- Persistence of vegetation patterns Part 1: Turing instability
- Persistence of vegetation patterns Part 2: delayed Turing bifurcation due to noise and slow parameter drift
- Patch model of organic farming
- Notes on MEMS devices
- Turing instability
- Derivation of a mathematical model of crime
- Mean first passage time for small traps
- Perturbation of eigenvalues; domain perturbations
- Metastability: exponentially slow motion of
interfaces in 1D Allen-Cahn model
- See the FlexPDE script front1d-two.pde

- Travelling waves in thin domains
- Coarsening phenomenon for mesa patterns
- Stability of mesa patterns in the Brusselator | supplement: Examples of patterns in Brusselator
- Swarm aggregation models
- Matlab code: swarm.m

- Spike patterns in GM system 1: introduction
- Dynamics of a single interior spike in the GM system
- Spike patterns in GM system 2: Wei's proof of stability of NLEP problem
- Spike patterns in GM system 3: Stability of K spikes, large and small eigenvalues
- Shallow wave theory

- Random matrix theory and Wigner's semi-circle law
- Multiple scales:
- Some [rather rough] notes on traffic models: derivation, method of characteristics, shock formation, Burger's pde... See also FlexPDE script, burger.pde
- Rapidly convergent series for the regular part of modified Green's function on a rectangle: resummation.
- Fourier series: convergence, discrete fourier series, FFT, and Gibbs phenomenon.
- The motion of a hanging chain | Maple worksheet with animation

Note1: For *.pde files, you will need to download FlexPDE program ( they have a free student version, which is sufficient for these simulations).

Note2: to run Maple worksheets, you need to also download the following file: tools.mpl. Then replace the line

- Maple worksheet to compute the steady state and the eigenvalue of the interface by using numerical boundary problem solver.
- Questions on construction of mesa patterns
- Questions on NLEP problem
- Questions on NLEP problem part 2
- Computing a fold point for the ODE u''-u+u^2*(1+ax^2)=0 (Maple worksheet)
- FlexPDE simulation of spike instabilities in the GM model:
- Simulation of a simple pulse-splitting model (FlexPDE script file)
- Simulation of a pulse-splitting behaviour in GS model model (FlexPDE script file)