Bi-continuum modelling of layered structures and crystalline interfaces
  The bi-continuum model composed of two interpenetrating and dynamically coupled material continua is analysed as a simplified but relatively accurate way to describe some physical phenomena in crystalline solids. The essential novelty of our approach consists in treating a crystalline medium as bi-continuum, even if the crystalline lattice is structurally single-component. Particular attention is paid to the oscillatory behaviour of solutions on the atomic level. Starting from a discrete atomic chain, the basic formulation of the bi-continuum model is derived. The essential features of the model, including accuracy of the results as functions of physical parameters, are discussed. 
M. Sztyren (Department of Mathematics and Information Science, Warsaw   University of Technology)