Lattice simulations, efficient techniques

Wetting phenomena on irregularly rough surfaces have not been studied so far. It seems quite reasonable to use computer simulation methods for this purpose. Of course, such computer simulation would be very expensive as the finite size of the simulation cells would require appropriate averaging over different spatial distributions of surface inhomogeneities. Nevertheless, with modern fast computers and using multispin coding techniques such calculations can be efficiently carried out for lattice gas systems. 

In addition to the direct solution of PDEs corresponding to reaction-diffusion equations, in recent years attention has begun to be focused on the use of coupled lattice methods. In this approach, diffusion is not treated explicitly, but, rather, a lattice of elements in which the kinetic processes occur are coupled together in a variety of ways. The simulation of excitable media by cellular automata techniques has grown in popularity because they offer much greater computational efficiency for the two- and three-dimensional configurations required to study complex wave activity such as spirals and scroll waves. 

Equation [2] is known as a simple sampling MC method, and such techniques were already in use in the 1950s in a polymer context and stiU find some applications more recendy, " but only for the study of self-avoiding walks (SAWs) on lattices, for rather short chain lengths N. Although SAW is one of the most primitive models for a macromolecule in dilute solution trader good solvent conditions, this model is still widely in use, as its simplicity allows the use of both elaborate mathematical methods and very efficient simulation algorithms. " ... 

This technique is most often used in lattice quantum chromodynamics ((JCD) simulations. Mehlig et al. [55] demonstrated its use by simulating Lennard-Jonesium as an example of a condensed matter system. Similarly, Clamp et al. [56] simulated a 2D Lennard-Jones fluid using both MD and hybrid MC and found that hybrid MC is more ergodic and samples phase space more efficiently than MD. A more realistic system was studied by Brotz et al. [57], employed hybrid MC to calculate the phase diagram of silicon. 

---