Course detail

Modelling of Physical Processes

FSI-TMPAcad. year: 2007/2008

Introduction into Non-linear Dynamic Systems Theory - Dynamic System, Phase and Configuration Space, Linear Systems and their classification, Topological Equivalence, Linearization, Bifurcation.
Analytical tools - Phase Portrait, Poincare maps, Basins of Attraction, Ljapunov's Exponents, Strange Attractors and their fractal properties, numeric methods for simulation of dynamic systems behaviour.
The aim of the course is to make students familiar with the Dynamic Systems Theory by means of basic simulation techniques - implementation of simple physical system, simulation experiment - verification of natural and statistical laws. Animation techniques, visualization of Poincare maps, basins of attraction, attractors, bifurcation diagram. The course represents interdisciplinary relations: it focuses both on the modern programming techniques and on the mathematical and physical point of view.

Language of instruction

Czech

Number of ECTS credits

3

Mode of study

Not applicable.

Guarantor

doc. RNDr. Jiří Macur, CSc.

Department

Institute of Physical Engineering (ÚFI)

Learning outcomes of the course unit

In the course basic principles of simulation of experiment are presented. Particular attention is paid to applications, especially to creating of useful software for visualisation of simulated physical processes.

Prerequisites

Mathematical description of the physical problem, statistics of the data processing, basic principles of software linking.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Assesment methods and criteria linked to learning outcomes

The exam has a written and an oral part. Requirement for the exam will be specified by the teacher.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

Students will acquire basic knowledge necessary for modelling of physical processes and approximate calculations of simple systems. In the practicals students solve calculations of real physical systems focused on their practical utilisation.

Specification of controlled education, way of implementation and compensation for absences

Attendance at the practicals is compulsory. Absence may be compensated for by the agreement with the teacher depending on the length of absence.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Macur, J.: Dynamické systémy a jejich simulace, PC-Dir, 1997
BAKER, G.L. - GOLLUB, J.P.: Chaotic Dynamics - an Introduction
ECKSTEIN, W: Computer Simulation of Ion-Solid Interactions

Recommended reading

Macur J. : Úvod do teorie dynamických systémů a jejich simulace

Classification of course in study plans

  • Programme B3901-3 Bachelor's

    branch B3940-00 , 3. year of study, summer semester, compulsory-optional

  • Programme N3901-2 Master's

    branch N3940-00 , 1. year of study, summer semester, compulsory-optional
    branch N2311-00 , 1. year of study, summer semester, compulsory-optional

Type of course unit

 

Lecture

13 hours, optionally

Teacher / Lecturer

doc. RNDr. Jiří Macur, CSc.

Syllabus

1. Basic terminology - definition of continuous dynamic system, phase space, status variables, configuration space, solution of dynamic system, trajectories.
2. Fixed points, phase portrait, autonomous systems, using of operator of flow.
3. Planar linear systems analysis, canonical systems, criteria of classification, reduction of configuration space, qualitative equivalence, topological classification of planar systems
4. 3D systems, diffeomorfisms, first return map of Poincare, eigenspaces, hyperbolic and non-easy points.
5. Non-linear systems, local linearization, asymptotic and neutral stability, hyperbolic orbits, tangent spaces, limit set, limit cycle, attractor.
6. Attracting sets and basins of attraction, period doubling, Ljapunov exponents, chaotic behaviour.
7. Conservative and dissipative systems and their differences from viewpoint of evolution.
8. Homoclinic and heteroclinic structures, structural stability and bifucations, bifurcation diagrams.
9. Fractal dimension of strange attractors and boundaries of basins of attraction.
10. Symbolic dynamic, non-linear time series analysis.
11. Basics of numerical methods and algorithms for observing dynamic system behaviuor.
12-13. Simulation of physical dynamic systems, investigation of their non-linear phenomena.

Computer-assisted exercise

26 hours, compulsory

Teacher / Lecturer

doc. RNDr. Jiří Macur, CSc.

Syllabus

Priciples of Object Oriented Programming.
Object implementation of dynamic system - variables of status and configuration.
Numeric methods for simulation of dynamic system evolution.
Visualization techniques.
Separation of simulated object and visualization - threads and their management.
Event Driven Programming, interactive management of dynamic system.
Multicomponent system - techniques for component creation and anihilation.
Solution of interactions between components in dynamic system.