[论文解读] Further Experimental Evidence of the Dead Matter Has Memory Conjecture in Capacitive Devices

Anis Allagui, Di Zhang+1 more|arXiv (Cornell University)|Jun 30, 2022

stochastic dynamics and bifurcation被引用 4

一句话总结

本研究提供了实验证据，表明由于非理想、分数阶动力学特性，电荷双电层电容器（EDLCs）表现出记忆效应，即先前电压激励的统计特性（尤其是噪声方差）会影响后续的电荷响应。尽管达到相同的电压和电荷终点，不同噪声水平的充电波形会产生不同的放电行为，证实EDLCs通过分数阶电压-电荷动力学保留了其激励历史的记忆。

ABSTRACT

This study provides new sets of experimental results supporting Westerlund's conjecture that Dead Matter Has Memory. Memory effects in the dynamic response of electric double-layer capacitors (EDLCs) that integrate its prior history of stimulation and state have been experimentally observed and reported in a few recent studies. The different excitation signals used to quantify such effects in these studies aimed at charging a device to the same voltage value and the exact same accumulated charge level but in different manners. Having reached the same unique voltage-charge point, it was observed that different yet repeatable discharge patterns occur, proving the existence of memory. The aim of this work is to provide further experimental evidence of the inherent memory effect in EDLCs in response to time-varying stationary input excitations with different statistical properties. In particular, different sets of charging voltage waveforms composed of fixed dc values with superimposed uniformly-distributed random fluctuations of different amplitudes were created and used to charge the same EDLC device to a unique voltage-charge point. The duration of these signals was the same but with different values of variance around the mean value. We observed different time-charge responses depending on the extent of the noise level in these charging waveforms. This is interpreted and discussed in the context of inherent memory using fractional-order voltage-charge equations of non-ideal capacitors.

研究动机与目标

• 为Westerlund提出的‘非理想电容器中‘死物质具有记忆’的猜想提供进一步的实验验证。
• 研究时变电压激励的统计特性（特别是叠加噪声的方差）如何影响EDLC的动态响应。
• 证明EDLC并非理想电容器，其电荷响应依赖于输入信号的历史，而不仅取决于当前状态。
• 将观察到的记忆效应与分数阶建模联系起来，特别是通过输入中高频分量对记忆痕迹项的影响。

提出的方法

• 对同一EDLC施加由固定直流分量与不同幅度（方差）的均匀分布随机波动叠加而成的电压波形，使其充电至相同的电压-电荷终点。
• 使用离散时间傅里叶变换（DTFT）分析输入信号的频谱成分，将较高方差与更强的高频分量关联起来。
• 在不同噪声水平下，测量并比较充电和放电阶段的时间-电荷响应与电压-电荷响应。
• 计算电压与电荷之间的归一化互相关，以量化相关性强度并检测与理想电容器行为（Δq = C₁Δv）的偏离。
• 通过估计的Cα = 0.660 F sec^(α−1)和α = 0.905，数值求解分数阶电压-电荷方程（式12），模拟电荷动力学并验证实验趋势。
• 使用基于协方差的相关系数ρvq量化记忆程度，其值在不同噪声水平下介于-0.0491至0.2141之间。

实验结果

研究问题

• RQ1 在最终电压和电荷相同的情况下，时变电压输入的统计方差是否仍会影响EDLC的动态电荷响应？
• RQ2 EDLC中的记忆效应在多大程度上通过偏离理想电容器本构关系Δq(t) = C₁Δv(t)表现出来？
• RQ3 输入信号的频谱成分与谐波分量如何与分数阶模型中记忆痕迹强度相关联？
• RQ4 记忆效应能否通过分数阶参数α及CPE模型参数进行定量关联？

主要发现

• 具有相同最终电压和电荷终点但噪声方差不同的充电波形，产生了不同的放电模式，证实EDLC中存在记忆效应。
• 电压与电荷之间的归一化互相关随噪声方差增加而降低，表明相关性减弱，且偏离理想电容器行为。
• 相关系数ρvq从低方差时的-0.0491增加到高方差时的0.2141，表明更高噪声水平导致更强的记忆效应。
• DTFT分析显示，高方差输入含有更强的高频分量，这与分数阶模型中记忆痕迹幅值的增加相关。
• 对分数阶电压-电荷方程（式12）的数值模拟重现了实验中的互相关趋势，验证了模型的预测能力。
• 结果证实EDLC通过依赖于α和输入频谱成分的记忆痕迹项整合了过去的激励历史，支持了‘死物质具有记忆’的猜想。