一维双原子颗粒晶体中通过离散间隙呼吸子的内禀能量局域化
Intrinsic Energy Localization through Discrete Gap Breathers in One-Dimensional Diatomic Granular Crystals
摘要：
我们提出了一个系统的研究离散呼吸的存在和稳定性的空间本地化的压缩弹性珠，通过赫兹接触相互作用的一维链的大部分。链是双原子的，由重和轻的球形粒子的周期性排列组成。我们研究两个家庭的离散间隙呼吸：（1）不稳定的离散间隙呼吸，是以重粒子为中心，其特征在于由一个对称的空间能量分布和（2）一个潜在的稳定的离散间隙呼吸，是以轻粒子为中心，其特征在于由一个不对称的空间能量分布。我们调查他们的存在，结构和稳定性，在整个带隙的线性光谱，并将它们分为四个制度：一个政权附近的线性光谱的下光学带边，一个适度的离散制度，一个强烈的离散制度，位于带隙内的线性化版本的系统，和一个政权附近的上声学带边。我们对比非谐FPU型双原子链中的离散呼吸子与双原子颗粒晶体中的呼吸子，这些双原子颗粒晶体在相邻粒子之间具有无张力的相互作用势，并强调后者相互作用势的不对称性质可能导致混合体表面局部化解决方案的形式。
英文摘要：
We present a systematic study of the existence and stability of discrete breathers that are spatially localized in the bulk of a one-dimensional chain of compressed elastic beads that interact via Hertzian contact. The chain is diatomic, consisting of a periodic arrangement of heavy and light spherical particles. We examine two families of discrete gap breathers: (1) an unstable discrete gap breather that is centered on a heavy particle and characterized by a symmetric spatial energy profile and (2) a potentially stable discrete gap breather that is centered on a light particle and is characterized by an asymmetric spatial energy profile. We investigate their existence, structure, and stability throughout the band gap of the linear spectrum and classify them into four regimes: a regime near the lower optical band edge of the linear spectrum, a moderately discrete regime, a strongly discrete regime that lies deep within the band gap of the linearized version of the system, and a regime near the upper acoustic band edge. We contrast discrete breathers in anharmonic FPU-type diatomic chains with those in diatomic granular crystals, which have a tensionless interaction potential between adjacent particles, and highlight in that the asymmetric nature of the latter interaction potential may lead to a form of hybrid bulk-surface localized solutions.
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