FY818: Random walks and fractional dynamics (5 ECTS)

STADS: 07012401

Level
Master's level course

Teaching period
The course is offered in the spring semester.

Teacher responsible
Email: mlomholt@sdu.dk

Additional teachers
krog@sdu.dk

Timetable
Show entire timetable
Show personal time table for this course.

Prerequisites:
None

Academic preconditions:
Students taking the course are expected to:

• Have knowledge of probability theory and Fourier transforms

Course introduction
The aim of the course is to give the students fundamental knowledge of continuous time random walks and their connection with fractional differential equations.

The course gives a foundation for applying random walk theory in modelling of various phenomena: diffusion of molecules, fluctuations of stock prices, speed of Monte Carlo simulation methods. This can for instance be used in projects in the rest of the education.

In relation to the competence profile of the degree it is the explicit focus of the course to:

• give skills to apply mathematical tools to formulate and solve physical models
• give knowledge and understanding of random walks
• give ability to acquire new knowledge in an effective and autonomous way and communicate this knowledge to colleagues

 

Expected learning outcome
The learning objective of the course is that the student demonstrates the ability to:

• Autonomously acquire the knowledge about random walks described under Contents
• Solve mathematical exercises about random walks
• Present theory and exercises
• Apply the theory of random walks within a chosen subject (final project)

Subject overview
The following main topics are contained in the course:

• Continuous time random walks
• The central limit theorem
• Lévy stable probability distributions
• Tauberian theorems
• Fractional Fokker-Planck equations
• First passage time problems
• Aging phenomena

Literature

• J. Klafter og I.M. Sokolov: First Steps in Random Walks.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam

1. Active participation in the teaching, i.e., a number of presentations around the level of the total number divided by the number of students.

Assessment and marking:

1. Oral exam, passed/not passed, internal examination. The exam takes its starting point in a written report about the final project. It takes the form of a presentation followed by questions. (5 ECTS). (07012402).

Expected working hours
The teaching method is based on three phase model.
Intro phase: 15 hours
Skills training phase: 15 hours, hereof:
 - Tutorials: 15 hours

Educational activities

• Study of the textbook
• Solving of exercises
• Preparation of presentations
• Undertaking of the final project

Educational form
The teaching method in the course is built around the students presenting the material for each other. At every class (2 hours) there will be typically 3 students who each spend approximately 10 min. on presenting af section from the textbook (intro phase), as well as 3 students presenting an exercise (training phase). The teachers will be available in between the classes if the presenters have questions to their material or exercise. Due to the additional time needed for preparing the presentations then the number of classes is lower than usual.

Language
This course is taught in English, if international students participate. Otherwise the course is taught in Danish.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.