[Illinois] PHYS466 2013 Lecture 14: Fundamentals of Monte Carlo

By David M. Ceperley

Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL

Published on

Abstract


Bio

Professor Ceperley received his BS in physics from the University of Michigan in 1971 and his Ph.D. in physics from Cornell University in 1976. After one year at the University of Paris and a second postdoc at Rutgers University, he worked as a staff scientist at both Lawrence Berkeley and Lawrence Livermore National Laboratories. In 1987, he joined the Department of Physics at Illinois. Professor Ceperley is a staff scientist at the National Center for Supercomputing Applications at Illinois.

Professor Ceperley's work can be broadly classified into technical contributions to quantum Monte Carlo methods and contributions to our physical or formal understanding of quantum many-body systems. His most important contribution is his calculation of the energy of the electron gas, providing basic input for most numerical calculations of electronic structure. He was one of the pioneers in the development and application of path integral Monte Carlo methods for quantum systems at finite temperature, such as superfluid helium and hydrogen under extreme conditions.

Professor Ceperley is a Fellow of the American Physical Society and a member of the American Academy of Arts and Sciences. He was elected to the National Academy of Sciences in 2006.

Cite this work

Researchers should cite this work as follows:

  • David M. Ceperley (2013), "[Illinois] PHYS466 2013 Lecture 14: Fundamentals of Monte Carlo," https://nanohub.org/resources/18085.

    BibTex | EndNote

Time

Location

University of Illinois, Urbana-Champaign, IL

Submitter

NanoBio Node

University of Illinois at Urbana-Champaign

Tags

[Illinois] Phys 466 Lecture 14: Fundamentals of Monte Carlo
  • Today: Fundamentals of Monte Carlo 1. Today: Fundamentals of Monte C… 0
    00:00/00:00
  • Simple example: Buffon's needle Monte Carlo determination of  2. Simple example: Buffon's needl… 138.20748379958906
    00:00/00:00
  • MC is advantageous for high dimensional integrals -the best general method 3. MC is advantageous for high di… 255.49721398933019
    00:00/00:00
  • Improved Numerical Integration 4. Improved Numerical Integration 855.996245801225
    00:00/00:00
  • Other reasons to do Monte Carlo: Conceptually and practically simple. Comes with built in error bars. Many methods of integration have been tried, and will be tried in this world of sin and woe. No one pretends that Monte Carlo is perfect or all-wise. Indeed, it has been said that Monte Carlo is the worst method except all those other methods that have been tried from time to time. Churchill 1947 5. Other reasons to do Monte Carl… 918.59988144635452
    00:00/00:00
  • Probability Distributions 6. Probability Distributions 1078.3941118356056
    00:00/00:00
  • Mappings of random variables 7. Mappings of random variables 1214.386563920174
    00:00/00:00
  • What is Mapping Doing? 8. What is Mapping Doing? 1639.7193835210433
    00:00/00:00
  • Example: Drawing from Normal Gaussian 9. Example: Drawing from Normal G… 1650.8764671013635
    00:00/00:00
  • Reminder: Gauss' Central Limit Theorem 10. Reminder: Gauss' Central Limit… 2287.6980043469671
    00:00/00:00
  • Cumulants 11. Cumulants 2625.3857340446552
    00:00/00:00
  • Approach to normality 12. Approach to normality 2973.1148389646314
    00:00/00:00
  • Conditions on Central Limit Theorem 13. Conditions on Central Limit Th… 3017.3712704999011
    00:00/00:00
  • Multidimensional Generalization 14. Multidimensional Generalizatio… 3026.2969373641572
    00:00/00:00
  • 2d histogram of occurrences of means 15. 2d histogram of occurrences of… 3082.8261608377788
    00:00/00:00