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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
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.
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.
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.