Spatial pattern formation in external noise: theory and simulation

Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jul;86(1 Pt 1):011124. doi: 10.1103/PhysRevE.86.011124. Epub 2012 Jul 20.

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 types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Algorithms*
  • Computer Simulation*
  • Models, Statistical*
  • Pattern Recognition, Automated / methods*
  • Signal-To-Noise Ratio