Nonlinear Dynamics II: Continuum Systems

Calendar

LEC #	TOPICS	KEY DATES
1	Introduction, overview & mathematical basics
2	Dimensional analysis & scalings
3	Hamiltonian dynamics & Kepler’s laws
4	Random walkers
5	Diffusion equation: Fourier method
6	Diffusion equation: Green’s function method
7	Linear stability analysis & pattern formation	Problem Set 1 due
8	Calculus of variations
9	Surface tension
10	Elasticity
11	Deformation of a thin beam	Problem Set 2 & Proposal due
12	Towards hydrodynamics
13	Navier-Stokes equations I
14	Hydrodynamics equations
15	Stokes limit & Oseen tensor	Problem Set 3 due
16	Navier-Stokes equations II
17	Singular perturbations
18	Towards airplane flight	Problem Set 4 due
19	Euler equations: Basic solutions and forces	Mid-term posted
20	2D hydrodynamics	Mid-term due
21	Conformal maps & airfoils
22	Waves & solitons
23	Final projects: Student presentations
24	Final projects: Student presentations (cont.)	Project Report due
25	Bouncing droplets
26	Topological defects & active matter