Abstract
We review the long wavelength description of three-dimensional liquids of entangled lines with an average orientation along the z-axis. Originally developed for polymer nematics, a closely related approach is applicable to the vortex liquid state of high temperature superconductors, and to ferro- and electrorheological fluids. The theory predicts unusual behavior of the three-dimensional structure function near the origin of reciprocal space. Density fluctuations in a constant- z cross section also provide a precise signature that one is dealing with a liquid of lines rather than a liquid of points. Under favorable circumstances, it is even possible to deduce the average length of the lines from such a cross section. Freeze-fracture experiments on polymer nematics are proposed to test these ideas.
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