The complex interplay of molecular scale effects, nonlinearities in the orientational field and long-range elastic forces makes liquid-crystal physics very challenging. A consistent way to extract information from the microscopic, molecular scale up to the meso- and macroscopic scale is still missing. Here, we develop a hybrid procedure that bridges this gap by combining extensive Monte Carlo (MC) simulations, a local Landau-de Gennes theory, classical density functional theory, and finite-size scaling theory. As a test case to demonstrate the power and validity of our novel approach we study the effective interaction among colloids with Boojum defect topology immersed in a nematic liquid crystal. In particular, at sufficiently small separations colloids attract each other if the angle between their center-of-mass distance vector and the far-field nematic director is about 30 degrees. Using the effective potential in coarse-grained two-dimensional MC simulations we show that self-assembled structures formed by the colloids are in excellent agreement with experimental data.DFG, GRK 1524, Self-Assembled Soft-Matter Nanostructures at Interface
