标题： 关于光滑与奇异体积生长的注释 显示英文标题

标题： Notes on Smooth and Singular Volumetric Growth

摘要： 考虑发生生长的物体的材料结构。 在描述物理空间的广义微分流形和描述时空的纤维丛的几何框架下，对于存在光滑通量场的任何广延性质，都可以定义物体点，即使该性质不守恒。 利用德勒姆（de Rham）上电流的概念来研究奇异通量场。 通过使用对应于奇异通量场的电流边界写出广义平衡定律，将表面生长与体积生长统一起来。 显示英文摘要

摘要： The material structure of bodies undergoing growth is considered. In the geometric framework of a general differential manifold modeling the physical space and a fiber bundle modeling spacetime, body points may be defined for any extensive property for which a smooth flux field exists, even if the property is not conserved. Singular flux fields are considered using the notion of a de Rham current. Writing a generalized balance law using the boundary of the current corresponding to a singular flux field, surface growth is unified with volumetric growth.