22.103 | Fall 2003 | Undergraduate

Microscopic Theory of Transport

Lecture Notes

1 Course Overview and Introduction (PDF)
Part I - Correlation Functions
2 Diffusion: mean square displacement (PDF)
3 Diffusion: velocity autocorrelation - Green Kubo relations (PDF)
4 Diffusion: Van Hove self correlation function Gs(r,t) (PDF)
5 The density correlation function G(r,t) (PDF)
6 Properties of time correlation functions (PDF)
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
11 Hydrodynamic theory of dynamic structure factor
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
17 Kinetic theory of Gs(r,t) - Nelkin-Ghatak model
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
22 Continuation of Lecture 21
Part III - Atomistic Simulation of Transport and Related Phenomena
23 Mean Free Path Treatment of Transport (viscosity, conductivity, diffusion)
24 Continuation of Lecture 22
25 Role of atomistic simulations in transport (PDF)
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

Course Info

As Taught In
Fall 2003
Learning Resource Types
Problem Sets
Lecture Notes