标题： 时空调制材料离散模型中的参数不稳定性 显示英文标题

标题： Parametric Instability in Discrete Models of Spatiotemporally Modulated Materials

摘要： 我们研究了时空调制材料离散模型中的参数不稳定现象。这些材料因其表现出非互易传输特性而备受关注。然而，对于强调制或者偶尔即使是非常小的调制幅度，参数不稳定可能会发生，并由于响应幅度的指数增长，从而阻止时空调制设备的安全运行。我们利用Floquet理论对参数不稳定进行了详细的计算研究。我们探讨了调制参数（频率、幅度、波数）、调制单元数量以及阻尼对系统稳定性的影响。我们强调了空间调制在参数不稳定中的关键作用，这一特性在此背景下往往被忽视。我们采用摄动法得到了响应变得不稳定时的调制频率的解析表达式。我们希望我们的发现能够推动和激励更高幅度下运行的时空调制材料的新应用。 显示英文摘要

摘要： We investigate the phenomenon of parametric instability in discrete models of spatiotemporally modulated materials. These materials are celebrated in part because they exhibit nonreciprocal transmission characteristics. However, parametric instability may occur for strong modulations, or occasionally even at very small modulation amplitudes, and prevent the safe operation of spatiotemporally modulated devices due to an exponential growth in the response amplitude. We use Floquet theory to conduct a detailed computational investigation of parametric instability. We explore the roles of modulation parameters (frequency, amplitude, wavenumber), the number of modulated units, and damping on the stability of the system. We highlight the pivotal role of spatial modulation in parametric instability, a feature that is predominantly overlooked in this context. We use the perturbation method to obtain analytical expressions for modulation frequencies at which the response becomes unstable. We hope that our findings enable and inspire new applications of spatiotemporally modulated materials that operate at higher amplitudes.