Scaling, self-similarity and intermediate asymptotics
Math 488 Sec. G1
- Instructor: Richard Laugesen
- Office: 376 Altgeld Hall
- Class meets: Probably MWF at 3 pm, but that might
- Room: Altgeld 441
This is a "topics" course in applied mathematics. We aim for
a working knowledge of similarity and asymptotic methods
that will be useful for the future research of students in the class.
We will attempt to digest G. I. Barenblatt's book
"Scaling, self-similarity and intermediate asymptotics"
(Cambridge Texts in Applied Mathematics 14, 1996).
There will be only occasional homework. Students will make final
presentations, hopefully on papers from the similarity literature.
Prerequisites: classical ordinary and partial differential equations.
For example, Math 444 should provide plenty of background. But you
also need a love of calculus and applications!
We plan to cover the following topics:
And I'll try to arrange some guest lectures from workers in the field.
- Dimensions, dimensional analysis and similarity
Self-similar solutions of the first and second kinds
Classification of similarity solutions
- Scaling and transformation groups, renormalization group
- Traveling waves
- Stability of self-similar solutions
- Scaling in turbulence
- Whatever else interests us, e.g. papers from the recent literature
Application areas we will encounter include: heat flow, nuclear
explosions, fluid flow, filtration, shock waves, flame fronts,
and fracture of solids. No prior knowledge of those areas is needed. We
will just dive in and see what we can learn.
If you have any questions or concerns,
please contact me by e-mail at email@example.com.
- Richard Laugesen