DYNAMICS OF LABYRINTHINE PATTERN-FORMATION IN MAGNETIC FLUIDS
DYNAMICS OF LABYRINTHINE PATTERN-FORMATION IN MAGNETIC FLUIDS
复制标题
DOI：
10.1103/physreva.46.4894
复制
发表时间：
1992-10-15
影响因子：
2.9
通讯作者：
JACKSON, DP
中科院分区：
文献类型：
--
作者：
LANGER, SA;GOLDSTEIN, RE;JACKSON, DP
针对横向磁场中磁流体（铁磁流体）的准二维域中图案形成的动力学发展了一种理论。图案形成被视为耗散动态过程，其中运动使用最小假设从静态能量函数中变分导出。这种动力学是适用于任何可以建模为平面中闭合曲线的系统的一般形式主义的一个实例。在将形式主义应用于铁磁流体时，我们提出了二维偶极域能量的计算，作为其边界形状的函数。提出了近圆形形状的详细线性稳定性分析，并通过非线性非局部演化方程的数值求解来研究远离不稳定开始的非线性状态中的图案形成。数字获得的高度分支模式与实验发现的模式在质量上相似。时间演化表现出对初始条件的敏感依赖性，表明在可访问形状的空间中存在许多局部最小值。该分析还为空气-水界面偶极单层图案形成理论提供了确定性起点，其中热波动发挥着更主导的作用。
A theory is developed for the dynamics of pattern formation in quasi-two-dimensional domains of magnetic fluids (ferrofluids) in transverse magnetic fields. The pattern formation is treated as a dissipative dynamical process, with the motion derived variationally from a static energy functional using minimal assumptions. This dynamics is one instance of a general formalism applicable to any system that can be modeled as a closed curve in a plane. In applying the formalism to ferrofluids, we present a calculation of the energy of a two-dimensional dipolar domain as a functional of the shape of its boundary. A detailed linear stability analysis of nearly circular shapes is presented, and pattern formation in the nonlinear regime, far from the onset of instability, is studied by numerical solution of the nonlinear, nonlocal evolution equations. The highly branched patterns obtained numerically bear a qualitative resemblance to those found experimentally. The time evolution exhibits sensitive dependence on initial conditions, suggesting the existence of many local minima in the space of accessible shapes. The analysis also provides a deterministic starting point for a theory of pattern formation in dipolar monolayers at the air-water interface, in which thermal fluctuations play a more dominant role.