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Phase growth in bistable systems with impurities.

C Echeverria¹, K Tucci, M G Cosenza

¹Laboratorio de Física Aplicada y Computacional, Universidad Nacional Experimental del Táchira, San Cristóbal, Venezuela.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|March 21, 2008

Summary

Adding impurities to chaotic bistable maps slows phase growth. Increased impurity density reduces domain size, offering control over spatiotemporal systems.

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Area of Science:

Statistical Physics
Nonlinear Dynamics
Complex Systems

Background:

Phase growth in nonuniform media is a complex phenomenon.
Understanding spatiotemporal systems requires modeling their dynamics in the presence of disorder.
Chaotic bistable maps provide a framework for studying pattern formation.

Purpose of the Study:

To investigate phase growth in a lattice of coupled chaotic bistable maps with random impurities.
To model the effects of nonuniformity on domain growth and pattern formation.
To explore the control mechanisms for phase domain size and velocity.

Main Methods:

Statistical analysis of coupled chaotic bistable maps on a lattice.
Characterization of system properties using average domain size of spin variables.
Phase diagram construction to identify homogeneous, heterogeneous, and chessboard patterns.
Calculation of critical boundaries for domain growth regimes.

Main Results:

Impurities reduce the rate of phase domain growth.
Increased impurity density leads to smaller average domain sizes.
A phase diagram reveals distinct pattern formation regions.
A critical boundary separating slow and fast domain growth regimes was identified and explained.

Conclusions:

Spatial inhomogeneities act as a control mechanism for phase domain dynamics.
The stability of local phase configurations governs transitions between growth regimes.
This model provides insights into phase growth in disordered spatiotemporal systems.