Postgraduate course "Stochastic Modelling of Transport in Heterogeneous Media" addressed to physicists, chemists and engineers

"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.


Martes, 23 de Abril de 2019