A Unstructured Nodal Spectral-Element Method for the Navier-Stokes Equations

An unstructured nodal spectral-element method for the Navier-Stokes equations is developed in this paper. The method is based on a triangular and tetrahedral rational approximation and an easy-to-implement nodal basis which fully enjoys the tensorial product property. It allows arbitrary triangular and tetrahedral mesh, affording greater flexibility in handling complex domains while maintaining all essential features of the usual spectral-element method. The details of the implementation and some numerical examples are provided to validate the efficiency and flexibility of the proposed method.

NEW RESULTS ON DYNAMICAL DISORDER IN AMORPHOUS III–V COMPOUNDS

For amorphous III–V semiconductors, infrared spectrum corresponding to dynamical disorder is considered in the context of one-phonon absorption. In particular, an expression for the frequency of transversal optical mode is derived for minimum absorption. Various properties of this frequency as a function of distance are discussed. Furthermore, this frequency and minimum spectrum are determined in terms of a tensorial product of matrices. Our results are compared with experiment. Average absorption due to structural disorder is also formulated.

A Micromechanical Description of Granular Material Behavior

Considered is a sample of cohesionless granular material, in which the individual granules are regarded rigid, and which is subjected to overall macroscopic average stresses. On the basis of the principle of virtual work, and by an examination of the manner by which adjacent granules transmit forces through their contacts, a general representation is established for the macroscopic stresses in terms of the volume average of the (tensorial) product of the contact forces and the vectors which connect the centroids of adjacent contacting granules. Then the corresponding kinematics is examined and the overall macroscopic deformation rate and spin tensors are developed in terms of the volume average of relevant microscopic kinematical variables. As an illustration of the application of the general expressions developed, two explicit macroscopic results are deduced: (1) a dilatancy equation which both qualitatively and quantitatively seems to be in accord with experimental observation, and (2) a noncoaxiality equation which seems to support the vertex plasticity model. Since the development is based on a microstructural consideration, all material coefficients entering the results have well-defined physical interpretations.