Phase-Field Crystals:Fast Interface Dynamics by Peter Galenko & Vladimir Ankudinov & Ilya Starodumov

Author:Peter Galenko & Vladimir Ankudinov & Ilya Starodumov
Language: eng
Format: epub
Publisher: Walter de Gruyter
Published: 2018-07-15T00:00:00+00:00

Substituting equation (2.57) into the balance law (2.45) gives the following hyperbolic (modified) PFC equation:

Equation (2.58) shows that, in addition to dissipation described by the parabolic PFC equation (2.44), inertia is also taken into account due to the kinetic contribution (2.56). Alternatively, equation (2.58) was proposed by Stefanovic et al. [133], [134] to incorporate both fast elastic relaxation and slower mass diffusion. Linearizing equation (2.58) in gives

Before conducting a marginal stability analysis of this equation near the front, some basic features of this equation will be discussed below.

To obtain the dispersion relation let us substitute equation (2.49) into equation (2.59), which gives

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