NUCE 525





Description: Monte Carlo Methods and Applications


Instructor: Dr. Kostadin Ivanov (, (814) 865-0040, Nuclear Engineering Program, Mechanical and Nuclear Engineering Department, 206 Reber Building, University Park)




1. K. Ivanov,NUCE 525 Class Notes and Handouts”, The Pennsylvania State University, 2007.


2. M. Kalos, and P. Whitlock, “Monte Carlo Methods (Vol.I Basics)”, John Wiley 

& Sons, 1986


3. E. Lewis, and W. Miller, “Neutron Transport Method (Chapter 7)”, American  Nuclear Society, 1993.




1.   J. Spanier, and E. Gelbard, “Monte Carlo Principles and Neutron Transport Problems”, Addison-Wesley, 1969


2.   I. Lux, and L. Koblinger, “Monte Carlo Particle Transport Methods: Neutron and Photon Calculations”, CRC Press, 1991


3.   J. Liu, “Monte Carlo Strategies in Scientific Computing”, 2001.




30% - One mid-term exam

40% - Homework

30% - Course project

List of Topics


  1. Introduction
  2. Random Processes and Basic Principles
  3. Fundamental Formulation of Monte Carlo (FFMC)
  4. Sampling Procedures
  5. Random Number Generation
  6. Analog Monte Carlo Simulation
  7. Fundamentals of Probability Theory and Statistics
  8. Error Estimation
  9. Non-Analog Monte Carlo Methods and Variance Reduction Techniques
  10. Energy-Dependent Neutron-Nucleus Interactions in Monte Carlo Simulations
  11. Tracking in Phase Space
  12. Tallying Procedures
  13. Geometry and Model Representation
  14. Monte Carlo Evaluation of Integrals
  15. Monte Carlo Methods for Criticality or Eigenvalue Problems
  16. Monte Carlo Methods for Shielding Problems and Simulation of Experiments
  17. Vector and Parallel Processing of Monte Carlo Methods
  18. Fuel Pin Cell, Fuel Assembly, and Core Depletion Calculations
  19. Propagation of Uncertainties in Monte Carlo Depletion Calculations
  20. Recent Monte Carlo Method Developments and Applications