Partition function propagators of a homopolymer at the chain ends along the x direction under (a) sine and (b) nanoparticle fields solved from the pseudo-spectrum or LB methods. The space discretization is set to dx = 0.05. The LB relaxation constant is τ = 2.5, 1.7( ), and 1.1 for sine field and τ = 1.7, 1.2( ), and 0.8 for nanoparticle field.
Error values (see text for definition) as a function of the relaxation constant τ for different fields with (a) dx = 0.1 in 2D, (b) dx = 0.1 in 3D, and (c) dx = 0.05 in 2D.
Error values as a function of τ for (a) sin field (mode = 1) and (b) tanh field (ξ = 1) with different field amplitudes.
Error values for as a function of τ for s = 0.4, 0.6, 0.8, and 1.0.
(a) Density distributions of a diblock copolymer system with f = 0.5 and χN = 13 from SCFT simulations with the PS or LB methods. (b) Errors in the free energies and the densities comparing the LB result to the PS result.
Density distributions of a diblock copolymer system with f = 0.5 and χN = 40 (a) without or (b) with local refinements. The solid lines are the solutions from the pseudo-spectrum method and the symbols are the solutions from the lattice Boltzmann method.
2D SCFT simulations of the self-assembly of block copolymers on commensurate templates using the LB method. The parameters of the copolymers are (a) to (c) f = 0.5 and χN = 13 and (d) to (f) f = 0.25 and χN = 18.
Runtime per iteration as a function of the total number of lattice points for different processing units and methods.
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