Physics 171.636: Spring 2005

Modeling Matter Across Multiple Length and Time Scales

Page Contents:

  1. Important Messages From the Professor
  2. Professor Contact Information
  3. Class Meeting Times
  4. Course Description
  5. Textbooks
  6. Syllabus

Messages from the Professor

The third homework set is posted.  As a final project teams of two students each will present the results of a research paper to the class.  The list of topics and some references are listed below.  Please read the relevant papers before the presentation in class so that we can discuss them.

Contact Information  

Professor

Mark Robbins

mr@pha.jhu.edu

410-516-7204 

Bloomberg 317 

Office Hours: TBA

Class:
9-10:30 AM Thursday and Friday in Bloomberg 178.

Course Description:
This course is aimed at graduate students and advanced undergraduates that are interested in computational modeling of matter of all kinds.  The course will begin by introducing standard single-scale methodologies for continuum fluid and solid mechanics, classical and quantum molecular dynamics, Monte Carlo methods and density functional theory.  Next, kinetic Monte Carlo and other methods for accessing long time behavior and rare events will be introduced. The final section of the course will describe algorithms that treat each region of space with the appropriate spatial and temporal resolutions.  These include standard multigrid methods and new hybrid methods that treat some regions of space atomistically and others using a continuum description.

Prerequisite: Condensed Matter Physics, Statistical Mechanics, or permission of the instructor.

Textbooks:
  Recommended: Crystals, Defects and Microstructures  by Rob Phillips.
  The course will also use current research and review papers in the area.

Grading:

Grades will be based on homework and a final presentation of a journal article to the class.

 

Homework:
Students will be asked to use public domain codes of different types to solve simple problems and gain familiarity with the basic techniques discussed in lecture.  They will also be asked to read a recent article and explain it to the class.  The computer problems will require access to a unix/linux based computer.

Syllabus: The syllabus will be updated as the course progresses.
 

Week of

Subject Matter

Reading

Homework

Jan. 31

Overview of Methods, Molecular Dynamics

 Statistical Mechanics Handout

 Details at Home1, due Feb. 17

Feb. 7

Molecular Dynamics

Correlation Handout

 

Feb. 14

Molecular Dynamics cont.

 

 

Feb. 21

Fluid Dynamics from Molecular Motion

Handout on Boltzman Transport

 

Feb. 28

Numerical Methods for Fluid Dynamics

 

Details at Home2 program sor0.f due March 11

March 7

Multiscale Modeling of Fluids

Emailed journal articles

 

March 14

SPRING BREAK

 

 

March 21

Elasticity

Handout on General Elasticity

 

March 28

Finite Element Methods

Handout

 

April 4

Message-Passing Algorithms, Defect Dynamics

 

Details at Home3, due April 15

April 11

Quasicontinuum Method

Emailed papers

 

April 18

Monte Carlo Method

Handout

 

April 25

Accelerated MD, Equation Free Method

References below

 

May 2

MAAD, Finite Temperature QC, HMMD

References below

 

 

References:   

General books on computer simulations:

Allen and Tildesley, “Computer Simulation of Liquids,” Oxford (1987).  (Mainly molecular dynamics)

D. Frenkel and B. Smit, “Understanding Molecular Simulation: From Algorithms to Applications,” 2nd Edition, Academic (2002).

D. P. Landau and K. Binder, “A Guide to Monte Carlo Simulations in Statistical Physics,” Cambridge (2000).

 

References on potentials:

Beyond Pair Potentials, A. E. Carlsson in Solid State Physics, Edited by H. Ehrenreich and D. Turnbull. Academic Press, San Diego, Vol. 43, p. 1 (1990). Review of effective potential construction.

Modern Electron Theory by M. W. Finnis in Electron Theory in Alloy Design, Edited by D. G. Pettifor and A. H. Cottrell, Institute of Materials, London, 1992.  Article on first-principles calculations.

 

Tight-binding references:

C. M. Goringe and D. R. Bowler and E. Hernandez, "Tight-binding modelling of materials", Reports on Progress in Physics 60,

1447-1512 (1997).

X.-P. Li and R. W. Nunes and D. Vanderbilt “Density-matrix electronic-structure method with linear system-size scaling,” Phys. Rev. B47, 10891-10894 (1993).

N. Bernstein, "Linear scaling nonorthogonal tight-binding molecular dynamics for nonperiodic systems", Europhysics Letters 55, 52-58 (2001).

 

References on Coulomb Interactions

Multipole:

“A hierarchical O(N-log(N)) force-calculation algorithm.” J. E. Barnes and P. Hut, Nature 324, 446-449 (1986)

“A fast algorithm for particle simulations,” L. Greengard and V. Rokhlin, J. Comput. Phys. 73, 325-348 (1987).

FFT and Ewald:

M. Deserno and C. Holm, “How to mesh up Ewald sums. I. A theoretical and numerical

 comparison of various particle mesh routines,” J. Chem. Phys. 109, 7678-7693 (1998).

Finding fields dynamically:

Rottler, Jorg and Maggs, A. C., “Local Molecular Dynamics with Coulombic Interactions,” Phys. Rev. Lett. 93, 170201 (2004).

 

References on modulus of heterogeneous materials

Z. Hashin and S. Shtrikman, J. Mech. Solids 10, 343 (1962).

R. Meister and L. Peselnick, J. Appl. Phys. 37, 4121 (1966).

Shih, Aksay and Kikushi, J. Chem. Phys. 86, 5127 (1987).

 

Quasicontinuum references (more at www.qcmethod.com):

Miller and Tadmor, J. Computer-Aided Materials Design, 9, 203-239 (2002).

Curtin and Miller, Modelling and Simulation in Materials Science and Engineering 11, R33-R68 (2003).

 

Finite temperature references:

Curtarolo and Ceder, Phys. Rev. Lett. 88, 255504 (2002).

Wu, Diestler, Feng and Zeng, J. Chem. Phys. 119, 8013-8023 (2003).

 

Accelerated Molecular Dynamics (Thursday April 28 Masica and Huan)

Check out www.t12.lanl.gov/home/afv/ for presentations and references on accelerated dynamics.
"Extending the Time Scale in Atomistic Simulation of Materials," A.F. Voter, F. Montalenti and T.C. Germann, Annu. Rev. Mater. Res., 32, 321 (2002).

The presentation will include:
 Voter, A. F. J. Chem. Phys. 106{11}, 1997, 4665

 Voter, A. F. Phys. Rev. Lett.  78{20}, 1997, 3908

 

Equation Free Method (Friday, April 29 Cheng and Kraft)

I. G. Kevrekidis, C. W. Gear and G. Hummer, “Equation-Free: The Computer-Aided Analysis of

Complex Multiscale Systems, A.I.Ch.E Journal 50{7} 1346 (2004)

 

MAAD (Thursday, May 5 Hoy and Raghupathy)

 

Finite Temperature Quasicontinuum (Friday, May 6 Luan and Pei)

 

HMMD (Friday, May 6 Rapaka)

 

 

 

Homewood-wide statement on Disabilities

If you are a student with a disability or believe you might have a disability that requires accommodations, please contact Dr. Richard Sanders, Homewood Undergraduate Disability Services Coordinator, in the Office of Academic Advising, Garland Suite 3A, (410) 516-8216, sanders@jhu.edu , to discuss reasonable and appropriate accommodations.

 

University-wide statement on Academic Ethics

The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful. Ethical violations include cheating on exams, plagiarism, reuse of assignments, improper use of the Internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition.  As noted above, collaboration on homework sets is encouraged.  However, you should attempt problems independently before collaborating and must write up your homework independently.

 

Report any violations you witness to the instructor. You may consult the associate dean of students and/or the chairman of the Ethics Board beforehand. See the guide on "Academic Ethics for Undergraduates" and the Ethics Board web site (http://ethics.jhu.edu )  or http://www.advising.jhu.edu/ethics.html for more information.