Lecture Outline
WEEK # 
TOPICS 
1 
Overview 
2 
Transport Coefficients  Green Kubo Relations 
3 
Density and Self Correlations, Botlzmann Equation 
4 
NavierStokes 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 
1114 
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. McGrawHill, 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.
Calendar
DAY #

TOPICS 
ASSIGNMENTS 
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 G_{s}(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 phasespace 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: Htheorem and equilibrium solution 

16 
Linearized Boltzmann equation: relaxation time models 
Problem Set 3 Due 
17 
Kinetic theory of G_{s}(r,t)  NelkinGhatak 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, fluctuationdissipation 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 