A consistency study of coarse-grained dynamical chains through a Nonlinear wave equation of mixed type

A dynamical atomistic chain to simulate mechanical properties of a one-dimensional material with zero temperature may be modelled by the molecular dynamics (MD) model. Because the number of particles (atoms) is huge for a MD model, in practice one often takes a much smaller number of particles to formulate a coarse-grained approximation. We shall mainly consider the consistency of the coarse-grained model with respect to the grain (mesh) size to provide a justification to the goodness of such an approximation. In order to reduce the characteristic oscillations with very different frequencies in such a model, we either add a viscous term to the coarse-grained MD model or apply a space average to the coarse-grained MD solutions for the consistency study. The coarse-grained solution is also compared with the solution of the (macroscopic) continuum model (a nonlinear wave equation of mixed type) to show how well the coarse-grained model can approximate the macroscopic behavior of the material. We also briefly study the instability of the dynamical atomistic chain and the solution of the Riemann problem of the continuum model which may be related to the defect of the atomistic chain under a large deformation in certain locations.Comment: 25 pages, 15 figure

Enhancement of Optical Nonlinearity Through Anisotropic Microstructures

We investigate the polarization dependence of optical nonlinearity enhancement for a uniaxial anisotropic composite of metal nanocrystals in a dielectric host. Three cases are distinguished depending on whether the polarization is parallel, perpendicular or unpolarized with respect to the axis of anisotropy. For the parallel polarization, the results show that the 3D results are qualitatively similar to the 2D case reported recently. For the perpendicular polarization, the results are markedly different from the parallel counterpart: In contrast to the absorption, the enhancement factor actually increases with the anisotropy. Thus the separation of the absorption and enhancement peaks becomes even more pronounced than the parallel polarization case. These results indicate a strong polarization dependence of the nonlinear optical response.Comment: 12 pages, LaTeX format, 9 figures, preliminary results were Reported in the 2nd Tohwa University International Meeting on Statistical Physics held on November 4-7, 1997, accepted for publication by Optics Communications on 7 November 199