Contents

• Introduction
• Experiments on granular materials
  • Metastable granular materials
    • Janssen effect and the distribution of internal stresses
    • Vibration induced compaction and glassy granular systems
    • Sandpiles
  • Granular flows
    • Slow vs. rapid granular flows
    • Couette cylinders
    • Flow under gravity acceleration
    • Vibrated grains
  
  
• Transport equations for elastic and inelastic gases
  • The binary collision
    • Kinematics of the elastic collision
    • Statistics of the elastic collision
    • Hard spheres
    • Elementary transport calculations
    • The effects of inelasticity and the reduced models
  • From the Liouville to the kinetic equations
    • The Liouville and the pseudo-Liouville equations
    • The BBGKY hierarchy
    • The Boltzmann hierarchy and the Boltzmann equation
    • Collision invariants, H-theorem and hydrodynamical limit
    • The Maxwell molecules
    • The Enskog correction
    • The ring kinetics equations for hard spheres
    • The Boltzmann equation for granular gases
  • The hydrodynamical limit
    • The phase space distribution function and its moments
    • The Maxwell equation
    • The moment equations
    • The Euler equations
    • The Grad closure
    • The Chapman-Enskog closure
    • The Navier-Stokes approximation
    • Burnett and super-Burnett orders
    • Corrections at high densities
  • Granular hydrodynamics
    • The energy sink
    • The first hydrodynamical models
    • The new generation of granular hydrodynamics
  • Granular gases without hydrodynamics
    • The break of equipartition
    • The problem of scale separation
  
  
• The randomly driven granular gas
  • The model
    • Equations of motion and collisions
    • Characteristic times, elastic limit, collisionless limit, cooling limit: the two stationary regimes
    • Interpretation of the random driving
  • MD and DSMC simulations: outcomes
    • Differences between MD and DSMC
    • Kinetic energy and dissipated kinetic energy, stationarity, thermodynamic limit
    • Density correlations
    • One-particle distribution of velocities
    • Self-diffusion and time self-correlation in 2D
    • Velocity structure factors in 2D
  • Deviations from the homogeneous Boltzmann equation
    • The scaling of the local temperature with the cluster mass
    • The convolution model
  • Toy models for a mean field analysis
    • The hopping model
    • The mean field collision model
  
  
• The driven granular gas with gravity
  • The models
    • Equations of motion and collisions
    • The boundary conditions of the 2D Inclined Plane Model
    • The boundary conditions of the 2D Inclined Channel Model
    • A discussion on the approximations: dilute density and absence of tangential forces
  • The 2D Inclined Plane Model
    • Macroscopic profiles (transport)
    • Density correlations
    • Distributions of velocity
  • The 2D Inclined Channel Model
    • Macroscopic profiles (transport)
    • Profiles with tangential forces
    • Density correlations
    • Distributions of velocity
  • A tentative hydrodynamic approach
    • The transport equations for the Inclined Plane Model
    • The solution of the equations
  
  
• Instability development in cooling granular fluids
  • Phenomenology and theory
    • The Homogeneous Cooling State
    • Linear stability analysis
    • Structure formations: vortices and clusters
    • The asymptotic decay of energy
    • Burgers hypothesis, TDGL hypothesis and a note on pseudo-Maxwell molecules models
  • Models in 1D
    • The models
    • The decay of energy and the problem of the universal clock
    • Velocity and density profiles
    • Structure factors
    • Distribution of velocities
  • The exact distribution of velocities for the 1D pseudo-Maxwell model
    • The pseudo-Maxwell molecules
    • The ``Baldassarri solution'' in $d=1$
  • The Inelastic Lattice Gas: outcomes of 2D simulations
    • The Inelastic Lattice Gas model
    • The decay of energy
    • The structure factors and the self-correlation functions: more than diffusive behavior
    • Internal temperature and scale separation
    • Distributions of velocities and velocity gradients
  • A synthesis of the cooling granular gas problem
  
  
• Conclusions
• Appendix A - The Direct Simulation Monte Carlo
• Appendix B - Coefficients of granular hydrodynamics of 2D Inclined Plane Model
• Papers
• Bibliography
• Credits for pictures
• About this document ...