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Theory of diffusion controlled growth.

R C Ball1, E Somfai

  • 1Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom.

Physical Review Letters
|September 13, 2002
PubMed
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We developed a new theory for diffusion limited aggregation and dielectric breakdown models. This framework reveals interrelations between models and predicts a new superuniversality in tip scaling exponents.

Area of Science:

  • Theoretical physics
  • Complex systems

Background:

  • Diffusion limited aggregation (DLA) and dielectric breakdown models (DBM) are crucial for understanding pattern formation.
  • Existing models often lack a unified theoretical framework, especially concerning parameter variations.

Purpose of the Study:

  • To establish a novel theoretical framework unifying DLA and DBM in two dimensions.
  • To investigate the impact of ultraviolet cutoff strategies on model interrelations.
  • To explore analogies with turbulence and employ logarithmic field variables.

Main Methods:

  • Developed a new theoretical framework for DLA and DBM.
  • Utilized logarithmic field variables and explored analogies with turbulence.
  • Employed Gaussian truncation of mode-mode coupling for property calculations.

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Main Results:

  • Established interrelations between DLA and DBM under varying ultraviolet cutoff strategies.
  • Successfully calculated all model properties within the Gaussian truncation.
  • Predicted and confirmed a new superuniversality in the tip scaling exponent.

Conclusions:

  • The new theoretical framework provides a unified approach to DLA and DBM.
  • The findings confirm the predicted superuniversality, offering new insights into fractal growth.
  • The results align well with prior simulation data, validating the theoretical model.