论文标题
在随机强迫下波动的薄床单的结构
The Structure of Fluctuating Thin Sheets Under Random Forcing
论文作者
论文摘要
我们提出了一个数学模型，以描述由薄板类型驱动的薄板的无关波动，而随机驾驶的类型可能会在弱弯曲之前经历。该模型是通过合并弹性理论的Föppl-vonKármán方程与来自平衡外统计学物理学的技术，以获得非线性强烈耦合的$ ϕ^{4} $ - langevin field方程，并具有空间变化的kernel。借助自洽扩张（SCE），该方程式可以分析地解决波动板的结构因子。与先前的研究相反，该研究表明结构因子遵循异常的幂律，我们发现结构因子实际上遵守了对数校正的理性函数。我们模型的数值模拟确认了我们的分析解决方案的准确性。
We propose a mathematical model to describe the athermal fluctuations of thin sheets driven by the type of random driving that might be experienced prior to weak crumpling. The model is obtained by merging the Föppl-von Kármán equations from elasticity theory with techniques from out-of-equilibrium statistical physics to obtain a nonlinear strongly coupled $ϕ^{4}$-Langevin field equation with spatially varying kernel. With the aid of the self-consistent expansion (SCE), this equation is analytically solved for the structure factor of a fluctuating sheet. In contrast to previous research which has suggested that the structure factor follows an anomalous power-law, we find that the structure factor in fact obeys a logarithmically corrected rational function. Numerical simulations of our model confirm the accuracy of our analytical solution.
