1. Introduction: non-equilibrium nature of granular media, phases of granular media, phase transitions in granular media, pattern formation in granular media, uses of granular media in the industry and geophysics.
2. Interactions between dry and wet grains: types of granular media, grain size distribution, friction, dissipation, elastic and electrical interaction. Molecular dynamics simulations.
3. Sedimentation and surface growth, scaling and data collapse, fractal dimension and roughness exponents, finite size scaling
4. Basics of stochastic processes and randomness, deriving equations of motion from symmetry (Landau theory)
5. Elastic and viscous behavior, viscoelasticity, dynamic linear response, basics of continuum mechanics, calculation of stress in systems of particles.
6. The jamming transition, critical behavior at point J, growing length scale and soft modes, the cutting argument, random close packing, jamming in living cells.
7. The glass transition, complex energy landscapes, compaction, the Edwards measure, Monte-Carlo simulations, detailed balance.
8. The yielding transition, reversibility transition and hysteresis, mesoscopic models, structural evolution, strain localization, shear band instability.
9. Avalanches, critical behavior, depinning, sand pile models, angle of repose.
10. Granular flows and rheology (shear thickening, shear thinning), mixing and chaos, convection, the brazil-nut effect, dimensional analysis, pi-theorem.
11. Granular gases: effective temperature and granular cooling, the Boltzmann equation.
12. Erosion and sediment transport, pattern formation in sand, aoelian processes, sand dunes, ripples.
13. Student presentation, visit to the university wind-tunnel.
1. Bruno Andreotti, Yoel Forterre, Olivier Pouliquen, Granular media: between fluid and solid (2013)
2. Albert-Laszlo Barabasi, Harry Eugene Stanley, Fractal Concepts in Surface Growth (1995)
3. Werner Krauth, Statistical Mechanics: Algorithms and Computations (2006)
4. Michael Rubinstein, Ralph H. Colby, Polymer Physics (2003)
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