2D Phase Diagram for Minimizers of a Cahn-Hilliard Functional with Long-Range Interactions

2011/03/15 by Rustum Choksi, Choksi, Rustum, Mirjana Maras +3 · 1 citation
Computer Science · Materials Science · #Advanced Mathematical Modeling in Engineering #Block Copolymer Self-Assembly #Dynamical Systems (math.DS) #FOS: Mathematics #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.1103.2964

openalex publication_date 2011/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper presents a detailed asymptotic and numerical investigation of the phase diagram for global minimizers to a Cahn-Hilliard functional with long-range interactions in two space dimensions. We introduce a small parameter measuring perturbation from the minimal orderdisorder transition, and derive asymptotic estimates for stability regions as the parameter tends to zero. Based upon the H^-1 gradient ow, we introduce a hybrid numerical method to navigate through the complex energy landscape and access the ground state of the functional. We use this method to numerically compute the phase diagram. Our asymptotic predictions show surprisingly good agreement with our numerical results.

Citations

• Block Copolymers—Designer Soft Materials

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