Year-end Sale % OFF 
Abstract
Fronts dynamics of periodic crystalline state, which invades the homogeneous state (liquid phase), are analysed. These fronts are considered as traveling waves of atomic density amplitudes. The propagation of amplitudes is described by the hyperbolic equation of an extended Allen-Cahn type for which the complete set of analytical traveling-wave solutions are obtained by tanh-method. The set of solutions includes previously known traveling waves for the parabolic Allen-Cahn equation of both extended and standard form.
Highlights
The phase field crystal model (PFC-model) has been used to examine the dynamics of liquid-solid transformations, grain boundary migration and dislocation motion [1,2]
Taking into account slow and fast degrees of freedom for the crystal-liquid interface propagation, the amplitude equation of the PFC-model is described by the following partial differential equation (PDE) [7]:
We have obtained traveling wave solutions represented by hyperbolic tanh-functions (23) that confirms the correctness of the particular solutions for the dynamical problem of fast diffuse interfaces [32,33]
Summary
Series: Materials Science and Engineerin1g23149526(72809107) 012004 doi:10.1088/1757-899X/192/1/012004. General set of traveling-wave solutions for amplitude equations in the phase field crystal model. I G Nizovtseva, P K Galenko1,2 1Friedrich-Schiller-Universität Jena, Physikalisch-Astronomische Fakultät, D-07743 Jena, Germany
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: IOP Conference Series: Materials Science and Engineering
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
