Microscopic Theory of Transport

Calendar

DAY #	TOPICS	ASSIGNMENTS
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)	Problem Set 1 Issued (PDF)
6	Properties of time correlation functions (PDF)	Problem Set 1 Due (PDF) Problem Set 2 Issued (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	Problem Set 2 Due (PDF)
11	Hydrodynamic theory of dynamic structure factor	Problem Set 3 Issued (PDF)
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 (PDF)
17	Kinetic theory of Gs(r,t) - Nelkin-Ghatak model	Problem Set 4 Issued (PDF)
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 (PDF)
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 (PDF)
24	Continuation of Lecture 22
25	Role of atomistic simulations in transport (PDF)	Problem Set 5 Due (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