250031 VU Modelling Interacting Particle Systems in Science (2021S)
Prüfungsimmanente Lehrveranstaltung
Labels
An/Abmeldung
Hinweis: Ihr Anmeldezeitpunkt innerhalb der Frist hat keine Auswirkungen auf die Platzvergabe (kein "first come, first served").
- Anmeldung von Mo 08.02.2021 00:00 bis Do 25.02.2021 17:30
- Abmeldung bis Mi 30.06.2021 23:59
Details
max. 25 Teilnehmer*innen
Sprache: Englisch
Lehrende
Termine (iCal) - nächster Termin ist mit N markiert
- Donnerstag 04.03. 12:45 - 16:00 Digital
- Donnerstag 11.03. 12:45 - 16:00 Digital
- Donnerstag 18.03. 12:45 - 16:00 Digital
- Donnerstag 25.03. 12:45 - 16:00 Digital
- Donnerstag 15.04. 12:45 - 16:00 Digital
- Donnerstag 22.04. 12:45 - 16:00 Digital
- Donnerstag 29.04. 12:45 - 16:00 Digital
- Donnerstag 06.05. 12:45 - 16:00 Digital
- Donnerstag 20.05. 12:45 - 16:00 Digital
- Donnerstag 27.05. 12:45 - 16:00 Digital
- Donnerstag 10.06. 12:45 - 16:00 Digital
- Donnerstag 17.06. 12:45 - 16:00 Digital
- Donnerstag 24.06. 12:45 - 16:00 Digital
Information
Ziele, Inhalte und Methode der Lehrveranstaltung
Art der Leistungskontrolle und erlaubte Hilfsmittel
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.
Mindestanforderungen und Beurteilungsmaßstab
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.
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.
Prüfungsstoff
Literatur
Zuordnung im Vorlesungsverzeichnis
ZWM; MFE;
Letzte Änderung: Fr 12.05.2023 00:21
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)