Density and concentration field description of nonperiodic structures.
Density and concentration field description of nonperiodic structures.
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非周期结构的密度和浓度场描述
DOI：
10.1103/physreve.84.051505
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通讯作者：
Andreas M. Menzel
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作者：
Andreas M. Menzel
我们提出了一种简单的非局部能量泛函，适用于非周期性和局部纹理的连续场表征。唯象泛函基于以固定距离分隔的场梯度的成对方向相关相互作用。在附录中，我们描述了函数的数值最小化。在此基础上，我们研究了当我们从最初的无序状态开始时由泛函创建的线状条纹图案的动力学演化。在后期阶段，我们发现粗粒度显示出与 Cahn-Hilliard 方程相同的缩放行为。事实上，Cahn-Hilliard 模型作为极限情况包含在我们的表征中。我们的模型稍作修改就忽略了这种粗粒化并导致非周期性条纹相。对于后一种情况，我们研究了线状条纹的缺陷（端点）的时间演变。鉴于该功能的实际应用，我们讨论了聚合物系统和囊泡观察到的过程的表征。将线状结构生长的统计数据与逐步生长聚合反应的情况进行比较。此外，我们证明泛函可以应用于连续域描述中的囊泡研究。再现了简单剪切流中坦克踩踏的趋势和管流中降落伞折叠等基本特征。
We propose a simple nonlocal energy functional that is suitable for the continuum field characterization of nonperiodic and localized textures. The phenomenological functional is based on the pairwise direction-dependent interaction of field gradients that are separated by a fixed distance. In an appendix, we describe the numerical minimization of our functional. On that basis, we investigate the kinetic evolution of threadlike stripe patterns that are created by the functional when we start from an initially disordered state. At later stages, we find a coarse graining that shows the same scaling behavior as was obtained for the Cahn-Hilliard equation. In fact, the Cahn-Hilliard model is contained in our characterization as a limiting case. A slight modification of our model omits this coarse graining and leads to nonperiodic stripe phases. For the latter case, we investigate the temporal evolution of the defects (end points) of the threadlike stripes. In view of actual applications of this functional, we discuss the characterization of processes observed for polymeric systems and vesicles. The statistics of the growth of the threadlike structures is compared to the case of step-growth polymerization reactions. Furthermore, we demonstrate that the functional may be applied for the study of vesicles in a continuum field description. Basic features, such as the tendency of tank treading in simple shear flows and parachute folding in pipe flows, are reproduced.