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Spatial and temporal spectra of noise driven stripe patterns.
1Physikalisch Technische Bundesanstalt, 38116 Braunschweig, Germany. Kestutis.Staliunas@PTB.DE
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 12, 2001
Summary
Noise in stripe patterns follows a 1/f power law, with fluctuations in stripe position exhibiting subdiffusive behavior. This research analyzes spatial and temporal noise spectra in a stochastic Swift-Hohenberg model.
Area of Science:
- Complex systems
- Nonlinear dynamics
- Statistical physics
Background:
- Stripe patterns emerge in various physical and biological systems.
- Understanding noise effects is crucial for predicting pattern stability and evolution.
- The Swift-Hohenberg equation is a standard model for pattern formation.
Purpose of the Study:
- Investigate spatial and temporal noise power spectra in stripe patterns.
- Analyze the behavior of stochastic fluctuations in stripe position.
- Determine the relationship between noise spectra and system dimensionality.
Main Methods:
- Analytical investigation of the stochastic Swift-Hohenberg equation.
- Numerical simulations of the model.
- Calculation of spatial and temporal noise power spectra.
- Analysis of stripe position fluctuations.
Main Results:
- Temporal noise spectra exhibit a 1/f(alpha) form, where alpha depends on the spatial dimension (D).
- The exponent alpha is determined by the relation alpha=1+(3-D)/4.
- Stochastic fluctuations in stripe position demonstrate subdiffusive behavior.
Conclusions:
- The study provides a quantitative description of noise in stripe patterns.
- Results offer insights into the dynamics of pattern formation under stochastic influences.
- The findings are relevant for systems exhibiting similar pattern dynamics and noise characteristics.