A Differential-Geometric Approach to Model Isotropic Diffusion on Circular Conic Surfaces in Uniform Rotation

Summary

We outline a differential-geometric approach to analytically solve the diffusion equation on a static circular conic surface assuming isotropic and sourceless diffusion. We also extend the proposed technique to find general solutions for a cone in arbitrary axisymmetric and uniform rotation. The new, analytical expressions for these solutions rely on the construction of the kernel function for the diffusion operator on the corresponding Riemannian manifold. Given particular boundary conditions, the resulting series expansions may for practical purposes be approximated numerically, providing a valuable tool for diffusion models.