Spatial pattern formation in external noise: Theory and simulation
Abstract
Spatial pattern formation in fluctuating media is researched analytically from the point of view of the order parameters concept. A reaction-diffusion system with external noise is considered as a model of such media. Stochastic equations for unstable mode amplitudes (order parameters), the dispersion equation for averaged amplitudes of unstable modes, and the Fokker-Planck equation for the order parameters are obtained. The theory developed makes it possible to analyze different noise-induced effects including the variation of boundaries of ordering and disordering phase transitions depending on the parameters of external noise
- Publication:
-
Physical Review E
- Pub Date:
- July 2012
- DOI:
- 10.1103/PhysRevE.86.011124
- arXiv:
- arXiv:1201.4695
- Bibcode:
- 2012PhRvE..86a1124K
- Keywords:
-
- 05.40.Ca;
- 89.75.Kd;
- 02.50.Ey;
- 05.65.+b;
- Noise;
- Patterns;
- Stochastic processes;
- Self-organized systems;
- Nonlinear Sciences - Pattern Formation and Solitons
- E-Print:
- 22 pages, 10 figures