NFYK10006U Diffusive and Stochastic Processes
MSc Programme in Physics
MSc Programme in Physics with a minor subject
Stochastic descriptions offer powerful ways to understand fluctuating and noisy phenomena, and are widely used in many disciplines including physics, chemistry, biology, and economics. In this course, basic analytical and numerical tools to analyze stochastic phenomena are introduced and will be demonstrated on several important examples. Students will learn to master stochastic descriptions for analyzing non-equilibrium complex phenomena.
Skills
At the conclusion of the course students are expected to be able
to:
- Describe diffusion process using Langevin equation and Fokker-Plank equation.
- Solve several examples of the first passage time problems.
- Explain basic concepts in stochastic integrals, and use it to describe geometric Brownian motions.
- Explain the Poisson process and the birth and death process. Use master equations to describe time evolution and steady state of the processes.
- Explain the relationship between master equations and Fokker-Plank equations using approximation methods such as Kramers-Moyal expansions.
- Explain asymmetric simple exclusion process and related models to describe traffic flow and jamming transition in one-dimensional flows.
- Apply the concepts and techniques to various examples of stochastic phenomena.
Knowledge
In this course, the basic tools to analyse stochastic phenomena are
introduced by using the diffusion process as one of the most useful
examples of stochastic process. The topics include Langevin
equations, Fokker-Planck equations, first passage problems, and
master equations. The tools are then used to analyze selected
stochastic models that have wide applications to various real
phenomena. The topics are chosen from non-equilibrium stochastic
phenomena, including geometric Brownian motion (used in e.g.
modeling finance), birth and death process (used in e.g. chemical
reactions and population dynamics), and asymmetric simple exclusion
process (used in e.g. traffic jam formation). Throughout the
course, exercises for analytical calculations and numerical
simulations are provided to improve the students' skills.
Competences
This course will provide the students with mathematical tools that
have application in range of fields within and beyond physics.
Examples of the fields include non-equilibrium statistical physics,
biophysics, soft-matter physics, complex systems, econophysics,
social physics, chemistry, molecular biology, ecology, etc. This
course will provide the students with a competent background for
further studies within the research field, i.e. a M.Sc.
project.
Academic qualifications equivalent to a BSc degree is recommended.
- Category
- Hours
- Lectures
- 24
- Preparation
- 142
- Theory exercises
- 35
- Exam
- 5
- Total
- 206
Written feedback to assignments
- Credit
- 7,5 ECTS
- Type of assessment
- Written assignment, 8 daysOral examination, 25 minutes with no preparation time
- Type of assessment details
- 20% of the grade from a programming assignment given at least
two weeks before the final exam.
80% of the grade from a 25-minute oral examination with no aids allowed and no preparation time.
The two parts of the exam do not need to be passed separately. - Aid
- Only certain aids allowed
All aids allowed for the written assignment.
No aids allowed for the oral examination.
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
Several internal examiners
- Re-exam
Same as ordinary exam.
It is possible to arrange a new programming assignment (20% of the grade) two weeks before the re-exam date. Please contact the course responsible to arrange this.
Criteria for exam assesment
See Learning outcome
Course information
- Language
- English
- Course code
- NFYK10006U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 4
- Schedule
- A
- Course capacity
- 60
The number of places might be reduced if you register in the late-registration period (BSc and MSc) or as a credit or single subject student.
Study board
- Study Board of Physics, Chemistry and Nanoscience
Contracting department
- The Niels Bohr Institute
Contracting faculty
- Faculty of Science
Course Coordinators
- Namiko Mitarai (mitarai@nbi.ku.dk)