This is the first part of an effort to connect molecular dynamics to a well-established continuum theory, micromorphic theory. This effort includes two parts: mechanical variables and balance laws. In this paper, the physical picture of micromorphic theory is introduced. A geometric model of an...

In this paper, the time evolution laws for the averaged conserved dynamical variables are derived based on a molecular dynamic model. It is found that they follow exactly the balance laws in micromorphic continuum, derived by Eringen in a top-down approach. Since all the mechanical variables in...

Set valued probability theory is used to analyze and model highly uncertain probability systems. In this work a set valued probability is defined over the measurable space. The range of set valued probability is the set of subsets of the unit interval. Some basic properties and the connection...