A rigorous theory of liquid-crystal transitions is developed starting from the Liouville equation. The starting point is an all-atom description and a set of order-parameter field variables that are shown to evolve slowly via Newton's equations. The separation of time scales between that of atomic collision or vibrations and the order-parameter fields enables the derivation of rigorous equation...

The volume averaging technique for obtaining macroscopic equations of motion for materials that are microscopically inhomogeneous is extended to the situation in which multiple solid constituents form a porous matrix while a uniform uid lls the pores. Previous volume averaging eeorts of Pride et al. (1992) and others have concentrated on single solid constituent porous media. The analysis for m...

A stabilizing criterion is derived for equations governing vascular growth and remodeling. We start from the integral state equations of the continuum-based constrained mixture theory of vascular growth and remodeling and obtain a system of time-delayed differential equations describing vascular growth. By employing an exponential form of the constituent survival function, the delayed different...