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Voting and catalytic processes with inhomogeneities.

Mauro Mobilia1, Ivan T Georgiev

  • 1Center for Stochastic Processes in Science and Engineering, Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061-0435, USA. mmobilia@vt.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 21, 2005
PubMed
Summary

Competing inhomogeneities create complex, fluctuating steady states in voter and catalytic models. System behavior depends on dimensionality, inhomogeneity strength, and distance, with parallels to electrostatics.

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Area of Science:

  • Statistical Physics
  • Complex Systems Dynamics

Background:

  • The voter model and monomer-monomer catalytic process are fundamental models for understanding opinion dynamics and surface reactions.
  • Investigating the impact of inhomogeneities is crucial for realistic modeling of complex systems.

Purpose of the Study:

  • To analyze the steady-state properties of the voter model and monomer-monomer catalytic process with multiple competing inhomogeneities.
  • To determine how system dimensionality, inhomogeneity strength, and separation influence the emergent non-trivial fluctuating steady states.

Main Methods:

  • Exact analytical calculations for order parameters in arbitrary dimensions.
  • Numerical simulations for cases with more than two inhomogeneities.
  • Exploration of spatial dependence and connections to electrostatic systems.

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Main Results:

  • Derived formal expressions for order parameters (magnetization, adsorbed particle concentration) with 'n' inhomogeneities.
  • Explicitly computed static and long-time properties for n=1,2, capturing generic system features.
  • Identified specific dependencies on dimensionality, inhomogeneity strength, and distances.

Conclusions:

  • Competing inhomogeneities lead to non-trivial fluctuating steady states in these models.
  • System behavior exhibits dimensional dependence and formal analogies with electrostatic phenomena.
  • The study provides a comprehensive understanding of order parameter behavior under various inhomogeneity configurations.