Classically, macroscopic continuum models have been developed from microscopic discrete models via the principles of statistical mechanics.
A basic concept from statistical mechanics relevant to this is that of coarse-graining or averaging.
Two important averaging processes in statistical mechanics are time averaging and ensemble averaging.
In particular, these provide a means to calculate macroscopic quantities from the properties of discrete systems.
The purpose of the Ph.D. research is to examine the applicability and limitations of various coarse-grained continuum models
on the basis of their theoretical (i.e., mathematical and physical) frameworks as well as the coarse-graining methods they employ.
Furthermore, on this basis, new coarse-grained methods and models will be developed.