Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-81-34-M-7

Mathematical Methods for Interacting Particle Systems (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-81-34-M-7 Mathematical Methods for Interacting Particle Systems 4.5 CP (135 h)

Basedata

CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-TEMA] Industrial Mathematics
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V MAT-81-34-K-7
Mathematical Methods for Interacting Particle Systems
P 28 h 107 h - - PL1 4.5 irreg.
  • About [MAT-81-34-K-7]: Title: "Mathematical Methods for Interacting Particle Systems"; Presence-Time: 28 h; Self-Study: 107 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 86297 ("Mathematical Models for Interacting Particle Systems")

Evaluation of grades

The grade of the module examination is also the module grade.


Contents

Particle systems with a large number of particles and their approximation by means of mesoscopic, kinetic and macroscopic models are considered. In particular, the following topics are covered:
  • systems of independent particles: Newton, Liouville, hyperbolic and diffusive limits,
  • systems of independent particles: Langevin, fiber equations, Fokker-Planck equations, hyperbolic and diffusive approximation,
  • systems of interacting particles: coupled Newton systems, Liouville equation, Mean-Field equations, Boltzmann equation, linear transport equations, macroscopic limits,
  • interacting particles: stochastic particle systems.

Competencies / intended learning achievements

Upon successful completion of this module, the students know and understand advanced mathematical methods for the analysis of interacting particle systems. In particular, they are familiar with the model hierarchies of interacting particle systems, they understand the asymptotic approach, and they can apply the methods in examples.

They are able to name and to prove the essential propositions of the lecture as well as to classify and to explain the connections.

Literature

  • H. Spohn: Large scale dynamics of interacting particles.

Requirements for attendance (informal)

Modules:

Requirements for attendance (formal)

None

References to Module / Module Number [MAT-81-34-M-7]

Module-Pool Name
[MAT-81-MPOOL-7] Specialisation Partial Differential Equations (M.Sc.)
[MAT-8x-MPOOL-7] Specialisation Modelling and Scientific Computing (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)