lecture |
date |
topic |
00 |
01/23 |
Introduction: movies |
01 |
01/25 |
Stirring & mixing |
02 |
01/28 |
Filament model |
03 |
01/30 |
Lagrangian
coordinates |
04 |
02/01 |
Solving
the Lagrangian equation |
05 |
02/04 |
Solving
the Lagrangian equation (part 2) |
06 |
02/06 |
Shear
flows |
07 |
02/08 |
The
tangent map |
08 |
02/11 |
Lyapunov
exponents |
09 |
02/13 |
Finite-time
Lyapunov exponents |
10 |
02/15 |
FTLEs
for the baker's map
[Matlab files] |
11 |
02/18 |
Renovating
flows |
12 |
02/20–02/22 |
Generalized
Lyapunov exponents
[Matlab
file] |
13 |
02/25 |
Rate of
decay and local stretching |
14 |
02/27–03/01 |
Strange
eigenmodes and intermittency
[Matlab files] |
15 |
03/04–03/06 |
Homogenization
theory [Matlab
files] |
16 |
03/08 |
Biomixing,
part 1: hitting distribution |
– |
03/11 |
Eriko
Hironaka: Small
dilatation pseudo-Anosov mapping classes (Room B113) |
17 |
03/13 |
Biomixing,
part 2: effective diffusivity |
18 |
03/15 |
Biomixing,
part 3: displacements in inviscid flow |
19 |
03/18–03/20 |
Biomixing,
part 4: viscous swimmer |
20 |
04/01 |
Topological
mixing on the torus |
21 |
04/03 |
Anosov
homeomorphisms |
22 |
04/05 |
From the
torus to the sphere |
23 |
04/05 |
Topological
stirring |
24 |
04/08 |
The
Thurston–Nielsen classification |
25 |
04/10 |
Computing
with train tracks |
26 |
04/12 |
The
Bestvina–Handel algorithm |
27 |
04/15 |
Coordinates for loops |
28 |
04/17 |
The
braidlab Matlab package |
29 |
04/19 |
Mix-norms |
30 |
04/22 |
Mixing
in the presence of sources and sinks
[Matlab files] |
31 |
04/24 |
Shuffling
cards |
32 |
04/26 |
Strong
uniform stopping rules |
33 |
05/01 |
Riffle
shuffling |
34 |
05/03 |
Permutations
generated by Brownian particles |
35 |
05/06 |
Random
braids and winding numbers |
– |
05/08 |
Discussion |