Lecture Outline
| WEEK # |
TOPICS |
| 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.
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 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 |