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dc.contributor.authorZhou, Hong
dc.contributor.authorWang, H. Y.
dc.contributor.authorWang, Q.
dc.contributor.authorForest, M. G.
dc.date2007
dc.date.accessioned2013-01-18T19:11:52Z
dc.date.available2013-01-18T19:11:52Z
dc.date.issued2007
dc.identifier.citationNonlinearity / Volume 20, Issue 2, 277-297
dc.identifier.urihttp://hdl.handle.net/10945/25557
dc.descriptionThe article of record as published may be located at http://dx.doi.org/10.1088/0951-7715/20/2/003en_US
dc.description.abstractWe study equilibria of the Smoluchowski equation for rigid, dipolar rod ensembles where the intermolecular potential couples the dipole-dipole interaction and the Maier-Saupe interaction. We thereby extend previous analytical results for the decoupled case of the dipolar potential only (Fatkullin and Slastikov 2005 Nonlinearity 18 2565-80; Ji et al Phys. Fluids at press; Wang et al 2005 Commun. Math. Sci. 3 605-20) or the Maier-Saupe potential only (Constantin et al 2004 Arch. Ration. Mech. Anal. 174 365-84; Constantin et al 2004 Discrete Contin. Dyn. Syst. 11 101-12; Constantin and Vukadinovic 2005 Nonlinearity 18 441-3; Constantin 2005 Commun. Math. Sci. 3 531-44; Fatkullin and Slastikov 2005 Commun. Math. Sci. 3 21-6; Liu et al 2005 Commun. Math. Sci. 3 201-18; Luo et al 2005 Nonlinearity 18 379-89; Zhou et al 2005 Nonlinearity 18 2815-25; Zhou and Wang Commun. Math. Sci. at press), and prove certain numerical observations for equilibria of coupled potentials (Ji et al Phys. Fluids at press). We first derive stability conditions, on the magnitude of the polarity vector (the first moment of the orientational probability distribution function) and on the direction of the polarity. We then prove that all stable equilibria of rigid, dipolar rod dispersions are either isotropic or prolate uniaxial. In particular, all stable anisotropic equilibrium distributions admit the following remarkable symmetry: the peak axis of orientation is aligned with both the polarity vector (first moment) and the distinguished director of the uniaxial second moment tensor. The stability is essential in establishing the axisymmetry. To demonstrate that the stability is indeed required, we show that there exist unstable non-axisymmetric equilibria.en_US
dc.rightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.en_US
dc.titleCharacterization of stable kinetic equilibria of rigid, dipolar rod ensembles for coupled dipole-dipole and Maier-Saupe potentialsen_US
dc.typeArticleen_US
dc.contributor.departmentApplied Mathematics


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