Shape Minimization of Dendritic Attenuation
偏微分方程分析
2008-11-04 v2 最优化与控制
摘要
What is the optimal shape of a dendrite? Of course, optimality refers to some particular criterion. In this paper, we look at the case of a dendrite sealed at one end and connected at the other end to a soma. The electrical potential in the fiber follows the classical cable equations as established by W. Rall. We are interested in the shape of the dendrite which minimizes either the attenuation in time of the potential or the attenuation in space. In both cases, we prove that the cylindrical shape is optimal.
引用
@article{arxiv.math/0702017,
title = {Shape Minimization of Dendritic Attenuation},
author = {Antoine Henrot and Yannick Privat},
journal= {arXiv preprint arXiv:math/0702017},
year = {2008}
}