This chapter presents microscopic models of diffusion (Brownian motion). The discussed diffusion models explicitly describe the dynamics of solvent molecules. Such molecular dynamics models provide many more details than the models discussed in Chapter 4 (which simply postulate that the diffusing molecule is subject to a random force) and can be used to assess the accuracy of the stochastic diffusion models from Chapter 4. The analysis starts with theoretical solvent models, including a simple “one-particle” description of the solvent (heat bath), which is used to introduce the generalized Langevin equation and the generalized fluctuation–dissipation theorem. Analytical insights are provided by theoretical models with short- and long-range interactions. The chapter concludes with less analytically tractable, but more realistic, computational models, introducing molecular dynamics (molecular mechanics) and applying it to the Lennard-Jones fluid and to simulations of ions in aquatic solutions.

This chapter discusses multi-resolution simulation methods for modelling reaction–diffusion processes. They use a detailed modelling approach only in certain parts of the computational domain, whilst in the remainder of the domain a coarser, less detailed, method is used. Two examples of multi-resolution methods are presented. The first example couples the Brownian dynamics with the corresponding compartment-based description. The second example couples molecular dynamics together with its coarser Langevin description. The chapter concludes with an overview of related multi-resolution approaches in the literature.