Universität Wien

250160 VU Kinetic theory applied to biology (2018W)

7.00 ECTS (4.00 SWS), SPL 25 - Mathematik
Prüfungsimmanente Lehrveranstaltung

Details

max. 25 Teilnehmer*innen
Sprache: Englisch

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

  • Montag 01.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Mittwoch 03.10. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 08.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Mittwoch 10.10. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 15.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Mittwoch 17.10. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 22.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Mittwoch 24.10. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 29.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Mittwoch 31.10. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 05.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Mittwoch 07.11. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 12.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Mittwoch 14.11. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 19.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Mittwoch 21.11. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 26.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Mittwoch 28.11. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 03.12. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Mittwoch 05.12. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 10.12. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Mittwoch 12.12. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 07.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Mittwoch 09.01. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 14.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Mittwoch 16.01. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 21.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Mittwoch 23.01. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Montag 28.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Mittwoch 30.01. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock

Information

Ziele, Inhalte und Methode der Lehrveranstaltung

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. In this course we will explore the following four main topics:
1. What is emergence and how does kinetic theory contributes to its study?
a. Challenges in applications to biology.
2. Modeling of microscopic or agent-based dynamics (interacting particle systems).
a. What makes a good model?
b. Jump models (continuous-time Markov Chains).
c. Newtonian models.
d. Other types of models.
3. Mean-field limits: from microscopic models to kinetic equations.
4. Hydrodynamic limits: from kinetic equations to macroscopic models.
a. Hilbert expansion method.
b. Generalised Collision Invariant.
c. Bifurcations.

Art der Leistungskontrolle und erlaubte Hilfsmittel

Attendance to class is compulsory. The assimilation of the lectures will be based on 'learning by doing'. This is why there is no exam but instead many activities and exercises thorough the duration of the course. Particularly, evaluation will be based on the completion of exercises; reading and presenting research papers; writing and presenting a dissertation on a research topic.

Mindestanforderungen und Beurteilungsmaßstab

Previous knowledge required: knowledge in Mathematical Analysis (particularly functional analysis), a course in Partial Differential and some basics in Probability.

Prüfungsstoff

Literatur

Lecture notes will be provided with a comprehensive bibliography.

Zuordnung im Vorlesungsverzeichnis

MAMV, MBIV

Letzte Änderung: Mo 07.09.2020 15:40