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On the thermodynamics of the Swift–Hohenberg theory

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Abstract

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.

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Authors and Affiliations

  1. Computer, Electrical and Mathematical Sciences and Engineering, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia

    L. F. R. Espath & A. F. Sarmiento

  2. Extreme Computing Research Center, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia

    L. Dalcin

  3. Applied Geology, Western Australian School of Mines, Faculty of Science and Engineering, Curtin University, Perth, WA, 6845, Australia

    V. M. Calo

  4. Mineral Resources, Commonwealth Scientific and Industrial Research Organisation (CSIRO), Kensington, WA, 6152, Australia

    V. M. Calo

Authors
  1. L. F. R. Espath
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  2. A. F. Sarmiento
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  3. L. Dalcin
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  4. V. M. Calo
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Corresponding author

Correspondence to L. F. R. Espath.

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Communicated by Andreas Öchsner.

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Espath, L.F.R., Sarmiento, A.F., Dalcin, L. et al. On the thermodynamics of the Swift–Hohenberg theory. Continuum Mech. Thermodyn. 29, 1335–1345 (2017). https://doi.org/10.1007/s00161-017-0581-y

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  • DOI: https://doi.org/10.1007/s00161-017-0581-y

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