Port Hamiltonian systems with moving interface: a phase field approach

Authors

Benjamin Vincent, Françoise Couenne, Laurent Lefèvre, Bernhard Maschke

Abstract

In this paper, we give a formulation of distributed parameter systems with a moving diffuse interface using the Port Hamiltonian formalism. For this purpose, we suggest to use the phase field modeling approach. In the first part we recall the phase field models, in particular the Cahn–Hilliard and Allen–Cahn equations, and show that they may be expressed in terms of a dissipative Hamiltonian system. In the second part we show how this Hamiltonian model may be extended to a Boundary Port Hamiltonian System and illustrate the construction on the example of crystallization.

Keywords

Boundary control systems; Port Hamiltonian systems; Phase fields; Solidification

Citation

• Journal: IFAC-PapersOnLine
• Year: 2020
• Volume: 53
• Issue: 2
• Pages: 7569–7574
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2020.12.1353
• Note: 21st IFAC World Congress- Berlin, Germany, 11–17 July 2020

BibTeX

@article{Vincent_2020,
  title={{Port Hamiltonian systems with moving interface: a phase field approach}},
  volume={53},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2020.12.1353},
  number={2},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Vincent, Benjamin and Couenne, Françoise and Lefèvre, Laurent and Maschke, Bernhard},
  year={2020},
  pages={7569--7574}
}

Download the bib file

References

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