On a divergence penalized Landau-de Gennes model

• Lia Bronsard ^[1] ; Jinqi Chen ^[2] ; Léa Mazzouza ^[3] ; Daniel McDonald ^[4] ; Nathan Singh ^[5] ; Dominik Stantejsky ^[6] ; Lee van Brussel ^[1]
  1. [1] McMaster University

     McMaster University

     Canadá

     
  2. [2] Tufts University

     Tufts University

     City of Medford, Estados Unidos

     
  3. [3] University of Paris-Saclay

     University of Paris-Saclay

     Arrondissement de Palaiseau, Francia

     
  4. [4] University of Pennsylvania

     University of Pennsylvania

     City of Philadelphia, Estados Unidos

     
  5. [5] University of California System

     University of California System

     Estados Unidos

     
  6. [6] University of Lorraine

     University of Lorraine

     Arrondissement de Nancy, Francia

     

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• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 82, Nº. Extra 4, 2025 (Ejemplar dedicado a: 28 CEDYA/ 18 CMA SeMA Congress), págs. 499-513
• Idioma: inglés
• DOI: 10.1007/s40324-025-00379-7
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• Resumen

  • We give a brief introduction to a divergence penalized Landau-de Gennes functional as a toy model for the study of nematic liquid crystal with colloid inclusion, in the case of unequal elastic constants. We assume that the nematic occupies the exterior of the unit ball, satisfies homeotropic anchoring at the surface of the colloid and approaches a uniform uniaxial state as |x| → ∞. We study the “small particle” limit and obtain a representation formula for solutions to the associated Euler-Lagrange equations. We also present a numerical analysis of these equations based on a finite element approach and discuss the effect of the divergence penalization on the “Saturn ring” defects and on the properties of the Q-tensor.