Chong Luo et al 2005 Nonlinearity 18 379 doi:10.1088/0951-7715/18/1/018
Chong Luo1, Hui Zhang1 and Pingwen Zhang1
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We analyse the structure of steady state solutions of the one-dimensional Doi model for rod-like molecules. We prove that if the interaction strength parameter U is less than 4, then the constant solution is the only possible steady state solution. If U is larger than 4, then there is a new solution that corresponds to the nematic phase. All other non-constant solutions are obtained from this solution by translation. We prove further that the nematic solutions have period π instead of 2π, a property that signifies the fact the rods are symmetric, i.e. they have orientations but no directions.
61.30.Cz Molecular and microscopic models and theories of liquid crystal structure
76A15 Liquid crystals (See also 82D30)
35Q30 Stokes and Navier-Stokes equations (See also 76D05, 76D07, 76N10)
Issue 1 (January 2005)
Received 5 January 2004, in final form 16 September 2004
Published 25 October 2004
Chong Luo et al 2005 Nonlinearity 18 379
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