NOTICE: Due to a lapse in annual appropriations, most of this website is not being updated. Learn more.
Form submissions will still be accepted but will not receive responses at this time. Sections of this site for programs using non-appropriated funds (such as NVLAP) or those that are excepted from the shutdown (such as CHIPS and NVD) will continue to be updated.
An official website of the United States government
Here’s how you know
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
Secure .gov websites use HTTPS
A lock (
) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.
Numerical Analysis and Simulation for a Generalized Planar Ginzburg-Landau Equation in a Circular Geometry
Published
Author(s)
Sean A. Colbert-Kelly, Geoffrey B. McFadden, Daniel Phillips, Jie Shen
Abstract
In this paper, a numerical scheme for a generalized planar Ginzburg-Landau energy in a circular geometry is studied. A spectral-Galerkin method is utilized, and a stability analysis and an error estimate for the scheme are presented. It is shown that the scheme is unconditionally stable. We present numerical simulation results that have been obtained by using the scheme with various sets of boundary data, including those the form u(θ ) = exp(idθ), where the integer d denotes the topological degree of the solution. These numerical results are in good agreement with the experimental and analytical results. Results include the computation of bifurcations from pure bend or splay patterns to spiral patterns for d = 1, and computations of metastable or unstable higher-energy solutions as well as the lowest energy ground state solutions for values of d ranging from two to five.
Colbert-Kelly, S.
, McFadden, G.
, Phillips, D.
and Shen, J.
(2017),
Numerical Analysis and Simulation for a Generalized Planar Ginzburg-Landau Equation in a Circular Geometry, Communications in Mathematical Sciences, [online], https://doi.org/10.4310/CMS.2017.v15.n2.a3, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=916315
(Accessed October 10, 2025)