Validity Of Macroscopic Models Research Articles

Open problems in the optics of crystals: the role of multiple scattering.

The thickness b of the transition boundary layer, always present in crystals and giving still unsolved problems for the boundary conditions, is shown to be essentially determined by the multiple scattering of light, due to the inhomogeneity of any periodic structure. The parameter b depends on the orientation theta of the boundary plane with respect to the crystal lattice, and diverges for some critical orientations where strong macroscopic effects are found, which cannot be interpreted by any macroscopic model based on bulk and boundary equations. Our analysis exhaustively defines the limits of validity of macroscopic models for periodic nanoscale structures and solid crystals.

On the Validity of Macroscopic Models

The validity of macroscopic models in the limit of large mean-free path is examined by solving a one-dimensional model equation, where the term v Vf1 is retained in the kinetic equation. A standard thirteen-moments approximation yields accurate results in all collisionality regimes if the fluid velocity is sufficiently small. In contrast, the Chapman-Enskog scheme is only accurate in the collision-dominated regime