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The Nosé thermostat for the pattern formation dynamics

The Nosé thermostat method for pattern formation dynamics is developed by coupling the dynamical equation of the friction coefficient with the Langevin-type equation for diblock copolymer mesophases. It is clarified that the physical value obtained along the trajectory generated by the deterministic system reproduces Gibbs' canonical ensemble by keeping the kinetic energy of the system at a target value. Using this method, one can obtain well-defined three-dimensional ordered morphologies from numerical simulations within a finite small duration of computational time. In particular, we found the double gyroid and the F ddd mesophases in the transition region between layers and column phases from the random initial conditions.