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250043 VU Kinetic Theory Applied to Biology (2023S)

7.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Continuous assessment of course work

Moodle

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Registration is open from Su 12.02.2023 00:00 to Tu 07.03.2023 23:59
Deregistration possible until Fr 31.03.2023 23:59

Details

max. 25 participants

Language: English

Lecturers

Sara Merino Aceituno

Classes

Termine: Dienstag 13:15 - 14:45 und Mittwoch 11:30-13:00 im Besprechungszimmer im 9. Stock (OMP1)

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.

This course will be a short introduction to classical and modern techniques in kinetic theory to derive continuum equations from discrete equations. The course will be based on learning and applying techniques rather than on giving rigorous proofs.

The topics covered in this course include:
1. What is emergence and how does kinetic theory contribute to its study?
2. Agent-based models (deterministic and stochastic).
2. Mean-field limits: from agent-based models to transport equations.
3. Hydrodynamic limits: from transport equations to macroscopic models.
4. Applications to collective dynamics.

Assessment and permitted materials

Minimum requirements and assessment criteria

- Students must attend all classes, only a maximum of 3 can be missed.
- Students must participate in the class activities and do their homework, like solving exercises or commenting on articles. Small oral presentations on solutions may be requested.
- Evaluation will be based on the homework and a small test at the end of the course which will be based on the homework.

Previous knowledge required: very basic knowledge of ordinary differential equations and partial differential equations.

Examination topics

Reading list

Association in the course directory

MBIV; MAMV

Last modified: Tu 14.03.2023 12:09