Critical points and bifurcations of the three-dimensional Onsager model for liquid crystals

DOI10.1007/s00205-017-1146-8zbMath1373.35255arXiv1509.02469OpenAlexW2963536110WikidataQ59612764 ScholiaQ59612764MaRDI QIDQ1675117

Michaela A. C. Vollmer

Publication date: 26 October 2017

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.02469

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) (82D30) Liquid crystals (76A15) Bifurcations in context of PDEs (35B32) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38)

Related Items (6)

Modelling and computation of liquid crystals ⋮ Nematic first order phase transition for liquid crystals in the van der Waals–Kac limit ⋮ The Saturn ring effect in nematic liquid crystals with external field: effective energy and hysteresis ⋮ Long-time behaviour and phase transitions for the McKean-Vlasov equation on the torus ⋮ Solution landscape of the Onsager model identifies non-axisymmetric critical points ⋮ Γ-convergence of a mean-field model of a chiral doped nematic liquid crystal to the Oseen–Frank description of cholesterics

Uses Software

• DLMF

Cites Work

• Multiple branches of ordered states of polymer ensembles with the Onsager excluded volume potential
• Spherical harmonics and approximations on the unit sphere. An introduction
• The principle of symmetric criticality
• The geometry of spontaneous symmetry breaking
• On the stationary solutions of the 2D Doi-Onsager model
• Smooth functions invariant under the action of a compact Lie group
• Asymptotic states of a Smoluchowski equation
• On stationary solutions of the 2D Doi-Onsager model
• Axial symmetry and classification of stationary solutions of Doi-Onsager equation on the sphere with Maier-Saupe potential
• Some global results for nonlinear eigenvalue problems
• Exact multiplicity of nematic states for an Onsager model
• Random Fields on the Sphere
• Critical points of the Onsager functional on a sphere
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