We report on the modeling of the dynamics of confined lipid membranes. We derive a thin film model in the lubrication limit which describes an inextensible liquid membrane with bending rigidity confined between two adhesive walls. The resulting equations share similarities with the Swift-Hohenberg model. However, inextensibility is enforced by a time-dependent nonlocal tension. Depending on the excess membrane area available in the system, three different dynamical regimes, denoted as A, B and C, are found from the numerical solution of the model. In regime A, membranes with small excess area form flat adhesion domains and freeze. Such freezing is interpreted by means of an effective model for curvature-driven domain wall motion. The nonlocal membrane tension tends to a negative value corresponding to the linear stability threshold of flat domain walls in the Swift-Hohenberg equation. In regime B, membranes with intermediate excess areas exhibit endless coarsening with coexistence of flat adhesion domains and wrinkle domains. The tension tends to the nonlinear stability threshold of flat domain walls in the Swift-Hohenberg equation. The fraction of the system covered by the wrinkle phase increases linearly with the excess area in regime B. In regime C, membranes with large excess area are completely covered by a frozen labyrinthine pattern of wrinkles. As the excess area is increased, the tension increases and the wavelength of the wrinkles decreases. For large membrane area, there is a crossover to a regime where the extrema of the wrinkles are in contact with the walls. In all regimes after an initial transient, robust localised structures form, leading to an exact conservation of the number of adhesion domains. arXiv:1808.00316v1 [cond-mat.soft] 1 Aug 2018

The biaxial nematic phase is generally taken, either explicitly or implicitly, to have D 2h point group symmetry. However, it is possible for the biaxial phase to have a lower symmetry depending on that of its constituent molecules. Here we develop a molecular field theory for a nematogen composed of C 2h molecules in terms of the nine independent second rank orientational order parameters defining the C 2h biaxial nematic. In addition there is a rank one order parameter constructed from two pseudovectors which is only non-zero in the C 2h phase. The theory is simplified by removing all but the three dominant order parameters. The predicted phase behaviour is found to be rich with three possible biaxial nematic phases and with the transitions involving a biaxial nematic phase exhibiting tricritical points.

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