthermore, we argue that multiplicative noise is the appropriate choice to describe experiments where the interface between two flowing phases is considered. By numerically integrating the proposed equation we have obtained (i) surfaces remarkably similar to those observed in the experiments and (ii) a scaling of the surface width as a function of time with an exponent β = 0.65 being in an excellent agreement with the experimental value. In addition to the exponents we discuss other relevant features of the surfaces, including the scaling of the average velocity of the surface νa close to pinning and the non-trivial, power law distribution of waiting times and noise along the interface in the stationary regime.

Original languageEnglish
Pages (from-to)136-154
Number of pages19
JournalPhysica A: Statistical Mechanics and its Applications
Volume200
Issue number1-4
DOIs
Publication statusPublished - Nov 15 1993

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Disordered Media
Dimensional Analysis
Exponent
Scaling
dimensional analysis
exponents
scaling
Moving Interface
Inhomogeneous Media
Multiplicative Noise
Power-law Distribution
Additive Noise
Surface Roughness
Waiting Time
Universality
Evolution Equation
Experiment
Stochastic Equations
Crossover
Disorder

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

Dynamics of surface roughening in disordered media. / Csahók, Z.; Honda, K.; Somfai, E.; Vicsek, M.; Vicsek, T.

In: Physica A: Statistical Mechanics and its Applications, Vol. 200, No. 1-4, 15.11.1993, p. 136-154.

Research output: Contribution to journalArticle

Csahók, Z. ; Honda, K. ; Somfai, E. ; Vicsek, M. ; Vicsek, T. / Dynamics of surface roughening in disordered media. In: Physica A: Statistical Mechanics and its Applications. 1993 ; Vol. 200, No. 1-4. pp. 136-154.
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