| 1 |
Introduction: Dense Granular Flow in a Silo |
| 2-3 |
Linear Waves: PDE for Waves in an Elastic Medium, Characteristics, d'Alembert's Solution |
| 4-13 |
Nonlinear Kinematic Waves: Lighthill-Whitham Theory of Traffic Flow, Density Waves, General Method of Characteristics, Hodograph Method, Expansion Fans, Wave Breaking, Shocks
River Waves, Gas Compression Waves, Shallow Water Waves |
|
Midterm Exam |
| 14-16 |
Dispersive Waves: Fourier Transform, Group Velocity and Caustics
Envelope Equations, KdV Equation, Solitons |
| 17-18 |
Linear Diffusion: Green Function for the Diffusion Equation, Some Fourier Analysis
Similarity Solutions |
| 19-25 |
Nonlinear Diffusion: Burgers Equation and Shock Structure, Cole-Hopf Transformation
Porous Medium Equation, Similarity Solutions
Regular and Singular Perturbations, Boundary Layers, Matched Asymptotic Expansions
Nernst-Planck Equations |
|
Final Exam |