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Spatial pattern formation in external noise: theory and simulation
S E Kurushina1, V V Maximov, Yu M Romanovskii
1Physics Department, Samara State Aerospace University, Moskovskoye Shosse 34, Samara 443086, Russian Federation. kurushina72@gmail.com
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
Summary
This study analyzes spatial pattern formation in fluctuating media using order parameters. The research reveals how external noise influences phase transition boundaries in reaction-diffusion systems.
Area of Science:
- Statistical physics
- Non-equilibrium systems
- Pattern formation
Background:
- Spatial pattern formation is crucial in various natural phenomena.
- Fluctuating media present challenges for understanding pattern dynamics.
- Order parameters provide a framework for describing collective behavior.
Purpose of the Study:
- To analytically investigate spatial pattern formation in fluctuating media.
- To apply the order parameters concept to reaction-diffusion systems with noise.
- To understand noise-induced effects on phase transitions.
Main Methods:
- Utilized a reaction-diffusion system with external noise as a model.
- Derived stochastic equations for unstable mode amplitudes (order parameters).
- Obtained the dispersion equation for averaged amplitudes and the Fokker-Planck equation for order parameters.
Main Results:
- Developed a theoretical framework for analyzing pattern formation.
- Quantified the influence of external noise on system dynamics.
- Identified noise-dependent variations in ordering and disordering phase transition boundaries.
Conclusions:
- The order parameters concept offers a powerful tool for studying complex systems.
- External noise can significantly alter the stability and transitions of spatial patterns.
- The developed theory provides insights into noise-induced phenomena in reaction-diffusion systems.
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