Continuum mechanics of nonideal crystals : Microscopic approach based on projection-operator formalism

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Mikroskopische Zugänge zur nichtlinearen Mechanik defektreicher Kristalle
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Physical Review E ; 106 (2022), 5. - 054125. - American Physical Society (APS). - ISSN 2470-0045. - eISSN 2470-0053
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We present a microscopic derivation of the laws of continuum mechanics of nonideal ordered solids including dissipation, defect diffusion, and heat transport. The starting point is the classical many-body Hamiltonian. The approach relies on the Zwanzig-Mori projection operator formalism to connect microscopic fluctuations to thermodynamic derivatives and transport coefficients. Conservation laws and spontaneous symmetry breaking, implemented via Bogoliubov’s inequality, determine the selection of the slow variables. Density fluctuations in reciprocal space encode the displacement field and the defect concentration. Isothermal and adiabatic elastic constants are obtained from equilibrium correlations, while transport coefficients are given as Green-Kubo formulas, providing the basis for their measurement in atomistic simulations or colloidal experiments. The approach to the linearized continuum mechanics and results are compared to others from the literature.
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ISO 690MISEREZ, Florian, Saswati GANGULY, Rudolf HAUSSMANN, Matthias FUCHS, 2022. Continuum mechanics of nonideal crystals : Microscopic approach based on projection-operator formalism. In: Physical Review E. American Physical Society (APS). 106(5), 054125. ISSN 2470-0045. eISSN 2470-0053. Available under: doi: 10.1103/PhysRevE.106.054125
BibTex
@article{Miserez2022Conti-59160,
  year={2022},
  doi={10.1103/PhysRevE.106.054125},
  title={Continuum mechanics of nonideal crystals : Microscopic approach based on projection-operator formalism},
  number={5},
  volume={106},
  issn={2470-0045},
  journal={Physical Review E},
  author={Miserez, Florian and Ganguly, Saswati and Haussmann, Rudolf and Fuchs, Matthias},
  note={Article Number: 054125}
}
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