We study reduced nematic equilibria on regular two-dimensional polygons with Dirichlet tangent boundary conditions, in a reduced two-dimensional Landau-de Gennes framework, discussing their relevance in the full three-dimensional framework too. We work at a fixed temperature and study the reduced stable equilibria in terms of the edge length, λ of the regular polygon, E K with K edges. We analytically compute a novel "ring solution" in the λ → 0 limit, with a unique point defect at the centre of the polygon for K = 4. The ring solution is unique. For sufficiently large λ, we deduce the existence of at least [K/2] classes of stable equilibria and numerically compute bifurcation diagrams for reduced equilibria on a pentagon and hexagon, as a function of λ 2 , thus illustrating the effects of geometry on the structure, locations and dimensionality of defects in this framework.
We investigate the solution landscape of a reduced Landau-de Gennes model for nematic liquid crystals on a two-dimensional hexagon at a fixed temperature, as a function of λ-the edge length. This is a generic example for reduced approaches on regular polygons. We apply the high-index optimization-based shrinking dimer method to systematically construct the solution landscape consisting of multiple solutions, with different defect configurations, and relationships between them. We report a new stable T state with index-0 that has an interior −1/2 defect; new classes of highindex saddle points with multiple interior defects referred to as H-class and TD-class saddle points; changes in the Morse index of saddle points as λ 2 increases and novel pathways mediated by highindex saddle points that can control and steer dynamical pathways on the solution landscape. The range of topological degrees, locations and multiplicity of defects offered by these saddle points can be used to navigate the complex solution landscapes of nematic liquid crystals and other related soft matter systems.
A phase field model with two phase fields, representing the concentration and the head-tail separation of amphiphilic molecules, respectively, has been constructed using an extension of the Ohta-Kawasaki model (Macromolecules 19, 2621(Macromolecules 19, -2632(Macromolecules 19, (1986). It is shown that this molecularly-informed phase field model is capable of producing various self-assembled amphiphilic aggregates, such as bilayers, vesicles and micelles. Furthermore, pathways connecting two opposed bilayers with a fusion pore are obtained by using a combination of the phase field model and the string method. Multiple fusion pathways, including a classical pathway and a leaky pathway, have been obtained depending on the initial separation of the two bilayers. The study shed light to the understanding of membrane fusion pathways and, more importantly, laid a foundation for further investigation of more complex membrane morphologies and transitions. arXiv:1910.04878v1 [cond-mat.soft]
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.