Grebenkov Denis S
<a href="https://ror.org/02feahw73">Laboratoire de Physique</a> de la Matière Condensée (UMR 7643), CNRS-Ecole Polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France.
Phys Rev E. 2024 May;109(5-2):055306. doi: 10.1103/PhysRevE.109.055306.
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.
我们研究了狄利克雷 - 诺伊曼算子的谱性质以及在从针状到盘状的椭球域中的相关斯捷克洛夫问题。推导了该算子对于内部和外部问题的显式矩阵表示。我们展示了椭球体的各向异性如何影响该算子的特征值和特征函数。作为物理应用的例子，我们讨论了在椭球部分反应靶上的扩散控制反应以及扩散粒子与椭球边界之间相遇的统计情况。
