This acclaimed series provides survey articles on the present state and future direction of research in important branches of applied mechanics. Volume 31 provides the following fully referenced, and comprehensive articles:A New Integrable Shallow Water Equation discusses the initial value problem and soliton solutions for a newly discovered, completely integrable, dispersive shallow water equation as well as the elastic collision properties of the N-soliton solution The Onset and Development of Thermal Convection in Fully Developed Shear Flows focuses on a few basic states involving a Boussinesq fluid and fully developed forced flows, mainly of the Couette or Poiseuille type Vortex Element Methods for Flow Simulation covers vortex patches and filaments and a critical account of difficulties, limitations, and continuing efforts to improve the simulations of laminar or peturbulent flows through the use of vortex elementmethods Micromechanics Constitutive Description of Thermoelastic Martensitic Transformations is concerned with the micromechanics description of transformation plasticity, incorporating microstructure, crystallography, thermodynamics and micromechanics into the continuum formulation of the macroscopic constitutive behavior.