Mathematical Methods and Modelling

Lecturer:

Jaroslav Klusoň (gar.)

Tutor:

Jaroslav Klusoň (gar.)

Supervisor:

Department of Dosimetry and Application of Ionizing Radiation

Synopsis:

Application of mathematical methods, modelling and data processing in dosimetry, radiological physics, medicine and experimental physics. Processing, analysis and evaluation of spectra (peak search and fitting, deconvolution), data analysis, statistical processing and visualization (smoothing, numerical differentiation, creation of histograms), modelling (Monte Carlo method) and examples of applications (calculation of the response of detection systems, efficiency and resolution, calculations of the angular energy distributions of dosimetric quantities in radiation fields/beams, measuring methods simulation/design). Demonstration/training of applications of selected codes (Gnuplot, ROOT, MCNP, Vised, Sabrina, Body Builder,SRIM/TRIM, Geant).

Requirements:

Basic courses of matematics and statistics

Basic knovledge of programming and computer literacy

Syllabus of lectures:

1.Introduction (basic concepts of probability theory and mathematical statistics)

2.Application of numerical methods in dosimetry (computer implementation of numerical methods)

3.Monte Carlo method (modelling of the non-uniform distributions)

4.Transport of the indirectly ionizing radiation through matter, basic types of interactions, interactions physical models descriptions (cross sections, distributions), model geometrical arrangement description

5.Charged particles transport (electrons multiply scattering, grouped collisions technique, energy loss and/or angle of scattering fluctuations modelling)

6.Transport theory concept (transport equation approximate solution methods)

7.Ionising radiation detection (detectors responses and efficiency)

8.Experimental spectra processing (peaks identification and peak areas determination, spectra unfolding/deconvolution)

9.Dose and kerma calculations; phantom doses calculations

10.Application of the numerical methods for the shielding analysis/design; build-up factors calculation

11.Radiation biological effects (models of the radiation effects on the cells, reparation processes models

Syllabus of tutorials:

1. Basics of Unix, data filtering and sorting

2. Computer code ROOT, smoothing, differentiation and fitting of data

3. Detector responses a deconvolution of data

4. Computer codes SRIM, Geant and Fluka (properties, fields of application, demonstrations)

5. Methods of data visualization

6. Basics of radiation transport simulation

Study Objective:

Gain overview and practical skills in application of the selected mathematical methods for calculations and processing and analysis of data in the fields of dosimetry, spectrometry particle and radiation physics, radiation protection and medicine.

Study materials:

Key references:

1.Lux, I., Koblinger, L.: Monte Carlo Particle Transport Methods- Neutron and Proton Calculations, ISBN 0-8493-6074-9, CRC Press, 1991.2.Use of MCNP in Radiation Protection and Dosimetry, Edited by Gualdrini, G., Casalini, L., ENEA, ISBN 88-8286-000-1, Bologna - Italy, May 13-16 1996.

Computer code ROOT, http://root.cern.ch

Recommended references:

Computer code SRIM/TRIM, http://www.srim.org/

Media and tools:

computer lab

computer codes and SW/tools

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans: