“Stochastic Modelling of Transport in Heterogeneous Media”

Lecturers: Marco Dentz and Juan Hidalgo (IDAEA-CSIC)

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.
  • Strati ed 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.

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 “Stochastic Modelling of Transport in Heterogeneous Media” addressed to physicists, chemists and engineers