AI 中文总结
研究无序非晶固体中结构演化，通过分析广义黑塞矩阵本征模式，其能捕捉不稳定模式，经模拟证明不稳定模式激发导致结构重排，还推导弱非线性振幅方程，为理解无序固体构型变化提供途径。
AI 中文摘要
我们通过分析广义黑塞矩阵的本征模式来研究无序非晶固体中的结构演化，该矩阵通过波数纳入空间调制。与传统黑塞矩阵不同，这种广义公式通过基于傅里叶的黑塞矩阵扩展捕捉线性不稳定模式，使我们能够研究机械稳定状态之外的响应。我们通过模拟证明，不稳定本征模式的激发导致与初始扰动无关的结构重排。此外，我们推导了一个弱非线性振幅方程来描述这些不稳定模式的增长和饱和，类似于朗道方程。我们的框架为理解无序固体中不稳定性驱动的构型变化提供了一条途径。
英文摘要
We investigate the structural evolution in jammed amorphous solids by analyzing the eigenmodes of a generalized Hessian matrix that incorporates spatial modulation via wave numbers. Unlike the conventional Hessian, this generalized formulation captures linearly unstable modes through a Fourier-based extension of the Hessian matrix, enabling us to study responses beyond the mechanically stable regime. We demonstrate that the excitation of unstable eigenmodes leads to structural rearrangements independent of the initial perturbation by the simulation. Furthermore, we derive a weakly nonlinear amplitude equation to describe the growth and saturation of these unstable modes, analogous to the Landau equation. Our framework provides a pathway to understand instability-driven configuration changes in disordered solids.
Comments23 pages, 13 figures
