弹性系统临界点附近纵向相分离的精确解
Ballooning, bulging and necking: an exact solution for longitudinal phase separation in elastic systems near a critical point
摘要：
在弹性系统中纵向相分离的突出例子包括弹性颈缩、圆柱形聚会气球中膨胀的扩展和凝胶纤维受到表面张力的珠状化。在这里，我们证明，如果这样一个系统的参数被调整到临界点附近（两个阶段之间的差异消失），然后所有系统的行为是由一个简单的和普遍的弹性能量的最小化，熟悉金斯堡-朗道理论在外场。我们最小化这个能量分析，这不仅产生众所周知的界面双曲正切解，但也在有限和无限长系统的稳定和不稳定的解决方案，揭示了弹性系统的完整的形状演变和滞后。相应地，我们也发现分析结果的延迟发病，临界性的变化和最终抑制不稳定性与减少系统长度，表明我们简单的近临界理论捕捉到了大部分的复杂性和编排远离临界系统。最后，我们找到了上述三个突出的相分离例子的临界点，并演示了每个系统如何遵循通用的解决方案。
英文摘要：
Prominent examples of longitudinal phase separation in elastic systems include elastic necking, the propagation of a bulge in a cylindrical party balloon and the beading of a gel fiber subject to surface tension. Here we demonstrate that, if the parameters of such a system are tuned near a critical point (where the difference between the two phases vanishes) then the behaviour of all systems is given by the minimization of a simple and universal elastic energy familiar from Ginzburg-Landau theory in an external field. We minimize this energy analytically, which yields not only the well known interfacial tanh solution, but also the complete set of stable and unstable solutions in both finite and infinite length systems, unveiling the elastic system's full shape evolution and hysteresis. Correspondingly, we also find analytic results for the the delay of onset, changes in criticality and ultimate suppression of instability with diminishing system length, demonstrating that our simple near-critical theory captures much of the complexity and choreography of far-from-critical systems. Finally, we find critical points for the three prominent examples of phase separation given above, and demonstrate how each system then follows the universal set of solutions.
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