104,553 research outputs found

    Stabilization, amalgamation, and curves of intersection of Heegaard splittings

    Full text link
    We address a special case of the Stabilization Problem for Heegaard splittings, establishing an upper bound on the number of stabilizations required to make a Heegaard splitting of a Haken 3-manifold isotopic to an amalgamation along an essential surface. As a consequence we show that for any positive integer nn there are 3-manifolds containing an essential torus and a Heegaard splitting such that the torus and splitting surface must intersect in at least nn simple closed curves. These give the first examples of lower bounds on the minimum number of curves of intersection between an essential surface and a Heegaard surface that are greater than one.Comment: Version for publication. To appear in Algebraic and Geometric Topolog

    Spectral Deferred Correction Method for Landau-Brazovskii Model with Convex Splitting Technique

    Full text link
    The Landau-Brazovskii model is a well-known Landau model for finding the complex phase structures in microphase-separating systems ranging from block copolymers to liquid crystals. It is critical to design efficient numerical schemes for the Landau-Brazovskii model with energy dissipation and mass conservation properties. Here, we propose a mass conservative and energy stable scheme by combining the spectral deferred correction (SDC) method with the convex splitting technique to solve the Landau-Brazovskii model efficiently. An adaptive correction strategy for the SDC method is implemented to reduce the cost time and preserve energy stability. Numerical experiments, including two- and three-dimensional periodic crystals in the Landau-Brazovskii model, are presented to show the efficiency of the proposed numerical method.Comment: 20 pages, 5 figure

    Formation and kinetics of transient metastable states in mixtures under coupled phase ordering and chemical demixing

    Full text link
    We present theory and simulation of simultaneous chemical demixing and phase ordering in a polymer-liquid crystal mixture in conditions where isotropic- isotropic phase separation is metastable with respect to isotropic-nematic phase transition. It is found that mesophase formation proceeds by a transient metastable phase that surround the ordered phase, and whose lifetime is a function of the ratio of diffusional to orientational mobilities. It is shown that kinetic phase ordering in polymer-mesogen mixtures is analogous to kinetic crystallization in polymer solutions.Comment: 17 pages, 5 figures accepted for publication in EP
    • …
    corecore