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The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

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Published on: May 1, 2018

Crossover from isotropic to directed percolation.

Zongzheng Zhou1, Ji Yang, Robert M Ziff

  • 1Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230027, People's Republic of China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
PubMed
Summary
This summary is machine-generated.

We introduce the biased directed percolation (BDP) model, generalizing directed percolation with anisotropic probabilities. Critical exponents for BDP are consistent with directed percolation, indicating relevance of asymmetric scaling fields.

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Area of Science:

  • Statistical Physics
  • Complex Systems
  • Phase Transitions

Background:

  • Directed percolation (DP) is a fundamental model for phase transitions in systems with quenched disorder and continuous symmetry breaking.
  • Standard isotropic percolation (IP) and DP represent limiting cases of cluster growth dynamics.

Purpose of the Study:

  • To generalize the directed percolation (DP) model by introducing anisotropic probabilities for cluster growth.
  • To investigate the properties of the biased directed percolation (BDP) model in the region between isotropic and directed percolation.
  • To determine critical exponents and scaling behavior of the BDP model.

Main Methods:

  • Utilized the Leath-Alexandrowicz method for cluster growth from an active seed site.
  • Performed extensive Monte Carlo simulations on square and simple-cubic lattices.
  • Analyzed numerical data using finite-size scaling techniques.

Main Results:

  • Located percolation thresholds for the BDP model with anisotropy parameters p(d) = 0.6 and 0.8.
  • Determined critical exponents for the BDP model, finding consistency with standard DP.
  • Identified the renormalization exponent for asymmetric perturbations near isotropic percolation, confirming its relevance.

Conclusions:

  • The biased directed percolation (BDP) model provides a unified framework encompassing both isotropic and directed percolation.
  • The critical behavior of BDP is closely related to that of standard DP, even with anisotropic growth.
  • Asymmetric scaling fields are relevant perturbations near the isotropic percolation point.