植物生长动力学;一个基于黎曼几何的理论
Dynamics of Plant Growth; A Theory Based on Riemannian Geometry
摘要：
在这项工作中，一个新的宏观植物组织生长模型的基础上动态黎曼几何。我们将1D和2D组织视为尺寸大于1 mm的连续、可变形、不断生长的几何形状。生长组织的动力学描述的一组耦合张量方程在非欧（弯曲）空间。这些耦合方程代表了一种新的反馈机制之间的增长和曲率动力学。对于一维生长，数值模拟相比，两个措施的根生长。首先，模块化的增长沿模拟根显示了一个伸长区常见的许多种植物的根。第二，相对元素生长率（REGR）计算在硅片表现出时间动态最近在高分辨率的根生长研究，但迄今缺乏一个生物学假说来解释它们。也就是说，REGR可以从位于根尖附近的单峰演变为双峰结构。在我们的模型中，这是将增长视为几何反应扩散过程和由于新材料的分布式来源而引起的膨胀的直接结果。在二维空间中，我们研究了具有突现负曲率的圆对称生长盘。这些结果进行了比较薄盘实验，这是一个代理模型植物叶片。这些结果也适用于伞盖的曲率演化和不均匀生长模式。最后，我们将该模型扩展到各向异性磁盘和预测的增长动力学的二维曲面，开发一个细长的形状与本地的皱褶。我们的模型还提供了组织生长动力学的几个措施。这些包括度量和速度场的时间演化，它们是模型中的动态变量，以及膨胀、剪切和旋转，它们是表征组织生长的变形张量。
英文摘要：
In this work, a new model for macroscopic plant tissue growth based on dynamical Riemannian geometry is presented. We treat 1D and 2D tissues as continuous, deformable, growing geometries for sizes larger than 1mm. The dynamics of the growing tissue are described by a set of coupled tensor equations in non-Euclidean (curved) space. These coupled equations represent a novel feedback mechanism between growth and curvature dynamics. For 1D growth, numerical simulations are compared to two measures of root growth. First, modular growth along the simulated root shows an elongation zone common to many species of plant roots. Second, the relative elemental growth rate (REGR) calculated in silico exhibits temporal dynamics recently characterized in high-resolution root growth studies but which thus far lack a biological hypothesis to explain them. Namely, the REGR can evolve from a single peak localized near the root tip to a double-peak structure. In our model, this is a direct consequence of considering growth as both a geometric reaction-diffusion process and expansion due to a distributed source of new materials. In 2D, we study a circularly symmetric growing disk with emergent negative curvatures. These results are compared against thin disk experiments, which are a proxy model for plant leaves. These results also apply to the curvature evolution and the inhomogeneous growth pattern of the Acetabularia cap. Lastly, we extend the model to anisotropic disks and predict the growth dynamics for a 2D curved surface which develops an elongated shape with localized ruffling. Our model also provides several measures of the dynamics of tissue growth. These include the time evolution of the metric and velocity field, which are dynamical variables in the model, as well as expansion, shear and rotation which are deformation tensors characterizing the growth of the tissue.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
