标题： 二维相图用于具有长程相互作用的Cahn-Hilliard泛函的极小值点 显示英文标题

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

摘要： 本文详细研究了二维空间中具有长程相互作用的Cahn-Hilliard泛函全局极小值的相图。 我们引入一个衡量从最小有序无序转变扰动的小参数，并推导出当参数趋于零时的稳定性区域的渐近估计。 基于H^-1梯度流，我们引入一种混合数值方法来穿越复杂的能量景观并获取泛函的基态。 我们使用该方法进行数值计算以得到相图。 我们的渐近预测与数值结果显示出令人惊讶的良好一致性。 显示英文摘要

摘要： 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.