On the thermodynamics of the Swift–Hohenberg theory

by L.F.R. Espath, A. F. Sarmiento, Lisandro Dalcin, And V. M. Calo
Year: 2017


Espath, L. F. R., A. F. Sarmiento, Lisandro Dalcin, and V. M. Calo. "On the thermodynamics of the Swift–Hohenberg theory." Continuum Mechanics and Thermodynamics 29, no. 6 (2017): 1335-1345.


​We present the microbalance including the microforces, the first- and second-order microstresses for the Swift–Hohenberg equation concomitantly with their constitutive equations, which are consistent with the free-energy imbalance. We provide an explicit form for the microstress structure for a free-energy functional endowed with second-order spatial derivatives. Additionally, we generalize the Swift–Hohenberg theory via a proper constitutive process. Finally, we present one highly resolved three-dimensional numerical simulation to demonstrate the particular form of the resulting microstresses and their interactions in the evolution of the Swift–Hohenberg equation.​


Phase-field Gradient theory Thermodynamics of continua Swift–Hohenberg theory