The complex orthogonal decomposition (COD), a process of extracting complex modes from complex ensemble data, is summarized, as is the use of complex modal coordinates. A brief assessment is made on how small levels of noise affect the decomposition. The decomposition is applied to the posturing of Caenorhabditis elegans, an intensively studied nematode. The decomposition indicates that the worm has a multimodal posturing behavior, involving a dominant forward locomotion mode, a secondary, steering mode, and likely a mode for reverse motion. The locomotion mode is closer to a pure traveling waveform than the steering mode. The characteristic wavelength of the primary mode is estimated in the complex plane. The frequency is obtained from the complex modal coordinate's complex whirl rate of the complex modal coordinate, and from its fast Fourier transform. Short-time decompositions indicate the variation of the wavelength and frequency through the time record.
Complex Orthogonal Decomposition Applied to Nematode Posturing
Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received October 12, 2011; final manuscript received September 15, 2012; published online May 14, 2013. Assoc. Editor: D. Dane Quinn.
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Feeny, B. F., Sternberg, P. W., Cronin, C. J., and Coppola, C. A. (May 14, 2013). "Complex Orthogonal Decomposition Applied to Nematode Posturing." ASME. J. Comput. Nonlinear Dynam. October 2013; 8(4): 041010. https://doi.org/10.1115/1.4023548
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