Mathematics for Particle Systems

Course guarantor:

Milan Krbálek

Lecturer:

Milan Krbálek

Tutor:

Milan Krbálek

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:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: