Barua, Amlan K. and Chew, Ray and Li, Shuwang and Lowengrub, John and Münch, Andreas and Wagner, Barbara
(2023)
*Sharp-interface problem of the Ohta-Kawasaki model for symmetric diblock copolymers.*
Journal of Computational Physics, 481
.

Full text not available from this repository.

Official URL: https://doi.org/10.1016/j.jcp.2023.112032

## Abstract

The Ohta-Kawasaki model for diblock-copolymers is well known to the scientific community of diffuse-interface methods. To accurately capture the long-time evolution of the moving interfaces, we present a derivation of the corresponding sharp-interface limit using matched asymptotic expansions, and show that the limiting process leads to a Hele-Shaw type moving interface problem. The numerical treatment of the sharp-interface limit is more complicated due to the stiffness of the equations. To address this problem, we present a boundary integral formulation corresponding to a sharp interface limit of the Ohta-Kawasaki model. Starting with the governing equations defined on separate phase domains, we develop boundary integral equations valid for multi-connected domains in a 2D plane. For numerical simplicity we assume our problem is driven by a uniform Dirichlet condition on a circular far-field boundary. The integral formulation of the problem involves both double- and single-layer potentials due to the modified boundary condition. In particular, our formulation allows one to compute the nonlinear dynamics of a non-equilibrium system and pattern formation of an equilibrating system. Numerical tests on an evolving slightly perturbed circular interface (separating the two phases) are in excellent agreement with the linear analysis, demonstrating that the method is stable, efficient and spectrally accurate in space.

Item Type: | Article |
---|---|

Subjects: | Mathematical and Computer Sciences > Mathematics > Applied Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics |

ID Code: | 3023 |

Deposited By: | Monika Drueck |

Deposited On: | 17 Aug 2023 11:14 |

Last Modified: | 17 Aug 2023 11:14 |

Repository Staff Only: item control page