Incompatible Sets of Gradients and Metastability
Incompatible Sets of Gradients and Metastability
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DOI：
10.1007/s00205-015-0883-9
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发表时间：
2014-07
影响因子：
2.5
通讯作者：
J. Ball;Richard D. James
中科院分区：
文献类型：
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作者：
J. Ball;Richard D. James
我们对不相容性引起的亚稳态概念进行了数学分析。物理环境是一个单一的母相，即将经历转化为较低能量密度的产物相。在此能量密度的能量威尔斯不相容的一定条件下，我们证明了母相在很强的意义上是亚稳的，即它是其变形的L1邻域中自由能的局部极小值。这一结果背后的原因是，由于能量威尔斯的不相容性，产物相的小核必然伴随有应力过渡层，该应力过渡层的能量成本超过核的能量降低能力。我们定义和表征不相容的矩阵集，在这方面的过渡层估计的心脏亚稳态的证明表示。最后，我们将讨论与实验的联系，并将这一概念的亚稳态在更广泛的背景下，最近的理论和实验研究亚稳态和滞后。
We give a mathematical analysis of a concept of metastability induced by incompatibility. The physical setting is a single parent phase, just about to undergo transformation to a product phase of lower energy density. Under certain conditions of incompatibility of the energy wells of this energy density, we show that the parent phase is metastable in a strong sense, namely it is a local minimizer of the free energy in anL1neighbourhood of its deformation. The reason behind this result is that, due to the incompatibility of the energy wells, a small nucleus of the product phase is necessarily accompanied by a stressed transition layer whose energetic cost exceeds the energy lowering capacity of the nucleus. We define and characterize incompatible sets of matrices, in terms of which the transition layer estimate at the heart of the proof of metastability is expressed. Finally we discuss connections with experiments and place this concept of metastability in the wider context of recent theoretical and experimental research on metastability and hysteresis.