Plummer Abigail, Nelson David R
Department of Physics, Harvard University, 17 Oxford Street, Cambridge, Massachusetts 02138, USA.
Phys Rev E. 2020 Sep;102(3-1):033002. doi: 10.1103/PhysRevE.102.033002.
We study periodic arrays of impurities that create localized regions of expansion, embedded in two-dimensional crystalline membranes. These arrays provide a simple elastic model of shape memory. As the size of each dilational impurity increases (or the relative cost of bending to stretching decreases), it becomes energetically favorable for each of the M impurities to buckle up or down into the third dimension, thus allowing for of order 2^{M} metastable surface configurations corresponding to different impurity "spin" configurations. With both discrete simulations and the nonlinear continuum theory of elastic plates, we explore the buckling of both isolated dilations and dilation arrays at zero temperature, guided by analogies with Ising antiferromagnets. We conjecture ground states for systems with triangular and square impurity superlattices, and comment briefly on the possible behaviors at finite temperatures.
我们研究了杂质的周期性阵列，这些阵列在二维晶体膜中形成了局部膨胀区域。这些阵列提供了一个简单的形状记忆弹性模型。随着每个膨胀杂质尺寸的增加（或弯曲与拉伸的相对成本降低），对于M个杂质中的每一个来说，向上或向下弯曲到第三维在能量上变得有利，从而允许对应于不同杂质“自旋”构型的大约2^M个亚稳表面构型。通过离散模拟和弹性板的非线性连续介质理论，我们在零温度下探索了孤立膨胀和膨胀阵列的屈曲，这是受与伊辛反铁磁体的类比所引导。我们推测了具有三角形和方形杂质超晶格的系统的基态，并简要评论了有限温度下的可能行为。
