cu.

=20Advanced studies

=20The course is intended for undergraduate students of mathematics, physic=
s and chemistry

and mathematical biology. Prior courses in advanced cal=
culus and linear algebra are required

(Analyysi I+II, Vektorianalyysi a=
nd Lineaarialgebra 1, or Mapu 1-2).

The scope of the course is to give a practical introduction to methods o=
f perturbation theory

of wide use in theoretical and mathematical physi=
cs and mathematical biology. In order to

illustrate the use of these te=
chniques the second part of the course will focus on specific

problems =
discussed in recent research papers.

Weeks 36-42 and 44-50, Tuesday 14-16 in room C123. Two hours of exercise= classes per week.

=20 Notice: last two lectures

Friday 02.12=
at 14-16 in C123

Friday 09.12 at 14-16 in B321

Exam projects can be based on research articles using multi-scale pertur=
bation theory. Besides those available from Pavliotis's

web-page, resea=
rch articles of interest may be:

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- M. Vergassola and M. Avellaneda, Scalar Transport in Compressible Flow,= Physica D, 106 (1997) 148-166 arXiv:chao-dyn/9612001 =20
- A. Mazzino, S. Musacchio, A. Vulpiani, Multiple-scale analysis and reno=
rmalization for pre-asymptotic scalar transport,

Phys. Rev. E 71, 01111= 3 (2005), arXiv:nlin/0412004. =20
- L. Biferale, A. Crisanti, M. Vergassola, A. Vulpiani, Eddy diffusivitie= s in scalar transport, Phys. Fluids 7, 2725 (1995), co= nd-mat/9412115 =20
- Avellaneda, M. & Majda, A. J. An integral representation and bounds= on the effective diffusivity in passive advection by laminar and turbulent= flows Com. Math. Phys., 1991, 138, 339-391 =20

The lecture notes cover and sometimes integrate the material expounded i= n the lections. They also give bibliographic references for the same topics= .

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Lectures 1-10 |

Lecture_01-02: Motivat= ing examples |

Lecture_02: Functional= Analysis Background |

Lecture_03: Two-scale = convergence |

Lecture_04: Elements o= f Ito calculus |

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- Course lecture notes =20

- =20
- Pavliotis, G. A. & Stuart, A. M. Multiscale methods: averaging and homogenization Springer, 2008, 53,= 307 (further info here) =20

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- Berglund, N. & Gentz, B. Noise-induced phenomena in slow-fast dynamical sy= stems: a sample-paths approach Birkh=C3=A4user, 2006, 276 =20

Did you forget to register? What to do.

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Group | Day | Time | Place | Instructor |
---|---|---|---|---|

1. | On Fridays | 10-12 a.m. | CK107 | Seyedali Zahabi |