变形介质动力学
Kinematics of deformable media
摘要：
我们调查在二维和三维介质中的变形的运动学显式求解（解析）的演化方程（Raychaudhuri方程）的膨胀，剪切和旋转与变形。解析解使我们能够研究运动学量对初始条件的依赖性。特别是，我们能够确定区域的空间的初始条件，导致在有限时间内的奇点。变形的一些通用功能也进行了详细讨论。最后，我们指出的可行性和实用性，类似的练习流体和测地线流在平坦和弯曲的时空。
英文摘要：
We investigate the kinematics of deformations in two and three dimensional media by explicitly solving (analytically) the evolution equations (Raychaudhuri equations) for the expansion, shear and rotation associated with the deformations. The analytical solutions allow us to study the dependence of the kinematical quantities on initial conditions. In particular, we are able to identify regions of the space of initial conditions that lead to a singularity in finite time. Some generic features of the deformations are also discussed in detail. We conclude by indicating the feasibility and utility of a similar exercise for fluid and geodesic flows in flat and curved spacetimes.
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