Nonlinear Elasticity of the Phase Field Crystal Model from the Renormalization Group

Pak Yuen Chan; Nigel Goldenfeld

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arXiv · 0910.2776

Nonlinear Elasticity of the Phase Field Crystal Model from the Renormalization Group

Pak Yuen Chan·Nigel Goldenfeld

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Abstract

The rotationally-covariant renormalization group equations of motion for the density wave amplitudes in the phase field crystal model are shown to follow from a dynamical equation driven by an effective free energy density that we derive. We show that this free energy can be written purely as a function of the strain tensor and thence derive the corresponding equations governing the nonlinear elastic response.

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Pak Yuen Chan, Nigel Goldenfeld. 2009-12-23. Nonlinear Elasticity of the Phase Field Crystal Model from the Renormalization Group. https://arxiv.org/abs/0910.2776

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