NFYK10006U Diffusive and Stochastic
Processes
Volume
2015/2016  Language  English   Credit  7,5 ECTS   Level  Full Degree Master   Duration  1 block   Placement  Block 4  Schedule  A   Course capacity  No restriction to number of
participants  Continuing and further
education   Study board  Study Board of Physics, Chemistry and
Nanoscience   Contracting department    Course responsible   Namiko Mitarai (7716d786576656d4472666d326f7932686f)
  Saved on the
10092015 
Education  Master programme in Physics 
Content  Stochastic descriptions offer powerful ways to understand
fluctuating and noisy phenomena, and are widely used in many
scientific discipline including physics, chemistry, and biology. In
this course, basic analytical and numerical tools to analyze
stochastic phenomena are introduced and will be demonstrated on
several important natural examples. Students will learn to master
stochastic descriptions for analyzing nonequilibrium complex
phenomena.  Learning Outcome  Skills
At the conclusion of the course students are expected to be able
to:  Describe diffusion process using random walk, Langevin
equation, and FokkerPlank equation.
 Explain the first passage time and Kramers escape problem
 Explain the fluctuationdissipation theorem.
 Explain basic concepts in stochastic integrals.
 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
FokkerPlank equations using KramasMoyal expansion and the linear
noise approximation.
 Explain asymmetric simple exclusion process and some
related models to describe traffic flow and jamming transition in
onedimensional flows.
 Apply the concepts and techniques to various examples from
nonequilibrium complex phenomena.
Knowledge
In this course, first 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 random
walks, Langevin equations, FokkerPlanck equations, Kramars escape,
and the fluctuationdissipation theorem. Then selected stochastic
models that have wide applications to various real phenomena are
introduced and analysed. The topics are chosen from nonequilibrium
stochastic phenomena, including birth and death process and Master
equation, and asymmetric simple exclusion process. 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 nonequilibrium statistical physics,
biophysics, softmatter 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.  Teaching and learning methods  Lectures and exercise sessions. Computer exercise
included. 
Academic qualifications  Equilibrium statistical physics, physics bachelor
level mathematics (Especially: differential and integral calculus,
differential equations, Taylor expansions). 
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Exam  Credit  7,5 ECTS   Type of assessment  Oral examination, 30 min No preparation time   Aid  Without aids   Marking scale  7point grading scale   Censorship form  No external censorship
Several internal examiners    Criteria for exam assesment  See
Skills. 

Workload  Category  Hours  Lectures  24  Theory exercises  35  Exam  0,5  Preparation  146,5  Total 
206,0 

Saved on the
10092015

