Login for PhD students/staff at UCPH      Login for others
Diffusive and Stochastic Processes - PhD course
Provider: Faculty of Science

Activity no.: 5862-23-11-31
Enrollment deadline: 31/03/2023
Date and time24.04.2023, at: 00:00 - 25.06.2023, at: 00:00
Regular seats20
ECTS credits7.50
Contact personJulie Meier    E-mail address: juliemh@nbi.ku.dk
Enrolment Handling/Course OrganiserNamiko Mitarai    E-mail address: mitarai@nbi.ku.dk
Written languageEnglish
Teaching languageEnglish
Semester/BlockBlock 4
Scheme groupA (Tues 8-12 + Thurs 8-17)
Exam detailsWritten assignment, Programming assignment, 8 days Written assignment, 5 hours 20% of the grade from a programming assignment given at least two weeks before the final exam. 80% of the grade from a 5-hour written home assignment with all aids allowed. The two parts of the exam do not need to be passed separately.
Exam aidsAll aids allowed
Grading scalePassed / Not passed
Criteria for exam assessmentSee Learning outcome
Censorship formNo external censorship. Several internal examiners
Exam re-examinationSame as the regular 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. If there are 10 or fewer students signed up for the re-exam, the written home assignment part of the re-exam will be changed to an oral exam, 25 minutes without aids and with no preparation time.
Course workload
Course workload categoryHours
Lectures24.00
Theory exercises35.00
Exam5.00
Preparation142.00

Sum206.00


Content
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.

Learning outcome

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.


Teaching and learning methods
Lectures and exercise sessions. Computer exercise included.

Remarks
Equilibrium statistical physics, physics bachelor level mathematics (Especially: differential and integral calculus, differential equations, Taylor expansions). Basic programming skills.

Academic qualifications equivalent to a BSc degree is recommended.

Sign up:

This MSc course is approved for PhD students.
PhD students should apply as credit students using this form: SCI: Ansøgning om optagelse som meritstuderende (ku.dk)

The course code to enter is NFYK10006U

If you have any questions or problems, please contact Julie Meier Hansen juliemh@nbi.ku.dk

Search
Click the search button to search Courses.


Course calendar
See which courses you can attend and when
JanFebMarApr
MayJunJulAug
SepOctNovDec



Publication of new courses
All planned PhD courses at the PhD School are visible in the course catalogue. Courses are published regularly.