Apr 11, 2025
Several features of the eigenfunctions of the Laplacian on an annulus with homogeneous Neumann boundary condition are discussed. The distribution of the eigenvalues is discussed in detail, making use of a phase angle function called θ. The limiting cases of a disk and a circle are discussed.
Jan 18, 2023
Denote the length distribution of one’s hair to be f(l,t), where l is hair length, and t is time. Considering that each hair may be lost naturally from time to time (there is a probability of λdt for each hair to be lost within time range from t to t+dt) and then restart growing from zero length, how will the length distribution of hair evolve with time? It turns out that we may model it with a first-order PDE.