English L Q, Palmero F, Stormes J F, Cuevas J, Carretero-González R, Kevrekidis P G
Department of Physics and Astronomy, Dickinson College, Carlisle, Pennsylvania 17013, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Aug;88(2):022912. doi: 10.1103/PhysRevE.88.022912. Epub 2013 Aug 12.
We report the observation of spontaneous localization of energy in two spatial dimensions in the context of nonlinear electrical lattices. Both stationary and moving self-localized modes were generated experimentally and theoretically in a family of two-dimensional square as well as honeycomb lattices composed of 6 × 6 elements. Specifically, we find regions in driver voltage and frequency where stationary discrete breathers, also known as intrinsic localized modes (ILMs), exist and are stable due to the interplay of damping and spatially homogeneous driving. By introducing additional capacitors into the unit cell, these lattices can controllably induce mobile discrete breathers. When more than one such ILMs are experimentally generated in the lattice, the interplay of nonlinearity, discreteness, and wave interactions generates a complex dynamics wherein the ILMs attempt to maintain a minimum distance between one another. Numerical simulations show good agreement with experimental results and confirm that these phenomena qualitatively carry over to larger lattice sizes.
我们报告了在非线性电晶格背景下二维空间中能量自发局域化的观测结果。在由6×6个元件组成的二维方形以及蜂窝晶格族中，通过实验和理论方法生成了静态和移动的自局域模。具体而言，我们发现了驱动电压和频率的区域，在这些区域中，由于阻尼和空间均匀驱动的相互作用，静态离散呼吸子（也称为本征局域模，ILMs）存在且稳定。通过在晶胞中引入额外的电容器，这些晶格可以可控地诱导出移动离散呼吸子。当在晶格中通过实验生成多个这样的ILMs时，非线性、离散性和波相互作用之间的相互作用会产生复杂的动力学，其中ILMs试图彼此保持最小距离。数值模拟与实验结果显示出良好的一致性，并证实这些现象在定性上适用于更大的晶格尺寸。
