Riemann’s minimal surface, shown here, is a singly-periodic surface of channels connecting flat layers. In a new paper, we show that it can be decomposed into two more fundamental defects, called screw dislocations. See the paper:
S.A. Matsumoto, C.D. Santangelo and R.D. Kamien, “Smectic pores and defect cores,” accepted Interfaces Focus, [ARXIV] (2012).
Abstract: Riemann’s minimal surfaces are a complete, embeddable, one-parameter family of minimal surfaces with translational symmetry along one direction. It’s infinite number of planar ends are joined together by an array of necks, closely matching the morphology of a bicontinuous, lamellar system with pores connecting alternating layers. We demonstrate explicitly that Riemann’s minimal surfaces are composed of a nonlinear sum of two oppositely-handed helicoids. This description is particularly appropriate for describing smectic liquid crystals containing two screw dislocations.