New methods of characterizing spatio-temporal patterns in laboratory experiments

• Main Author: Kurtuldu, Huseyin
• Published: Georgia Institute of Technology 2011
• Subjects: Lyapunov dimension; Thermal convection; Pattern formation; Patter characterization techniques; Principal component analysis; Fourier analysis; Curvature; Image characterization techniques; Rayleigh-B´enard convection; Spatial analysis (Statistics); Pattern formation (Physical sciences); Homology theory; Differentiable dynamical systems
• Online Access: http://hdl.handle.net/1853/37121

Complex patterns arise in many extended nonlinear nonequilibrium systems in physics, chemistry and biology. Information extraction from these complex patterns is a challenge and has been a main subject of research for many years. We study patterns in Rayleigh-Benard convection (RBC) acquired from our laboratory experiments to develop new characterization techniques for complex spatio-temporal patterns. Computational homology, a new topological characterization technique, is applied to the experimental data to investigate dynamics by quantifying convective patterns in a unique way. The homology analysis is used to detect symmetry breakings between hot and cold flows as a function of thermal driving in experiments, where other conventional techniques, e.g., curvature and wave-number distribution, failed to reveal this asymmetry. Furthermore, quantitative information is acquired from the outputs of homology to identify different spatio-temporal states. We use this information to obtain a reduced dynamical description of spatio-temporal chaos to investigate extensivity and physical boundary effects in RBC. The results from homological analysis are also compared to other dimensionality reduction techniques such as Karhunen-Loeve decomposition and Fourier analysis.