Motivated by experiments on colloidal membranes composed of chiral rod-like viruses, we use Monte Carlo methods to determine the phase diagram for liquid crystalline order rods and membrane shape. We generalize Lebwohl-Lasher model a nematic with coupling curved surface edge tension resistance bending, include an energy cost tilting relative local normal. The is represented triangular mesh hard...

Abstract Decades of work have gone into developing efficient proof calculi, data structures, algorithms, and heuristics for first-order automatic theorem proving. Higher-order provers lag behind in terms efficiency. Instead a new higher-order prover from the ground up, we propose to start with state-of-the-art superposition E gradually enrich it features. We explain how extend prover’s $$\lambd...