Universität Wien

250031 VU Modelling Interacting Particle Systems in Science (2021S)

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).

Details

max. 25 participants
Language: English

Lecturers

Classes (iCal) - next class is marked with N

  • Thursday 04.03. 12:45 - 16:00 Digital
  • Thursday 11.03. 12:45 - 16:00 Digital
  • Thursday 18.03. 12:45 - 16:00 Digital
  • Thursday 25.03. 12:45 - 16:00 Digital
  • Thursday 15.04. 12:45 - 16:00 Digital
  • Thursday 22.04. 12:45 - 16:00 Digital
  • Thursday 29.04. 12:45 - 16:00 Digital
  • Thursday 06.05. 12:45 - 16:00 Digital
  • Thursday 20.05. 12:45 - 16:00 Digital
  • Thursday 27.05. 12:45 - 16:00 Digital
  • Thursday 10.06. 12:45 - 16:00 Digital
  • Thursday 17.06. 12:45 - 16:00 Digital
  • Thursday 24.06. 12:45 - 16:00 Digital

Information

Aims, contents and method of the course

The goal of this course is for students to learn how to model systems constituted by many particles. These systems can correspond, among many, to collective dynamics (flocking, pedestrian dynamics), opinion formation, cell dynamics, gas dynamics,...
Modelling requires knowledge from a wide variety of mathematical fields (particularly, probability and differential equations). This course will teach the basics needed. It will also show what constitutes a "good" mathematical model.
During the course the models presented in research papers will be read and analysed. By the end of the course, students should be able to understand the meaning of the models presented in these papers as well as being able to propose their own.
Topics covered include:
- modelling using Markov Chains, Markov Processes and Piece-wise Deterministic Markov Processes;
- modelling using Stochastic Differential Equations;
- modelling using Ordinary Differential Equations; Newton's law; minimisation of potential;
- computational models;
- derivation of partial differential equations (transport equations),
- simulation of some of the particle models.

The class will combine theory, exercises and simulations. For the simulations, we will work with Jupyter notebooks and use Julia programming language (all of this will be explained in the course so no previous knowledge of Julia and Jupyter are needed). The course will also be based on reading and understanding models directly from research papers.

To install Julia (with Atom and Juno), follow the instructions here:
http://docs.junolab.org/stable/man/installation/#
(it is free)

Assessment and permitted materials

This is a practical course, so attendance is compulsory, only a maximum of 3 classes can be missed. Evaluation will be based on solving class exercises, class participation, and a final project, which includes a report and a discussion.

Minimum requirements and assessment criteria

The course is in English.
Good knowledge of mathematical analysis is required as well as basic knowledge in Probability (concepts like probability space, random variable, probability distribution).
Some basic knowledge of ordinary differential equations.

The part of the course dedicated to numerical simulations of particle systems will use the programming language Julia. There is no need of previous knowledge of Julia. However, some experience in programming is needed.
Also a computer will be needed to be able to implement in Julia.

Examination topics

Reading list

Association in the course directory

ZWM; MFE;

Last modified: Fr 12.05.2023 00:21