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.

中文翻译：

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关于平滑和单一体积增长的注释

考虑正在生长的物体的材料结构。在模拟物理空间的一般微分流形和模拟时空的纤维束的几何框架中，可以为存在平滑通量场的任何广泛属性定义体点，即使该属性不守恒。使用德拉姆电流的概念来考虑奇异磁通场。使用对应于奇异通量场的电流边界编写广义平衡定律，表面生长与体积生长统一。