"Stochastic Modelling of Transport in Heterogeneous Media"
Lecturers: Marco Dentz and Juan Hidalgo (IDAEA-CSIC)
All sessions will take place on Monday, from 11h to 13 h, at room 3.20 (3rd floor of Physics UB, new building, campus Sud de Pedralbes).
Contact: Jordi Ortin
Contact: Marco Dentz
Organizer: UBICS
Postgraduate course addressed to physicists, chemists and engineers, organized in five 2-hour sessions:
- April 29: Introduction to transport in heterogeneous media.
- Introduction to transport in heterogeneous media.
- Review of probability: Transformation and summation of random variables. Central limit theorems. Stochastic processes: stationarity and ergodicity.
- May 13: Langevin and Fokker-Planck equations
- Brownian motion. Langevin equation. Diffusion equation. Fluctuation-dissipation theorem. First passage times
- Non-linear Langevin equations. Ito formula.
- Fokker-Planck equation. Derivation. Ito interpretation. Stratonovic interpretation.
- Fokker-Planck versus advection-dispersion equation.
- May 20: Dispersion
- Taylor dispersion: Discussion of mechanisms and time scales, derivation of the Taylor dispersion coeffcient.
- Hydrodynamic dispersion: Mechanisms and models, dependence of dispersion on Péclet number.
- Macrodispersion. Spatial stochastic models. Perturbation theory.
- Stratied media. Superdiffusion and the role of correlation.
- June 3: Continuous time random walks
- Continous time random walk basics: Generalized Master and Fokker-Planck equations, aging and stationarity.
- Continuous time random walks for diffusion in disordered media, quenched versus annealed disorder.
- Velocity Markov processes and (correlated) continous time random walks for hydrodynamic transport.
- July 1: Trapping models
- Subdiffusion in the comb model.
- Diffusive mass transfer for transport in fractured media.
- Equivalence between MRMT and CTRW approaches, memory functions and trapping time distributions.