Cluster potentials for multi-scale interactions

A cluster approach has been proposed to describe the process of heat transport in microscale. Molecular clustering is described by integrating the Lennard-Jones potential over specific physical domains, forming cluster potentials that possess repulsive and attractive forces sensitively varying with the geometrical shapes of the molecular clusters. The cluster potentials thus developed provides a consistent approach for describing multi-scale heat transport, in that different shapes/dimensions of the clusters take different exponents in the repulsive and attractive forces. A one-dimensional example is given to illustrate the essence of the cluster dynamics simulation, emphasizing devious behavior from molecular motion and replacement of a physical boundary by the cluster potential of a different scale.