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11:52
Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps
Published on: February 9, 2017
Statistical characterizations of spatiotemporal patterns generated in the Swift-Hohenberg model
Shaowen Hu1, Girish Nathan, Donald J Kouri
1Department of Chemistry, University of Houston, Houston, Texas 77204, USA.
Chaos (Woodbury, N.Y.)
|January 7, 2006
Summary
This study analyzes nonequilibrium patterns using two statistical measure families. These measures quantify disorder in labyrinthine and general structures, revealing distinct relaxation stages in spatiotemporal dynamics.
Area of Science:
- Physics
- Statistical Mechanics
- Nonlinear Dynamics
Background:
- Nonequilibrium patterns are crucial in various scientific fields.
- Characterizing disorder and evolution in these patterns is challenging.
- Existing methods may not fully capture complex spatiotemporal dynamics.
Purpose of the Study:
- To quantitatively characterize nonequilibrium patterns and their evolution.
- To analyze distinct relaxation stages in spatiotemporal dynamics.
- To apply statistical measures to Swift-Hohenberg equation dynamics.
Main Methods:
- Utilizing two families of statistical measures for pattern characterization.
- Quantifying disorder in labyrinthine patterns (domain size, defect density, wave number variations).
- Applying measures to general nonequilibrium structures, including domain growth.
Main Results:
- Successfully quantified disorder in complex patterns.
- Identified and characterized distinct relaxation stages.
- Demonstrated the utility of the statistical measures for analyzing spatiotemporal dynamics.
Conclusions:
- The two statistical measure families provide robust tools for analyzing nonequilibrium patterns.
- Distinct relaxation stages were identified in the Swift-Hohenberg equation dynamics.
- These methods offer a comprehensive approach to understanding pattern evolution.
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