Computationally cheap soft matter modelling: an introduction to dynamic density functional theory

Many standard models for particles suspended in a bath, such as Langevin dynamics or the Kramers/Fokker-Planck/Smoluchowski/forward Kolmogorov equation quickly become computationally intractable as the number of particles in the system increases.  Conventional mean-field approximations fail to capture crucial microscopic behaviour, which in turn has strong effects on the macroscopic dynamics.  I will present a statistical mechanics approach, dynamical density functional theory (DDFT), which is both computationally tractable and which captures a range of important physical effects.  As well as outlining the approximations made in the derivation, I will demonstrate the excellent agreement between DDFT and the underlying stochastic dynamics.  If time allows I will describe an efficient and accurate numerical scheme for solving the resulting PDEs.