Solution of Differential Equations in Mechanics of Granular Materials : Mathematical Methods and Applications

Analytical solutions of the nonlinear PDEs are presented to illustrate the wave propagation in granular materials. Theoretical investigations carried out for different values of the dispersion and microstructure parameters seem to show that the solutions of the models exhibit interesting features. Also, theoretical study of the two phase system of flow is presented to describe the fluid flow through porous granular matrix, and the various solutions of the magma equation are discussed to illustrate the evolution of porosity waves in the earth's interior. In addition, we consider the fluidization of granular materials by a vibrating wall. The system is studied in the case of viscous and inviscid model. Grains are modeled as smooth rigid disks and the collisions are characterized by a constant normal restitution coefficient. The solutions of the van der Waals model of a granular system, exhibit appearance of bubbles. The instability is caused by the energy dissipation at collisions. Painlev analysis is introduced to investigate the integrability. Dispersion properties are also discussed. This book is suitable and will be interesting for all researchers in related fields.