منابع مشابه
Renormalization-group theory for the phase-field crystal equation.
We derive a set of rotationally covariant amplitude equations for use in multiscale simulation of the two-dimensional phase-field crystal model by a variety of renormalization-group (RG) methods. We show that the presence of a conservation law introduces an ambiguity in operator ordering in the RG procedure, which we show how to resolve. We compare our analysis with standard multiple-scale tech...
متن کاملHyperbolic Phase-Field Dynamics with Memory
We consider a non-conserved phase-field system which consists of two nonlinearly coupled hyperbolic integrodifferential equations. This model is derived from two basic assumptions: the heat flux law is of Gurtin–Pipkin type and the response of the order parameter to the variation of the free energy functional is delayed. These hypotheses might be a reasonable attempt to describe, for instance, ...
متن کاملUnconditionally stable method and numerical solution of the hyperbolic phase-field crystal equation.
The phase-field crystal model (PFC model) resolves systems on atomic length scales and diffusive time scales and lies in between standard phase-field modeling and atomistic methods. More recently a hyperbolic or modified PFC model was introduced to describe fast (propagative) and slow (diffusive) dynamics. We present a finite-element method for solving the hyperbolic PFC equation, introducing a...
متن کاملGlobal Smooth Solutions of the Three-dimensional Modified Phase Field Crystal Equation
Abstract. The Modified Phase Field Crystal (MPFC) equation, a generalized damped wave equation for which the usual Phase Field Crystal (PFC) equation is a special case, is analyzed in detail in three dimensions. A time-discrete numerical scheme, based on a convex splitting for the functional energy, is utilized to construct an approximate solution, which is then shown to converge to a solution ...
متن کاملFirst and second order operator splitting methods for the phase field crystal equation
Article history: Received 16 October 2014 Received in revised form 8 May 2015 Accepted 30 June 2015 Available online 3 July 2015
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2016
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2015.12.056