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Yip, Sidney, 22.103 Microscopic Theory of Transport, Fall 2003. (Massachusetts Institute of Technology: MIT OpenCourseWare), (Accessed 07 Jul, 2010). License: Creative Commons BY-NC-SA

Microscopic Theory of Transport

Fall 2003

Molecular dynamics simulation of an exfoliated nanoclay-polymer composite.
Molecular dynamics simulation of an exfoliated nanoclay-polymer composite. (Image courtesy of NIST.)

Course Highlights

This course includes a selection of lecture notes and problem sets, as well as instructions for student projects.

Course Description

Transport is among the most fundamental and widely studied phenomena in science and engineering. This subject will lay out the essential concepts and current understanding, with emphasis on the molecular view, that cut across all disciplinary boundaries. (Suitable for all students in research.)
  • Broad perspectives of transport phenomena
  • From theory and models to computations and simulations
  • Micro/macro coupling
  • Current research insights


    Lecture Outline

    1 Overview
    2 Transport Coefficients - Green Kubo Relations
    3 Density and Self Correlations, Botlzmann Equation
    4 Navier-Stokes Equations
    5 Collisions and Transport Models
    6 Fluid Transport - Molecular Dynamics Simulations
    7 Radiation Transport - Monte Carlo Methods
    8 Linear Response Theory
    9 Micro/Macro Coupling (Multiscale Modeling)
    10 Solids and Soft Matter
    11-14 Special Topics to Illustrate Diverse Applications -- Subject to Class Interest
    15 Class Presentation

    Subject will be taught through class lectures. Written lecture notes will be posted on the server.

    There will be a few problem sets, a written quiz (after week 8), and at the end of the term a term project (with presentation) and an oral exam.

    General References

    Boon, J. P., and S. Yip. Molecular Hydrodynamics. McGraw-Hill, 1980, Dover edition, 1990.

    McQuarrie, D. A. Statistical Mechanics. Harper & Row, 1976.

    Duderstadt, J. J., and W. R. Martin. Transport Theory. Wiley, 1979.

    Bird, R. B., W. E. Stewart, and E. N. Lightfoot. Transport Phenomena. Wiley, 1960.


    DAY #

    1 Course Overview and Introduction  
    Part I - Correlation Functions
    2 Diffusion: mean square displacement  
    3 Diffusion: velocity autocorrelation - Green Kubo relations  
    4 Diffusion: Van Hove self correlation function Gs(r,t)  
    5 The density correlation function G(r,t) Problem Set 1 Issued
    6 Properties of time correlation functions Problem Set 1 Due
    Problem Set 2 Issued
    7 The radial distribution function g(r)  
    8 Dynamic structure factor and inelastic neutron and light scattering  
    9 Equations for G(r,t) and phase-space correlation  
    10 Equations of hydrodynamics Problem Set 2 Due
    11 Hydrodynamic theory of dynamic structure factor Problem Set 3 Issued
    Part II - Kinetic Theory
    12 Boltzmann equation: brief derivation  
    13 Boltzmann equation: collisional invariants and hydrodynamic limit  
    14 Continuation of Lecture 13  
    15 Boltzmann equation: H-theorem and equilibrium solution  
    16 Linearized Boltzmann equation: relaxation time models Problem Set 3 Due
    17 Kinetic theory of Gs(r,t) - Nelkin-Ghatak model Problem Set 4 Issued
    18 Continuation of Lecture 17  
    19 Kinetic theory of G(r,t): BGK model  
    20 Kinetic models, Boltzmann equation and neutron transport equation  
    21 Linear response theory - complex susceptibility, fluctuation-dissipation theorem Problem Set 4 Due
    22 Continuation of Lecture 21  
    Part III - Atomistic Simulation of Transport and Related Phenomena
    23 Mean Free Path Treatment of Transport (viscosity, conductivity, diffusion) Problem Set 5 Issued
    24 Continuation of Lecture 22  
    25 Role of atomistic simulations in transport Problem Set 5 Due
    26 Basic Molecular Dynamics: time integration, potential, book keeping, flow chart, unique properties  
    27 Continuation of Lecture 26  
    28 Atomistic simulation of liquids - structure and dynamics  
    29 Transport phenomena beyond Boltzmann - cage effects, molasses tail, phonon lifetimes  
    30 Diversity of atomistic simulation applications (concepts)  
    31 Thermal conductivity of a solid (SiC)  
    32 MD studies of phase transitions - melting, vitrification and amorphization  
    33 Continuation of Lecture 32  
    34 Multiscale materials modeling - perspective and visualization  
    35 Final topic on transport theory: memory function, mode coupling   Tell A Friend