LEARNING OUTCOMES

The study and the understanding of Monte Carlo simulation methods applied to transport processes

AIMS AND LEARNING OUTCOMES

Course will give mathematical and physical instrument to deeply understand

  Monte Cralo simulation of particle and radiation transport in matter. This

  will be pursued by the step-by-step construction of a Monte Carlo simulation -

  simplified in its GUI (Graphical User Interface) part - but complete with regard

  to methods to control and analyze statistical error (variance reduction, point  detectors, etc.)

  A specific conclusive section will be devoted to the analysis of Uncertaint Quantification

  problems, i.e. the error induced on simulation result by non precise knowlwedge of physical data

  needed for simulation (cross-section data, system dimensions and composition). This last is one of the most

  fast growing research field in recent years, while it is often neglected.

PREREQUISITES

No formal prerequisites, but a good knowledge of the methods of mathmatical analysis is strongly reccomended

TEACHING METHODS

Theoretical lectures and practical exercitations (48 h)

SYLLABUS/CONTENT

    Monte Carlo method

     Random processes

     Evaluation of definite integrals

    Momte Carlo sampling

     Probability and statistics

     Sampling

     Mean, variance and estimates

     Introduction to variance redcution

    Monte Carlo simulation of neutral particle transport

     Mean free path

     The mathematical basis for Monte Carlo simulation

    Energy-dependent transport

     Elastic scattering

     Lab and C.M. frame of references

    Variance reduction

     Source biasing

     Survival biasing

     Russian roulette

     Splitting

     Exponential transform

    Monte Carlo Detectors

     Next-event estimator

     Volumetric flux detectors

     Surface crossing flux estimator

     Time dependent estimators

    Advanced applications

     Correlated sampling

     Adjoint Monte Carlo

    Uncertainty Quantification

RECOMMENDED READING/BIBLIOGRAPHY

   S.A. Dupree, S.K. Fraley - A Monte Carlo Primer - A practical approach to radiation transport

   X-5 Monte Carlo team - MCNP, a general Monte Carlo N-particle Transport code, vol. 1: overview and theory - LA-UR-03-1987

   J.J. Duderstadt, L.J. Hamilton - Nuclear reactor analysis