In the late 1990s there has been a dramatic increase in the number of mathematical models developed to tackle geomechanics problems, largely as a result of the increasing availability and power of computers and the parallel evolution of versatile numerical techniques. This text examines the experimental and theoretical aspects of the pre-failure and post-failure behaviour of geomaterials within the frame of bifurcation theory. Coverage includes basic continuum mechanics for dry and fluid infiltrated porous media, bifurcation and stability analyses applied to layered geological media and...

The workshop "Nonhnear MHD Waves and Turbulence" was held at the - servatoire de Nice, December 1-4, 1998 and brought together an international group of experts in plasma physics, fluid dynamics and applied mathematics. The aim of the meeting was to survey the current knowledge on two main topics: (i) propagation of plasma waves (like Alfven, whistler or ion-acoustic waves), their instabilities and the development of a nonlinear dynamics lea ding to solitonic structures, wave collapse or weak turbulence; (ii) turbulence in magnetohydrodynamic flows and its reduced description in the presence...

Regardez les singularit es: il n y a que ca, qui compte. Gaston Julia The nonlinear Schr] odinger (NLS) equation provides a canonical descr- tion for the envelope dynamics of a quasi-monochromatic plane wave (the carrying wave) propagating in a weakly nonlinear dispersive medium when dissipative processes are negligible. On short times and small propagation distances, the dynamics are linear, but cumulative nonlinear interactions result in a signi?cant modulation of the wave amplitude on large spatial and temporal scales. The NLS equation expresses how the linear dispersion relation is...