Observability of the Doi orientation tensor model
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We apply the observability rank condition to the two-dimensional Doi orientation tensor model to investigate the observability of liquid crystalline polymers under imposed shear or extensional flows. Here the observability means the ability of determining the orientation tensor from the time history of the observations of the birefringence. The Doi model under shear or extensional flow is observable almost everywhere. In other words, all components of the orientation tensor can be determined from the observation of the birefringence provided that the points formed by the two components of the orientation tensor do not lie on certain curves in the plane. We also run simulations using the unscented Kalman filter (UKF) to reconstruct the orientation tensor from observations without and with noises. The UKF gives good estimates for the orientation tensor both in the absence and in the presence of observation noises.
The article of record as published may be located at http://www.m-hikari.com/ams/ams-2011/ams-5-8-2011/zhouAMS5-8-2011.pdf
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