Universität Wien

250078 VO Kinetic theory applied to biology (2019W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik
Moodle

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Wednesday 02.10. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 03.10. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 09.10. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 10.10. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 16.10. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 17.10. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 23.10. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 24.10. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 30.10. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 31.10. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 06.11. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 07.11. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 13.11. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 14.11. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 20.11. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 21.11. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 27.11. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 28.11. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 04.12. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 05.12. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 11.12. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 12.12. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 08.01. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 09.01. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 15.01. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 16.01. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 22.01. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 23.01. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 29.01. 13:15 - 14:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 30.01. 09:45 - 11:15 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

Emergent phenomena are ubiquitous in nature: it corresponds to the appearance of large-scale structure from underlying microscopic dynamics. At the microscopic level particles or agents interact following some rules, but the macroscopic structures are not encoded directly in these rules and, therefore, it is a challenge to explain how the macroscopic or observable dynamics emerge from the microscopic ones. Examples of emergence are collective dynamics (flocks of birds, school of fish, pedestrians…), network formation (capillary formation, leaf venation, formation of gullies…), opinion dynamics, tumor growth, tissue development… Understanding emergence in science is key to explaining why observable phenomena take place. The mathematical tools to studying emergence come from kinetic theory, which originally was developed to study problems in Mathematical Physics in the field of gas dynamics. The application of these tools to explore questions coming from biology poses many new interesting challenges at the level of the modeling and mathematical analysis.

The topics covered in this course include"
1. What is emergence and how does kinetic theory contributes to its study?
2. Mean-field limits: from microscopic models to kinetic equations.
3. Hydrodynamic limits: from kinetic equations to macroscopic models.
a. Hilbert expansion method.
b. Generalised Collision Invariant.
4. Bifurcations (phase transitions).
5. Analysis of macroscopic equations.

The course will be a combination of theory and exercises done during the class.

Assessment and permitted materials

Examination will be based on a mid-term and final exam.

Minimum requirements and assessment criteria

Knowledge in Mathematical Analysis (particularly functional analysis), a course in Partial Differential and some basics in Probability.

Examination topics

Reading list

Association in the course directory

MAMV, MBIV

Last modified: Mo 07.09.2020 15:21