SUPPLEMENTARY MATERIALS: CHEVRON PATTERNS IN AN ACTIVE NEMATIC LIQUID CRYSTAL FILM IN CONTACT WITH SMECTIC A from Chevron patterns in an active nematic liquid crystal film in contact with smectic A

We study a new mechanism of active matter confinement of a thin, active nematic sample consisting of microtubules, activated by adenosine triphosphate (ATP), placed between a slab of passive liquid crystal, the compound 8CB and water. The 8CB slab is kept at a temperature below the phase transition value between the nematic and the smectic A phases. The smectic A molecules are horizontally aligned with an applied magnetic field, with their centres of mass arranged on equally spaced layers perpendicular to the field. The contact with the active nematic prompts flow in the smectic slab, along the direction parallel to the layers. This flow direction is transferred back to the active nematic. We set up a model of such contact flow and make predictions on the experimentally observed pattern, from the point of view of asymptotic, linear and nonlinear analyses. We examine such results within the scope of the principle of minimum energy dissipation of the flow. For analytic convenience, we consider the active nematic confined between two symmetric 8CB slabs and show that the conclusions still hold when replacing the bottom smectic A substrate with water, as in the experimental setting.