Inhalt des Dokuments
Nonlinear Dynamics: Theory and Applications in Thermo-Fluid Systems
The Integrierte Lehrveranstaltung "Nonlinear Dynamics: Theory and Applications in Thermo-Fluid Systems" covers geometrical and analytical methods useful to understand the behavior of complex dynamical systems. The applied focus of the course is on the dynamics of systems relevant in fluid mechanics, acoustics, and energy.
The course takes place in the winter semester. The lectures are twice per week, and include theoretical lectures, applied exercises, and programming tasks with Python.
If you wish to attend the course, register to the the course page on the ISIS website. The course will be password protected: reach the responsible for the course to have access (see contact below).
https://isis.tu-berlin.de/course/view.php?id=30652
All the course material (lecture notes, Python scripts, assignments) will be made available on the ISIS webpage.
The course will be held in person, but if required we will hold some lectures online, using Zoom. The lectures will be in English. The full schedule of the course is provided on the ISIS webpage.
Content
- Linear vs Nonlinear dynamics
- 1D dynamical systems
- Bifurcations in 1D
- 2D dynamical systems
- Phase plane and Poincare Maps
- Limit Cycles
- Method of averaging
- Logistic map
- Non-periodic oscillations
- 3D+ dynamical systems and Chaos
- Applications to: cylinder flow, thermoacoustics, convection in the atmosphere
Dates and Location:
The lectures take place in room M 128 (Mechanik building) on Tuesdays from 12pm to 2pm, and Thursdays from 10am to 12pm.
Thu 20.10.2022, 10:00-12:00, Room M 128
Thu 27.10.2022, 10:00-12:00, Room M 128
Tue 01.11.2022, 12:00-14:00, Room M 128
Thu 03.11.2022, 10:00-12:00, Room M 128
Tue 08.11.2022, 12:00-14:00, Room M 128
Thu 10.11.2022, 10:00-12:00, Room M 128
Thu 17.11.2022, 10:00-12:00, Room M 128
Tue 22.11.2022, 12:00-14:00, Room M 128
Thu 24.11.2022, 10:00-12:00, Room M 128
Tue 29.11.2022, 12:00-14:00, Room M 128
Thu 01.12.2022, 10:00-12:00, Room M 128
Tue 06.12.2022, 12:00-14:00, Room M 128
Thu 08.12.2022, 10:00-12:00, Room M 128
Tue 13.12.2022, 12:00-14:00, Room M 128
Thu 12.01.2023, 10:00-12:00, Room M 128
Tue 17.01.2023, 12:00-14:00, Room M 128
Tue 24.01.2023, 12:00-14:00, Room M 128
Thu 26.01.2023, 10:00-12:00, Room M 128
from 27.01.2023 until 13.02.2023: Final project
Tue 14.02.2023, 12:00-14:00, Room M 128 (if required)
Thu 16.02.2023, 10:00-12:00, Room M 128
Requirements:
Knowledge of basic calculus and linear algebra is required. Programming skills (Python, Matlab or Julia) are advantageous but not strictly required.
Details:
Integrated lecture, 2 STE (4 SWS), 6 ECTS credits
Exam: Final Project + Oral exam