Journal
ANNALS OF PHYSICS
Volume 323, Issue 7, Pages 1621-1643Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aop.2008.01.006
Keywords
kinematics; flows; Raychaudhuri equations; deformable media
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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 a flat and curved spacetimes. (C) 2008 Elsevier Inc. All rights reserved.
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