Spectral properties of the Dirichlet-to-Neumann operator for spheroids
arXiv:2402.06372 · doi:10.1103/PhysRevE.109.055306
Abstract
We study the spectral properties of the Dirichlet-to-Neumann operator and the related Steklov problem in spheroidal domains ranging from a needle to a disk. An explicit matrix representation of this operator for both interior and exterior problems is derived. We show how the anisotropy of spheroids affects the eigenvalues and eigenfunctions of the operator. As examples of physical applications, we discuss diffusion-controlled reactions on spheroidal partially reactive targets and the statistics of encounters between the diffusing particle and the spheroidal boundary.
References in corpus (12)
- Paradigm shift in diffusion-mediated surface phenomena
- Probability distribution of the boundary local time of reflected Brownian motion in Euclidean domains
- Diffusion-mediated surface reactions and stochastic resetting
- Surface Hopping Propagator: An Alternative Approach to Diffusion-Influenced Reactions
- Statistics of boundary encounters by a particle diffusing outside a compact planar domain
- A probabilistic model of diffusion through a semi-permeable barrier
- The narrow capture problem: an encounter-based approach to partially reactive targets
- Statistics of diffusive encounters with a small target: Three complementary approaches
- Steady-state reaction rate of diffusion-controlled reactions in sheets
- An encounter-based approach to the escape problem
- Low energy scattering asymptotics for planar obstacles
- Effects of target anisotropy on harmonic measure and mean first-passage time