Wiki source code of Multiscale methods, fall 2011

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1 = Multiscale methods (Introduction to mathematical physics), fall 2011 =
2
3 === Lecturer ===
4
5 [[Paolo Muratore-Ginanneschi>>doc:mathstatHenkilokunta.Muratore-Ginanneschi, Paolo]]
6
7 === Scope ===
8
9 cu.
10
11 === Type ===
12
13 Advanced studies
14
15 === Prerequisites ===
16
17 The course is intended for undergraduate students of mathematics, physics and chemistry
18 and mathematical biology. Prior courses in advanced calculus and linear algebra are required
19 (Analyysi I+II, Vektorianalyysi and Lineaarialgebra 1, or Mapu 1-2).
20
21 === Description and contents ===
22
23 The scope of the course is to give a practical introduction to methods of perturbation theory
24 of wide use in theoretical and mathematical physics and mathematical biology. In order to
25 illustrate the use of these techniques the second part of the course will focus on specific
26 problems discussed in recent research papers.
27
28 === Lectures ===
29
30 Weeks 36-42 and 44-50, Tuesday 14-16 in room C123. Two hours of exercise classes per week.
31
32 (% style="color: red;" %)Notice: last two lectures
33 Friday 02.12 at 14-16 in C123
34 Friday 09.12 at 14-16 in B321
35
36 === Exams ===
37
38 Exam projects can be based on research articles using multi-scale perturbation theory. Besides those available from Pavliotis's
39 web-page, research articles of interest may be:
40
41 * M. Vergassola and M. Avellaneda, Scalar Transport in Compressible Flow, Physica D, 106 (1997) 148-166 [[arXiv:chao-dyn/9612001>>url:http://xxx.lanl.gov/abs/chao-dyn/9612001||shape="rect"]]
42 * A. Mazzino, S. Musacchio, A. Vulpiani, Multiple-scale analysis and renormalization for pre-asymptotic scalar transport,
43 Phys. Rev. E 71, 011113 (2005), [[arXiv:nlin/0412004>>url:http://lanl.arxiv.org/abs/nlin/0412004||shape="rect"]].
44 * L. Biferale, A. Crisanti, M. Vergassola, A. Vulpiani, Eddy diffusivities in scalar transport, Phys. Fluids 7, 2725 (1995), [[cond-mat/9412115>>url:http://lanl.arxiv.org/abs/cond-mat/9412115||shape="rect"]]
45 * 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>>url:http://dx.doi.org/10.1007/BF02099496||shape="rect"]]
46
47 === Lecture Notes ===
48
49 The lecture notes cover and sometimes integrate the material expounded in the lections. They also give bibliographic references for the same topics.
50
51 |(((
52 Lectures 1-10
53 )))
54 |(((
55 [[Lecture_01-02>>attach:lecture_01.pdf]]: Motivating examples
56 )))
57 |(((
58 [[Lecture_02>>attach:lecture_02.pdf]]: Functional Analysis Background
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60 |(((
61 [[Lecture_03>>attach:lecture_03.pdf]]: Two-scale convergence
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63 |(((
64 [[Lecture_04>>attach:lecture_04.pdf]]: Elements of Ito calculus
65 )))
66
67 === Bibliography ===
68
69 * Course lecture notes
70
71 * Pavliotis, G. A. & Stuart, A. M. [[Multiscale methods: averaging and homogenization>>url:http://books.google.com/books?id=qIaD19q7Tl8C&dq=Multiscale+Methods:+Averaging+and+Homogenization&source=gbs_navlinks_s||shape="rect"]] Springer, 2008, 53, 307 (further info [[here>>url:http://www2.imperial.ac.uk/~~pavl/multiscale.html||shape="rect"]])
72
73 * Berglund, N. & Gentz, B. [[Noise-induced phenomena in slow-fast dynamical systems: a sample-paths approach>>url:http://books.google.com/books?id=c3w0z--7QJAC&dq=Noise-induced+phenomena+in+slow-fast+dynamical+systems:+a+sample-paths+approach&source=gbs_navlinks_s||shape="rect"]] Birkhäuser, 2006, 276
74
75 === [[Registration>>url:https://oodi-www.it.helsinki.fi/hy/opintjakstied.jsp?html=1&Tunniste=57357||shape="rect"]] ===
76
77 Did you forget to register? [[What to do>>doc:mathstatOpiskelu.Kysymys4]].
78
79 === Exercise groups ===
80
81 |=(((
82 Group
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84 Day
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86 Time
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88 Place
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90 Instructor
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93 1.
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95 On Fridays
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97 10-12 a.m.
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99 CK107
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101 Seyedali Zahabi
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