Fall 2000 | Instructors: Sidney Yip, Ju Li | TA: Jingli Liu | Syllabus (ps,doc)

Lecture Outline

  1. Overview [1,ps,pdf]
    9/6: atomistic simulation, multiscale modeling, materials science

    A. Simulation Methodology

  2. Elements of Molecular Dynamics [4,ps,pdf]
    9/8: atomic tranjectories, Newtonian dynamics, simulation model
    9/11: equations of motion, integration algorithm, predictor-corrector
    9/13: force cutoff, min. image, pbc, Verlet list, initialization
    9/15: flow chart, eq. and time-dep properties, unique features, limitations

  3. Elements of Monte Carlo [2]
    9/18: probability distribution sampling, importance sampling
    9/20: Metropolis method, kinetic/dynamic interpretation

  4. Interatomic Potential Functions [6]
    9/22: overview: class. pot vs. electronic structure methods
    9/25: pair potentials
    9/27: empirical many-body potentials for metals (EAM)
    9/29: potentials for covalent bonding
    10/2: ab-initio approach - density-functional theory (LDA)
    10/4: tight-binding (LCAO) approximation

    Lab Sessions on Code Development and Property Calculations [2]
    10/6: description of MD Code [JL]
    10/11: applications of Code - various property calculations [JL]

    B. Statistical Processes

  5. Basic Principles [1]
    10/13: Phase-space sampling, Liouville equation, canonical distrib.

  6. Thermodynamic Equilibrium and Stability [3]
    10/16: thermodyn potentials and derivatives, phase transitions
    10/18: van der Waals eq. of state, critical behavior
    10/20: universal binding and eq. of state

  7. Free Energy Calculations [4]
    10/23: overview of approaches, harmonic methods
    10/25: thermodynamic integration and adiabatic switching
    10/27: reversible scaling
    10/30: application of reversible scaling

  8. Strength, Deformation and Toughness [7]
    11/1: free energy expansion, tij, Cijkl, Bijkl
    11/3: atomistic local strain, microcanonical vs. canonical ensembles
    11/6: stability criteria for homogeneous deformation, P-R method
    11/8: unifying Born's melting and stability criteria
    11/13: lattice vibration formalism, dispersion curves, dos, soft modes
    11/15: fracture simulations, Griffith criterion, BDT, Rice-Peierls model
    11/17: dislocaton simulations, core and kink energetics, mobility

  9. Linear Response Theory of Fluctuations and Transport [3]
    11/20: Green-Kubo formulas, density correlation functions
    11/22: hydrodynamics, kinetic theory, mode-coupling theory
    11/27: thermal conductivity simulations
    11/29: summary and review

    12/1: Quiz

    C. Selected Applications [3]

    Recent topics in materials modeling - melting, glass transitions, stability, defect mobility, and fracture.
    12/4: melting
    12/6: supercooled liquids and amorphized solids
    12/8: ASCI program on dislocation dynamics
    12/11: Project presentation I
    12/13: Project presentation II
total number of classes: 40
grades: problem sets, a term project, a written quiz, and an oral exam at the end of the term.


There is no suitable textbook for this course and therefore none are required. The following books are ordered by their relevance:
  1. M.P. Allen and D.J. Tildesley, Computer Simulation of Liquids (review).

  2. D. Frenkel, B. Smit, eds. Understanding Molecular Simulation: From Algorithms to Applications (review).

  3. D.C. Rapaport, The Art of Molecular Dynamics Simulation (review).

  4. A.P. Sutton, Electronic Structure of Materials (review).

Weekly handouts will be distributed in class and also be posted on the web.

Problem Sets and Solutions

Supplementary Materials


MMM | Ab-initio | SCRAM | Kaxiras | Arias | MSL | WAG | CMS | U.Belfast | CAMP | NCSU | SPaSM | IBM

Project Exhibition

It is very helpful to organize your term project (example) on a webpage, even before it is finished. We hope to have your links as early as possible, so you can compare your progress with others'.
Shon Yim Dynamics of Bubble Growth Shony@mit.edu MED C
Jingli Liu   jinglil@mit.edu NED C
Antonino Romano Mechanical Properties of Soft Matter: Membranes and SiC Thin Films aromano@mit.edu NED C
Zhihong Wang Atomistic Mechanisms of Oxygen Diffusion in Silicon wzh@mit.edu CED C
Markus Zimmermann   markusz@mit.edu MED L
Franco Capaldi  fcapaldi@mit.edu MED L
Jin Yi Monte Carlo simulation of grain growth and recrystallization yijin@mit.edu MED C
Tom Arsenlis   arsenlis@mit.edu MED L
Andrew Takahashi Atomistic Simulation of Island Zipping atakahas@mit.edu MSD C
Joshua Weitz  jsweitz@mit.edu Phys L
Dave Tuch  dtuch@mit.edu NED C
Sundar Subramanian   sundar@mit.edu NED L
Numan Waheed   nwaheed@mit.edu CED C
Shawn Mowry   mowrysw@mit.edu CED L
Richard Williams Massively Parallel MD in the Tecolote Framework mowrysw@mit.edu CED L
MED | NED | CED | MSD | Phys