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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

Mathematics for Particle Systems

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Code Completion Credits Range Language
01MCS KZ 3 2+1 Czech
Lecturer:
Milan Krbálek (guarantor)
Tutor:
Milan Krbálek (guarantor)
Supervisor:
Department of Mathematics
Synopsis:

Keywords:

Asymptotic Expansions, Balanced Distributions, Dyson gases, Particle Chain, Statistical Rigidity, Nonlinear PDE

Requirements:
Syllabus of lectures:

1. Special Functions

2. Asymptotic Methods

3. Class of Balanced Distributions

4. Dyson Gases

5. Poissonian and Semi-Poissonian Systems

6. Particle Chains and Associated Statistical Properties

7. Theory of Statistical Rigidity

8. Nonlinear PDE

9. Integral Equations with Hermitian Kernel

Syllabus of tutorials:
Study Objective:

Acquired knowledge:

Students learn to predict some advanced statistical properties of particle chains with specific type of mutual interactions.

Acquired skills:

Derivation of asymptotic properties, Derivation of stochastic properties of particle chains.

Study materials:

Compulsory literature:

[1]M.L. Mehta, Random Matrices (Third edition), New York: Academic, 2004

[2]E.T. Copson. Asymptotic Expansions. Cambridge University Press, Cambridge, England, 1965.

[3]V.S. Vladimirov, Equation of mathematical physics, Marcel Dekker INC, New York 1971

Optional literature:

[4]M. Krbálek, Theoretical predictions for vehicular headways and their clusters, J. Phys. A: Math. Theor. 46 (2013), 4451011

[5] M. Krbálek, Equilibrium distributions in a thermodynamical traffic gas, J. Phys. A: Math. Theor. 40 (2007), 5813-5821

Note:
Time-table for winter semester 2019/2020:
Time-table is not available yet
Time-table for summer semester 2019/2020:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2020-03-31
For updated information see http://bilakniha.cvut.cz/en/predmet5357406.html