# Introduction to Mathematical Statistics by P. Hoel

By P. Hoel

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70:1-124, 1997. M. Pismen. Nonlocal diffuse interface theory of thin films and the moving contact line. Phys. Rev. E, 64:021603, 2001. B. F. C. Armstrong, and O. Hassager. Dynamics of Polymeric Liquids, Vol. 2. Kinetic Theory. Wiley, New York, 1987. [65] G. Marrucci and F. Greco. The elastic constants of Maier-Saupe rodlike molecule nematics. Mol Cryst. Liq. , 206:17-30, 1991. H. Lin and C. Liu. Nonparabolic dissipative systems, modeling the flow of liquid crystals. Comm. Pure Appl. , 48:501-537, 1995.

A. Y. Zhu. Direct numerical simulations of fluid-solid systems using the arbitrary lagrangian-eulerian technique. J. Comput. , 169:427-462, 2001. [10] B. D. A. Basaran. Drop formation from a capillary tube: Comparison of one-dimensional and two-dimensional Emalyses and occurrence of satellite drops. Phys. Fluids, 14:2606-2621, 2002. W. F. W. J. Derby. Transient polymeric drop extension and retraction in uniaxial extensional flows. J. , 98:141-168, 2001. [12] S. G. Leal. The deformation of a viscoelastic drop subjected to steady uniaxial extensional flow of a Newtonian fluid.

As a result, their relative motion will be geometrically constrained, and the physics becomes non-trivial since many-particle correlations have to be considered. This situation will be applicable to a thermotropic nematic liquid as well. In general the orientation of the director in a flowing nematic is determined by four external influences which tend to compete with, and in the steady state balance one another. The first effect is the influence of flow alignment; in the case of simple planar shear this tends to rotate the director until it lies almost, though not quite, in the direction in which the fluid is moving.