104,553 research outputs found
Stabilization, amalgamation, and curves of intersection of Heegaard splittings
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 there are 3-manifolds containing an essential torus and a
Heegaard splitting such that the torus and splitting surface must intersect in
at least 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
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
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
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