Kinematics of deformable media

Details Kinematics of deformable media Kinematics of deformable media

2007-09-05

arxiv.org/abs/0709.0582v1

Ann.Phys.323:1621-1643,2008; AnnalsPhys.323:1621-1643,2008

Physics

Classical Physics

28 pages, 12 figures

Scientific paper

10.1016/j.aop.2008.01.006

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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